P

❯♥rsté ♦♥t♣r

❯ ❯ ❯

P♦r ♦t♥r r

❯ ❯❱ P

♦r♠t♦♥ ♦t♦r tr♦♥q

s♣♥ ♦♠♣♦s♥ts t ②stè♠s

♦ ♦t♦r

♣rés♥té t s♦t♥ ♣q♠♥t ♦♠r

♣r

r♦ ❱

♦♣♠♥t ♥ rtrst♦♥ ♦

t♦♥ ♦♥t♦r♥ ♥s♦rs ♦r t

♥r② P②ss ①♣r♠♥ts ♦ t

rt♦r

♥t r② ♦♠♣♦sé

ss Pr♦ssr ❯♥rsté ♦♥t♣r rtr tès

rr②r♦s rtr r ♦♦s ♣♣♦rtr

P ♦t Pr♦ssr ❳ ♥ ♣♣♦rtr

♦rst Pr♦ssr ❯♥rsté ♦♥t♣r Prés♥t

❱é tr ♦♥ér♥ ❯♥rsté ♦♥t♣r ①♠♥tr

♦r♠ ♦tr ♥è ①♠♥tr

ss♠s ♦tr ♥è ♥té

♦ ♦tr ♥è ♥té

sr ♥é♥r ♥è ♥té

Pr♣r t r♦♣♥ r♥③t♦♥ ♦r r sr

♥ t③r♥

CERN-THESIS-2007-013

17/11/2006

P

❯♥rsté ♦♥t♣r

❯ ❯ ❯

P♦r ♦t♥r r

❯ ❯❱ P

♦r♠t♦♥ ♦t♦r tr♦♥q

s♣♥ ♦♠♣♦s♥ts t ②stè♠s

♦ ♦t♦r

♣rés♥té t s♦t♥ ♣q♠♥t ♦♠r

♣r

r♦ ❱

é♦♣♣♠♥t t rtérst♦♥

♣trs ♣♦r ♠étr♦♦

r②♦♥♥♠♥t ♥s s ①♣ér♥s tr

éértr

♥t r② ♦♠♣♦sé

ss Pr♦ssr ❯♥rsté ♦♥t♣r rtr tès

rr②r♦s rtr r ♦♦s ♣♣♦rtr

P ♦t Pr♦ssr ❳ ♥ ♣♣♦rtr

♦rst Pr♦ssr ❯♥rsté ♦♥t♣r Prés♥t

❱é tr ♦♥ér♥ ❯♥rsté ♦♥t♣r ①♠♥tr

♦r♠ ♦tr ♥è ①♠♥tr

ss♠s ♦tr ♥è ♥té

♦ ♦tr ♥è ♥té

sr ♥é♥r ♥è ♥té

Pré♣ré ♦rt♦r r♦♣é♥ ♣♦r P②sq s Prts

♥è ss

s♠é

ért♦♥ s té♦rs q ①♣q♥t ♦♠♠♥t sst ♦r♠é sr ♥♦tr♣♥èt ♣♦ssé ♣②sq s ts é♥rs rs ♥♦① és t♥♦♦qs ♦♥t♦♥ ♦rt♦r r♦♣é♥ ♣♦r ♣②sq s ♣rts st ♦♥strr s éértrs ♣rts t s ①♣ér♥s ♣♦r ♣②sq sts é♥rs q ♦♥t ♣♦r t é♦rt ♥♦s ♣rts s♥érs t ért♦♥ s ♠♦s q ①♣q♥t rs ♥trt♦♥s

s éértrs P t P ♦♥t ♣r♠s é♦rt t ért♦♥♥ r♥ ♥♦♠r ♣rts q ét♥t ♣rés ♣r ♦ t♥r ② q♥ ♠ê♠ ♥♦r s qst♦♥s ♦rts t t♦ts s ♣rts ♣rés ♣r té♦r ♥ ♣rtr ♦s♦♥ s ♥♦♥t ♣s ♥♦r été é♦rts s é♥rs tt♥ts ♣r éértr P

♣r♦♥ ét♣ st ♦♥ ♦♥strt♦♥ t ♠s ♥ sr r♥♦s♦♥♥r r♦♥s ♣♦rr tt♥r s é♥rs ♥éssrs ♣♦r ért♦♥ ①st♥ ♦s♦♥ s t trs ♣rts s ♠sss♣s éés étt♦♥ s ♣rts sr t râ ① ①♣ér♥s ♣♦r ♣②sq s ts é♥rs ss♦s ① q sr♦♥t ♥stés ① qtr ♣♦♥ts♥trt♦♥ ♦ s ① s① ♣r♦t♦♥s ❱ r♥trr♦♥t ♥ ♦s♦♥

t ss ①♣ér♥s s♦♥t s ♠♥s très ♦♠♣①s ♥♦♥ s♠♥t ♥rs♦♥ t♥♦♦ ♠♣♦②é ♣♦r ♦♥strt♦♥s s éttrs ♠s ss ♣♦rs s②stè♠s ♦♥tr♦ t ♣r♦tt♦♥ q ♦♥t ssrr té t sr séq♣♠♥ts ♣♥♥t s ♥s ♦♥t♦♥♥♠♥t t ♥ s ♥t ss②stè♠s ♣♦r ♠étr♦♦ r②♦♥♥♠♥t s♦♥t ♣rt ♥tér♥t s s②stè♠s ♣r♦tt♦♥ éértr t ss ①♣ér♥s

s s②stè♠s ♣♦r ♠étr♦♦ r②♦♥♥♠♥t s♦♥t s s②stè♠s stréss♣♣♦sés ♠srr s ♥① r②♦♥♥♠♥t ♥s s ♥r♦ts très ♣r♦ ♣♦♥t♥trt♦♥ s ♣r♦t♦♥s ♥s q ♥s s ré♦♥s s ①♣ér♥s q ♦♥t s éttrs ♣s ①tr♥s ♠♣ r②♦♥♥♠♥t èr ♥ ♦♠♣♦st♦♥ t ♥ ♥t♥sté♥ ♦♥t♦♥ ♣♦st♦♥♥♠♥t ♥s ♦♠ ①♣ér♥ ♥s ♣rt ♥tr ♠♣ r②♦♥♥♠♥t sr très ♥t♥s ♦ss t♦ts ×5 ② t ♥séq♥ts s♠ Φeq ♣s q ×14 cm−2 t ♦♠♥é ♣r s ♣rtsrés ♣r♦t rt♠♥t ♣r s ♦s♦♥ s ♣r♦t♦♥s à ❱ ♥s s ré♦♥ss ♣s ①tr♥s ♠♣ st ♦♠♥é ♣r r②♦♥♥♠♥t s♦♥r é♦♣♣é ♣r

s ♥trt♦♥s s ♣rts rés s ♠tér① s ①♣ér♥s s♠ê♠s❯♥ ♠♣ r②♦♥♥♠♥t ♦♠♣♦sé ♣r♥♣♠♥t ♥tr♦♥s t r②♦♥s ♠♠ st♦rs tt♥ ♥ s ♥r♦ts st ♦♥ é♥t q s ♣trs ♠♣♦②r ♦♥t êtr ♣s trr ♥s ♥ ♥r♦♥♥♠♥t très rss s ♥① r②♦♥♥♠♥ts très ♥t♥ss ♠s s ♦♥t ss êtr ♣s ♦r♥r ♥ r♥s♥sté ♣♦r ♠srr s ♠♣s à ♥t♥sté ♦ù s ♦ss qq ② ts ♥s éq♥ts s♠ ♥s ♦rr ×8 cm−2 s♦♥t tt♥s ♣r ♥éts ♣r r♣♣♦rt ① s②stè♠s q ♦♠♣♦s♥t ss ①♣ér♥s t ♠♣ r②♦♥♥♠♥t sr♦♥t ♦♥♥és ♥s ①è♠ ♣tr tr

s ts s s②stè♠s ♣♦r ♠étr♦♦ r②♦♥♥♠♥t s♦♥t ♣r♥♣♠♥t ért♦♥ s ♣rét♦♥s s ♦s ♦♥t r♦ t q♥tt♦♥ séâts ♥ts ♣r s r②♦♥♥♠♥ts ♥s s éttrs t ♥s s ♦♠♣♦s♥ts étr♦♥qs s ① q♥ttés rtérstqs ♥térêt ♣♦r s t②♣s s ♠srs s♦♥t♦♥ ♥♦♠r ♣rts ♣r ♥té sr ♥ éq♥t ♥♦r♠sé éât ♥ts ♥s s♠ ♣r s ♥tr♦♥s ♥ ❱ Φeq t é♥r é♣♦sé ♥ss ♠r① rrs ♦s t♦t ♦ s ér♥t t②♣s ♣trs ♣ts ♠étr♦♦ s ① q♥ttés s♦♥t ① s♣♦sts s♠♦♥tr ♦s♠ètrss t s ♦s s♠ ♣♥ ♥s q s ♠tér① q s♥t r ♣r♦♣rétés♦s♠étrqs sr ♣r♥♣ ♠♥s♥ t♠és ♣tq♠♥t ♦ss ♣trs ♦♥t rtérstq ♦♠♠♥ ♣♦♦r êtr ♠♣♦②és ♣♦r trs ♠srs ♥ t♠♣s ré t s s♦♥t ♦♥sttés ♠tér① s rs t❩eff és ♣♦r ♠sr s t s r②♦♥♥♠♥t ♥s s éttrs t ♥s s♦♠♣♦s♥ts étr♦♥qs s éts rts ♦♥t♦♥♥♠♥t s ér♥ts t♥♦♦s ♦s♠ètrs ♠♣♦②és ♥s tr tès sr♦♥t ♦♥♥és ♥s ♣tr

s ér♥ts ♣trs ♥ t♠♣s ré ♦r♥s ♣r ér♥ts ♣r♦trs ♦♥t étértérsés t ①♣♦sés ♥ ♣srs tés rrt♦♥ ♣♦r s♠r s ♦♥t♦♥stt♥s ♥ tr♠ ♦♠♣♦st♦♥ ♠♣ r②♦♥♥♠♥t t ♥t♥stéP♦r tr rtérst♦♥ rô s tés rrt♦♥s à éértr PPr♦t♦②♥r♦tr♦♥ ♦♥ été très ♠♣♦rt♥t r s s②stè♠s rrt♦♥ t r♣r♦s♥t ♥ ♥r♦♥♥♠♥t rt tt♥ ♥s s ♣trs t tr ♥ sr♣t♦♥ ①st s ① s②stè♠srrt♦♥ étt t ♥s q♥ rtérst♦♥ été ♥ ♦s♠étr ts♥tér♥ts t♥♦♦s ♦s♠ètrs ♣sss

ss ♣r♦ér qt♦♥ ① s ♣tr t ①♦s ♣♥ ♣tr ♦♥t été sét♦♥♥és P♦r s s♣♦sts sét♦♥♥és ♥ tsts♣éq ♥s ♥ ♥r♦♥♥♠♥t ♠①t té sr ss ♣rés♥té ♣tr tst ♦♠♠ t ér ré♣♦♥s s qtr ♣trs ♥s ♥♠♣ r②♦♥♥♠♥t s éts ♦s t ♥t♥stés ♣rts ♣s ♣r♦s ♥r♦♥♥♠♥t tt♥ ♥tért♦♥ s s♣♦sts ♥♥été été ♣tr t♦tté s ♣trs ♣rés♥tés ♥s tt tès sr♦♥t♥stés ♥ qtr s ♥q ①♣ér♥s t rt♥ sr♦♥t ss ♥stés ♥s t♥♥ ♥s q sr s ♥rstrtrs

s ♠♦②♥s ♣♦r ♦s♠étr

s r♥s q ♦♥t♥♥♥ts ①♣ér♥s ♠ê♠s ♥ ♣rè ér♥ts ♠tér① s②♥tétsés ♣♦r ♦s♠étr ♥ ♠♣ ♠①t ♦♥t été rtérsés ♥ ♥tr tst♦♥ ♥s ♣tr

♣rés♥tt♦♥ té ♥s rés♠ s à ♥tr♦r ♥s ♥ ♣r♠r t♠♣ss ér♥ts t②♣s ♦s♠ètrs ♦♥sérés t s rtérstqs s tés rrt♦♥ tsés ♥s tr tès ♥s ♥ ①è♠ ♣rt s ♣r♥♣①réstts ♦t♥s sr♦♥t ①♣♦ss ♣♦r q t♥♦♦ ♣trs s résttssr♦♥t ♥♥ tsés ♣♦r sét♦♥♥r s ♣trs ♣tés ① ①♣ér♥s t♣♦r str s ♣r♦è♠s ♦♥r♥♥t r ♥tért♦♥ t①t à sr t réér♥ rt♥s rs rt♥s éqt♦♥s ♦ ♥t♦♥ ♦r♣qs ♦rrs♣♦♥♥t ♦r♣s tès ért ♥ ♥s

s ♠♦②♥s ♣♦r ♦s♠étr

t ♦s♠étr st q♥tr ♠♣ r②♦♥♥♠♥t ♥ s♥t ♠srs ♥ ♣rt t♦ é♣ôt é♥r ❬♦❪ ♥s s ♣rtr tté t②♣ ♠sr étt éà ré ét rés♠é ❬ ♦❪ Psrs t②♣s ♦s♠ètrs ♣sss ①st♥t ♣r♠ sqss ér♥ts t②♣s tsés ♥térêt ♣♦r tr s♦♥t ♥♥ P s P ss s ♠s r♦♠ s s ♠♥♠ tsés ♣♦r s ♠srs tt♦♥ t ♦s s♠ tsés ♣♦r q♥tr ért♦♥ ♦r♥t t♦rs r rrt♦♥ ♥s q s ♣r♠rs s♣♦sts s♦♥t tsés ♣♦r ♠sr ♦s s ① r♥rs s♦♥t tss ♣♦r étr♠♥t♦♥ ♥ ♣rts

♠♣♦ s ♦s♠ètrs ♣sss sr ♠té à s t ♥ r②♦♥♥♠♥t ré♠♥♥t tt♥ ♥ rt♥s ♥r♦ts t ss ♣♦r ♠♣♦ssté tt♥r rt♥s stt♦♥s ♠sr s s s♣s très étr♦ts s♣♦♥s ♥trs ér♥ts éttrs ♣s très réq♠♠♥t s ♦s♠ètrs ♣sss s♦♥t ét♦♥♥s♣♦r ♠sr ♦s r②♦♥♥♠♥t ♥s tss ♠♥ tt r rst à ♥tr♣rétr ♣♦r ét♦♥ s éâts ♥s s s♣♦sts étr♦♥qs

s ♦s♠ètrs ts ♦ ♥ t♠♣s ré r♣rés♥t♥t ♦♥ s♦t♦♥ à t♦s s♣r♦è♠s s ♣r♥♣s rtérstqs s t②♣s ♣trs étés ♥ tttès s♦♥t é♥♠érés

s tr♥sst♦rs tsés ♦♠♠ ♦s♠ètr s

♣r♥♣ r♣♦s sr s ♣r♦♣rétés ♣é rs ♥s♦①② r ♥ tr♥sst♦r s♦♠s à ♥ r②♦♥♥♠♥t ♦♥s♥t t t s♠♥st ♣r ♥ rt♦♥ s♥s t♥s♦♥ s st ♦♥ ♣♦ss tsr♥ t ♦♠♣♦s♥t ♣♦r r ♥ ♣tr rt♦♥s ♦♥ ♦♥sèr q ♥♦♠r ♣rs étr♦♥tr♦ é♥érés ♥s ♦①② tr♥sst♦r st ♣r♦♣♦rt♦♥♥ à ♦s é♣♦sé t q ♥♦♠r rs ♣éés st ♣r♦♣♦rt♦♥♥ ♥♦♠r ♣rs

réés ♦♥ ♣t ♠ttr q r ♣éé ♥s ♦①② st ♣r♦♣♦rt♦♥♥ à ♦s♦♥s♥t sr ♦♥ ♣♦ss à ♣rtr ♠sr rt♦♥ t♥s♦♥ s étr♠♥r ♣rès ♥ ét♦♥♥ ♦♥♥ r ♦s rç ❬♦ ♦❪ ♠sr t♥s♦♥ s ♣t s r ♥ t♠♣s ré s♥s ♦r r♦rs à ♥r♠s à ③ér♦ st ♠♣♦rt♥t ♥♦tr q t②♣ ♦s♠ètr ♣r♠t ♥ ♠sr♦ ♦s rç sqà strt♦♥ ♥ ♣t êtr ré♥tsé st ♦♥ às ♥q ♥ ç♦♥ é♥ér s ♦♥ ♥é ♦♥trt♦♥ s étts ♥tr♦♥ ♣t é♠♦♥trr q rt♦♥ t♥s♦♥ s st à ♥ rrt♦♥ st à r éq♥t ot ♦r q P q sté ♥ ♦rr ♦①② ♣r♦rt é ♥ t♥s♦♥ ❬♦ r ❪ ♣s t♦♦rs♣s q st ♣♦ss ♦r q♥ ♣♣q♥t ♥ t♥s♦♥ sr r ♣♥♥trrt♦♥ ♥ ♠① sé♣rr t♦ts s rs réés r ♣♦st srtr♦ r♣♦ssé à ♥tr 2 ♠①♠s♥t rt♦♥ s tr♥sst♦rt ♦♥ s♥sté s ♥♥ ♣s s ♦♥sért♦♥ étr♦sttqsts ♣♦r rr éqt♦♥ ♦♥ ♣t ♥♦r ♠♥tr s♥sté ♣tr ♥♠♥t♥t é♣ssr ♦①② tr♥sst♦r

♦♠♠ ♣♦r t♦t ♣tr st ♥s♣♥s q r♥r s♦rt t♥s♦♥ s tr♥sst♦r ♥s ♣r q s♦t ♠♦♥s é♣♥♥t ♣♦sstrs r♥rs ♥ ssrr ♥ stté ♥♦r♠t♦♥ ♥s t♠♣s st♣rtèr♠♥t r r ♥♦r♠t♦♥ ♦t êtr ♦♥sré ♣r ♣tr ♣srs♠♦s ♦r ♣srs ♥♥és ♦♠♠ ♥s s

s rs ♣és ♥s ♦①② rést♥t ♥ é♣ôt ♦s ♥s tr♥sst♦r♣♥t s r♦♠♥r t ♣r♦♦qr ♥s ♥ rt♦♥ t♥s♦♥ s ♥é♣♥♠♠♥t ♦s rç ♣♦r t ♦♥♥r ♥ r♥r s♦rtrr♦♥é ❬♦❪ ① ♣é♥♦♠è♥s ♣②sqs ♣rt♣♥t à tt r♦♠♥s♦♥ tt♥♥ ♥ ♣rt t érs♦♥ tr♠q tr ♣rt t t♥♥ q st ♣ré♣♦♥ér♥t à ♥tr 2 t ♥tr♥r ♣ss ♥ étr♦♥ ♣s s♠rs ♦①② ♥trî♥♥t r♦♠♥s♦♥ r♥r ♥ tr♦ ♣éé à ♥tr♦r ♣rr♣ ❬ ❪

❯♥ tr tr q ♣rtrr ♠sr st rt♦♥ t♥s♦♥ s tr♥sst♦r ♥ ♦♥t♦♥ t♠♣értr ♠♥t ♦♠♠ ♠♦♥tr ♥s Pr ♥ s♦t♦♥ ♦♥sst à ♦♥♥îtr ♥t rrt♦♥ ♥♥ t♠♣értr ♥ ♥t♥r ♦♠♣t ♦rs ♠sr ❬r r❪

s ♦s s♠ ♣♥ tsés ♥ ♣♦rst♦♥ rt

♦rs ♥ sér s ♦s♦♥s ♥érs ♥ ♣rt èr ♥ ♦ ♣srs t♦♠s r très é♥rétqs q ♦♥t ♦♥sr ♦ ①tr ♦rtè étr♦♥q s♠ ♠s ss ♥r s trs ♦s♦♥s éstqs t ♥éstqs s t♦♠s s♠ ♠ê♠ ❬♦❪ s réstts ①♣ér♠♥t① ♠♦♥tr♥t q s ③♦♥s éts s♦♥t ♥s rés ♥s rét rst♥ s♠ t s s ♦♠♣♦rt♥t♦♠♠ s ♥trs ♣trs ♣♦r s ♣♦rtr rs rs ♥s ♠tér s♠♦♥tr ♥ ♣♦♥t ♠r♦s♦♣q ♣rès ♥ rrt♦♥ ♠♣♦rt♥t ♥

s ♠♦②♥s ♣♦r ♦s♠étr

♠♣ ♣rts ♥trs t♦ rés s ♣♦rtrs rs ♠♥♦rtrsτ ♠♥ s♦♥ q ❬❪ ♣s ♥s s ♥ ♠tér s♠♦♥trt♠♥t résst ♦♥ r♠rq ss ♥ t sr résstté s♠ q ♠♥ts♦♥ q ❬♦s❪

♥ ♣r♦s♥t s ♦s s♠ t②♣ ♣♥ ♥ ♣rt ♥tr♥sèq é♣ssr ❲ t t résstté st ♦♥ ♣♦ss ①♣♦tr ♠♥tt♦♥♦ résst♥ ① ① ♣é♥♦♠è♥s érts ♣r s q t q ♥s Pr s ♣é♥♦♠è♥s ♣♣rss♥t ♦rs ♥t♦♥ ♥ ♦r♥t ♦♥st♥t♥s ♦ ♥ ♣♦rst♦♥ rt ♥ ♦sr ♦rs ♥ ♥érté t♥s♦♥ rt❱F ① ♦r♥s ♦ ♥ ♣rts Φeq s ♦r♥ts rt à♣♣qr ① ♦r♥s s ♦s ♣♦r r tr s♦♥t rt♠♥t éés ♦rr ♠ ♣♣é ss t ♥ ♥t♦♥ ♠♥tt♦♥ résst♥ s♦r♥ts tr éés ♣♥t ♥r s ♣é♥♦♠è♥s ♦♠qs ré♠♥t♥s s s♣♦sts P♦r r à s ♣r♦è♠s ér♥ts t♥qs ♠srsés sr tst♦♥ ♣ss r♣s ♦r♥t ♦♥t été é♦♣♣és ❬♥t r❪

♦♠♠ ♥s s ♣réè♥t ♦s♠ètrs s t t♠♣értr t♥♥♥ s éts ♥s rst s♠ ♦♥t êtr étés t ♣rs ♥ ♦♠♣t♣♦r ssrr té s ♠srs ts s s♣♦sts ❬❪

♦s♠ètrs sé sr ♣é♥♦♠è♥ ♠♥s♥ t♠é ♣tq♠♥t

♥s tr tès s ♠tér① ♠s ♣♦♥t ♣r éq♣ tr♦♥q t②♦♥♥♠♥t ♦rt♦r 2 ♦♥t♣r ♦♥t été tsés ❬s❪ ♦① ♦rt♦r étt tsr ♦♠♠ sstrt s srs ♥♦trr① ♦♠♠ r♣♦r s rs♦♥s s♠♣té rt♦♥ ♥ rér s ♥① ♥r ♥s ♥ ♥trt s srs s♦♥t ♦♣és ♣r ♦♥t♦♥ ♥ ♦♥♥trt♦♥ ♦rr qqs ③♥s ♣♣♠ ♠♣rtés ♠ s ♥t♥s♣♣é ss trrs rrs ♦♠♠ ér♠ t ♠r♠ ♠ ❬s❪ ♥s s ♥ ♠tér ♦♠♥t ♦♣é ①♣ér♥ ♠♦♥tr q s♣tr ♠♥s♥st û à ♥ s ♦♣♥t ♣♣é ttr s♣tr st♠t♦♥ st ♦♥♥é ♣rtr ♦♣♥t ♣♣é ♦ttr st ♦♥ ♣♦ss ♦sr s♠♥t ♦♣ ♦♣♥ts ♥ sé♣rr ♠①♠♠ s s♣trs é♠ss♦♥ t st♠t♦♥ ♠♥èr à ♣rtrr ♠♦♥s ♣♦ss ♠sr ♠♦♥tr s s♣trs st♠t♦♥ t é♠ss♦♥ sr str♦♥t♠ r ♦♣é ♠r♠ ♣♦r ♦ttr t ♣♦r ér♠ ♦♠♠ ttrs P♦r s ♠tér① t ét s♣tr st♠t♦♥ sét♥♥t à ♥♠ ♣r♦ ♥rr♦ ♥♠①♠♠ t♦r µ♠ ♥t s ♦♥rs ♦♥ é♥r st ♥ ♣s ♣♦♦r rér ♣rs étr♦♥tr♦ ♣r t ♣♦t♦étrq ♦rs st♠t♦♥ s♣tr é♠ss♦♥ sét♥ ♦♥trr à ♥♠ s ♥ ♠①♠♠ ① ♥t♦rs ♥♠ rt ❬s❪ P♦r s ♦♥rs ♦♥s ①st ♦♣ ♣trs q ♣r♠tt♥t ♠srr ♠♥s♥ s ♠tér①

♠sr ♦s st ♦t♥ à ♣rtr étt♦♥ ♥t♥sté ♦♣tq é♠s♣r ♠tér ♦rs s st♠t♦♥ ♣r ♥ ① ♥rr♦ ♦♥st♥t P ♣rés♥t ♦r♠ s♥ ♦t♥ ❬❱❪ ♥ ♠sr♥t ♠①♠♠ ♣st ♣♦ss ♦t♥r ♥ r♥r ♣r♦♣♦rt♦♥♥ à ♦s ♦♥r♥♥t s♥stés ♠tér① ♠♥♠♠ étt ♣r î♥ ♠sr ♠tér t s②stè♠ étt♦♥ st ♦rr µ② ♥ ♦sr é♠♥t ♥ très ♦♥♥ ♥értésqà ♠♦♥s ② s♦t ♥r♦♥ ♥ ②♥♠q s♣t és

♠ê♠ q ♥s s s s ①st ♥s s ♠tér① s ♣ès♣ ♣r♦♦♥s ss♣ts êtr és ♣rès ♦ ♠ê♠ ♣♥♥t rrt♦♥ ♥ ♦rs t♦t st♠t♦♥ ♦♣tq st û à ♣♣♦rt é♥r s♦s ♦r♠ r♣r s ♥trt♦♥s ♣♦♥♦♥étr♦♥ ♦♥ rr ♥ é♥t♦♥ à ♥st♥t t tq♦♥ rè s♥ à ♥st♥t t ♦♥ ♣t ♦srr ♥ ♦r ér♦ss♥♣♣é ♦r ♥ ❬❱❪ ♥ t ♣s t♠♣értr sr ♠♣♦rt♥t t ♣s t♠♣s st♦ sr ♦rt ♦t êtr ♣rs ♥ ♦♠♣t ♦rs ♠sr ♣♦r ♥♣s ♦♠♣r♦♠ttr r té ♠s ♥ ♠ê♠ t♠♣s ♣r♠t ♥ ♦tr r ♥rst tr♠q s ♠tér①

s ♠♦②♥s ①♣ér♠♥t① t s ts rr

t♦♥ P

P♦r rtérsr s ér♥ts t②♣♦♦s ♦s♠ètrs ts ér♥t tésrrt♦♥s ♦♥t été tsés ♥s r tt tès s ♣trs t ♦♥t♥♥♥t ♥ sr♣t♦♥ ①st s s②stè♠s s♥ts

étr r ♥tr rr ♦③ t♥ ♥sttt ♥ ♥ ♦é♥ s♣tr ♥tr♦♥s ♦r ❬r❪

s ♥tr♦♥ à ❯♥rsté t♦q ♦♥ ❯ ♥q ♥tr♦♥s ❱ ❬❪

s ♣r♦t♦♥ P ♥tr rr P rrr ♥sttt P à❱♥ ♥ ss ♣r♦t♦♥s ❱ à ❱ ❬❪

♦rs ♠♠ 137s t 60♦ ② P❯t à ❯♥rsté ♦♥t♣r ♠♠s ❱ t ❱ à ér♥tséts ♦s s

é♥értr r②♦♥s ❳ s♣tr t♥stè♥ ♦① ér♥ts éts ♦s

s ♣r♦t♦♥ ❱ té ♥ tt ③♦♥ ①♣ér♠♥t s ♣r♦t♦♥s éèrs ♣r éértr P s♦♥t érés ♥♣qts ×10 particules/cm2 ♥ ❬❪ ♥ ♣r♦t♦♥s st ♠sré é♥ér♠♥t t♥q tt♦♥ s ♠♥♠ t♥sq s ♣r♦s s s♦♥t ♦t♥s ér♥ts ♠s s♥ss ① r②♦♥♥♠♥ts ♦♠♠ s t s ♠s r♦♠ s t♥qs ♥st étr♠♥é ♥ ♣rés♦♥ ± t s ♣r♦s s rés♦t♦♥ qq µ♠ ♣♥t êtr ♦t♥s Pr♠ s ér♥ts ♠♣♥s

Pr♥♣① réstts ♥s rtérst♦♥ s ér♥ts ♣trs

♠srs ♦♥ts t rtérsr s ♣r♦t♦♥ ♥ tr tès ♣rr♣ ért ♣r♠r tst ①été ♣♦r ♦♥strt♦♥ ♥ ♠♦♥tr ♣r♦ ♥ ♥ sé sr ♣é♥♦♠è♥ é♠ss♦♥ étr♦♥ss♦♥rs ♥ ♠♥♠ ❬P❪ ss♦é tt té ♥s tr tès ♥r♦♥♥♠♥t rt t♦r ♣♦r s ♣r♦t♦♥ été ss ♦♣ tsé ❬r❪ ♦♠♣♦st♦♥ t ♦s♠étr t ♥r♦t ♣tsé ♥ tr s♦♥t ssrés ♣r s s♠t♦♥s♦♥tr♦ ♦♠♠ ①♣qé ♣rr♣

♥r♦♥♥♠♥t ♠①t ♥tr♦♥s♠♠ té ♥s t♥r♦♥♥♠♥t rt ♥ ♥tr♦♥s st étr♠♥és ♣r ♠sr ért♦♥ ♦r♥t t ♦s s♠ ❬♦ ❪ ♦sst ♠sré s ér♥ts t♥♦♦s ♦s♠ètrs ♣sss P P♠s t ♦♠♠ ♠♦♥tré sr P ❬♦♥❪ réstt s♠srs ①♣ér♠♥ts ♠♦♥tr q ♥s ② ♥s st♦♠♣♥é ♥ Φeq ×11 cm−2 ♦♠♣rs♦♥ s ♠srs ♣rés♥tés♥s ♣rr♣ ♥ sér s♠t♦♥ ♦♥t r♦ ①étés ♣♦r ♠♦♥tr♥t ♥ ♦r ♥s étr♠♥t♦♥ Φeq

Pr♥♣① réstts ♥s rtérst♦♥ s

ér♥ts ♣trs

♦s♠ètrs s

❯♥ ♦t s ♣r♦♥♥t ér♥ts ♣r♦trs t s ♦①②s r é♣ssrs tox ér♥ts été s♦♠s à ♥ ♣r♦ér sét♦♥ ♦♠♠♥qé ♥s sé♠ tt ♣r♦ér ♦♠♣r♥ ét♦♥ s ér♥ts ♣trs ① t②♣s r②♦♥♥♠♥ts t②♣qs t s éts sttét♠♣♦r s♥t ♠ét♦ ♥♥♥ s♦r♦♥ ❬s ❪ ♥ tt ♣r♦ér ① t②♣ s ♦♥t été sét♦♥♥és t ♦♥sérés ♦♠♠♣tés ① s♦♥s s s ♥ é♣ssr ♦①② µ♠ ♣♦r ♠srr ♥s s ♠♣s r②♦♥♥♠♥t t ♥t♥sté ♦ù ♥ t s♥sté st ♠♥é s t②♣ ♥ é♣ssr ♦①② µ♠ ♣♦r ♠srr s ♠♣s r②♦♥♥♠♥t éé t t ♥t♥sté ♦ù ♠♥♠sr s ts r♦♠♥s♦♥ ♥t♥s ♦①② ❬ P❪ st ♣s ♠♣♦rt♥t q s♥stté ♥s étr♠♥t♦♥ ♦s ♦♠♠ ①♣qé ♥ ét ♣rr♣

s s ♦rs s ér♥ts rrt♦♥s ♦♥t é♠♦♥tré ♥s♥sté ♠❱② t ♥ ♠♠ ②♥♠q ♣rtr qq ♠② sqqqs ③♥ ② s s♣♦sts s♦♥t ♦♥ ♦♥ ♦① ♣♦r ♠étr♦♦ séttrs ♥stés ♥s s ③♦♥s ①tr♥s s ①♣ér♥s ♦ù s ♠♣s r②♦♥♥♠♥t ♦♠♣♦sés ♣r♥♣♠♥t ♥tr♦♥s t r②♦♥s ♠♠s s♦♥t tt♥s♥s tst rrt♦♥ à ét à té ♦r ♣tr séts ♦s ♠② ♦♥t été ♠srés ♣♦r s ♣trs s éts ♥♥♥

étés ♦♥t é♠♦♥tré q ♥s ♥r♦♥♥♠♥t s s♣♦sts ♣♥t s♦rr ts s éâts é♣♠♥t q♦ q ♣é♥♦♠è♥ ♣rtrt♦♥ ♠sr rst ♥érr à ♣rès ♣s ♥ ♥ ♣rs ♦♥♥és ♥s ♠♠ ♠sr ♥térêt ♣♦r s ♣trs s s♦♥t ♠♦♥trés ♥s♥ss ① ♥tr♦♥sr♣s ♥ ♦♥s♦♥ s rtérstqs ♣r♠tt♥t r♥tr ♥ ♣rés♦♥ ± sr ♠sr ♦s t♦t ♥s t♠♣s

s t②♣ ♦rs s ér♥ts rrt♦♥s ♦♥t é♠♦♥tré ♥ s♥sté ♠❱② t ♥ ♠♠ ②♥♠q ♣rtr ♠②sqà qqs ③♥ ② s s♣♦sts s♦♥t ♦♥ ♠r ♦① ♣♦r ♠étr♦♦ s éttrs ♥stés ♥s s ③♦♥s ♥tr♥s s ①♣ér♥s ♦ù s♠♣s r②♦♥♥♠♥t ♦♠♣♦sés ♣r♥♣♠♥t ♣rts ♠♥♠♠ ♦♥st♦♥ s♦♥t tt♥s ♥s tst rrt♦♥ à té ♦r ♣tr s s♣♦sts ♦♥t ♣r♦é qs ♦♥t♦♥♥♥t ♥ ♥s s ♠♣s ♠①ts ét s éts ♥♥♥ étés t s ♠srs rts s ♦rs r♥ str♥sst♦rs ♦♥t é♠♦♥trés q ♥s ♥r♦♥♥♠♥t sq ♥ ②t ♥ Φeq s♣érr à ×13 cm−2 s s♣♦st s♦♥t ♠♠♥s ① ts s éâts é♣♠♥t ♣rs ♦r été ①♣♦ss ♣srs ② ♦s s ♣trs ♠♦♥tr♥t s♥s ♥♥♥ ♥érrs à ♣rès ♣s ♥ ♥ t s rt♦♥ t♠♣értr ♣s ♣♥♥t ♣rs ♦♥♥és P♦r s s♣♦sts ♦♣érés ♦r♥t tr ♦♥sé ♣r ♣r♦tr µ ♥ ♦r♠ ①♣ér♠♥t été ♣r♦♣♦sé ♣♦r ♦rrr s ts t♠♣értr à P ♥s ♠♠ ♠sr ♥térêt ♣♦r s ♣trs ♦♥t ♠♦♥tré ♥ s♥sté rét ♥ tr ♣♦r s ♥tr♦♥s r♣s ❬❪ ♥ ♦♥s♦♥ s rtérstqs ♣r♠tt♥t r♥tr ♥ ♣rés♦♥ ± sr ♠sr ♦s t♦t ♥s t♠♣s

♦s s♠ ♣♥

♥s tr tès s ♦s ♦♠♠rs P❲ ❬♣❪ ♦♥t été étés♣♦r ♠étr♦♦ s ts ♥① tt♥s Φeq ♥s s éttrs s ♣s♣r♦s s ♣♦♥ts ♥trt♦♥ ① ①♣ér♥s ét té ♥s tr tès ♣r♠s étr♠♥r s ♦♥t♦♥s ♦♣t♠s ♣♦r tr s s♣♦sts ♣ss ♦r♥t ♠ ♥ ré ♠♦♥s s♦♥ ❯♥ét ♦♠♣èt s ♦rs ❱ ♣rès ér♥ts ét♣s rrt♦♥ ① ♥tr♦♥s t♣r♦t♦♥s ss étt ♠♥é ♦r♥t ♠ s s♣♦sts ♦♥t é♠♦♥tré ♥s♥sté ×9 cm2♠❱ t ♥ ♠♠ ②♥♠q à ♣rtr ×12 cm−2

t sqà ×14 cm−2 P♦r Φeq < ×12 cm−2 s s♣♦sts ♥ ♠♦♥tr♥t ♣s s♥sté ① é♣♠♥ts ♣r♦ts ♣r s ♣rts ♥s ♦♠ s♥s s♣♦st ♥s tst rrt♦♥ à té ♦r ♣tr s s♣♦sts♦♥t ♠♦♥tré q s ♣é♥♦♠è♥s ♥♥♥ ♦♥t êtr ♦rrés ♣♦r r♥tr ♥♣rés♦♥ ± sr ♠sr à ♦♥ tr♠ P♦r tt rs♦♥ ♥ ♣r♠étr ♦rrt♦♥ s♥ s ♦s été ♣r♦♣♦sé ♦♠♠ r♣♣♦rté ♥s éqt♦♥ ♣ ♥♥ ♥s tr tès été ♣r♦♣♦s ré♣érr ♠♥q s♥stté s s♣♦sts ① rs Φeq ♥ ♣r♦r ♣rrrt♦♥

s ♦s ♣r♦tr P ❬♦s❪ ♦♥t été étés ♣♦r ♠étr♦♦ s

Pr♥♣① réstts ♥s rtérst♦♥ s ér♥ts ♣trs ①

s ♥① Φeq tt♥s ♥s s éttrs s ♣s é♦♥és s ♣♦♥ts ♥trt♦♥ s ①♣ér♥s ét té ♥ tr tès ♣r♠s étr♠♥r q ♦r♥t ♠ s s♣♦sts ♦♥t é♠♦♥tré ♥ s♥sté ×8 cm2♠❱ t ♥ ♠♠ ②♥♠q sqà ×12 cm−2 ♥ ♦r ♥trs ér♥ts ♦rs ét♦♥♥ ± P♦r Φeq > ×12 cm−2 s s♣♦sts♠♦♥tr♥t ♦rs ré♣♦♥s s♣r♥rs q ♥ ♣♥t ♣s êtr tsés ♣♦r ♦s♠étr ♥s tst rrt♦♥ à té ♦r ♣tr ss♣♦sts ♦♥t ♠♦♥tré r ♣té à ♠srr sq ét ×9 cm−2 ·h−1

t q s ♣é♥♦♠è♥s ♥♥♥ rst♥t ♥érrs ① rrrs ♠sr ❯♥♣rés♦♥ ♠sr ± été étr♠♥é ♥ s♥t ♦♠♣rs♦♥ ♥tr s♠srs ♦t♥s ♥s t ♥ st s♠t♦♥s ♦♥t r♦ ①étés ♣♦r ♠ê♠ ♥r♦♥♥♠♥t s éts rts à é♣♥♥ ♥ t♠♣értr s♥s s♣♦sts s♦♥t ♦♥♥s ♥s

♥♥ ♥ ♣r♠èr rtérst♦♥ ♦s ♣♥ ♥ ♣r♦♥♥ ré♣qèq été té s s♣♦sts ♥♦♠♠és ①st♥t ♥ ① rs♦♥s ♦ t ♦ ❬Pr♦❪ rtérst♦♥ s ① t②♣s été t s♣r♦t♦♥s ❱ t ♥s ♠♣ ♥tr♦♥ rétr ♥sttt ♥♥ ♦é♥ éts s ♠srs tés ♥ ts♥t s ♦s ♥ ♦r♥t ♠ s♦♥t ♦♥♥és ♥s st♦♥ t ♥s s ♣r♠èrs ♠srs ♠♦♥tr♥tq s s♣♦sts ♣♥t r♣rés♥tr ♥ tr♥t ① ♦s P ♣♦r ♦s♠étr s ①♣ér♥s

tér①

ét♦♥ s s ♥s s ❱ té ①♣ér♠♥t st ♣rés♥té ♥s tr ré♣♦♥s ♣r s ♣r♦t♦♥ ♦♥r♠é ♥érté ♠♥s♥ é♠s ♣r ♠tér sqà ♥ ♦s t♦t ② s ♠srs ♥ ♠ê♠ ♠tér s♦♥t ♣rés♥tés ♥s r♥r ♣é♥♦♠è♥ été ♥té ♦♠♠ tr ♠t♥t ♣♦t♥t ♥s ss♠s ♣trs ♥ t♠♣s rés sés sr tt t♥♦♦ ♠tér① P♦r ♣r♠èr♦s ♥s tr tès rtérst♦♥ ♠tér① s♣é① s②♥tétsés♣♦r ♠♥tr r ré♣♦♥s ① ♥tr♦♥s tr♠qs t r♣s ss été ♣rés♥té♥ s é♥t♦♥s ♦♥sèrés ♣♦r tr ét♥t ♣ré♣rés ♣rtr ♠tér s ♦♣é ♦r s♥sté ① ♥tr♦♥s tr♠qs t ♠é♥és ♣♦②t♥ s♥sté ① ♥tr♦♥s r♣s tst rrt♦♥s ♥s ①♠♣s ♥tr♦♥s ér♥ts t rétr ♥ér ♥sttt ♦♥t é♠♦♥tré ♣♦ssté sr♠♥r s ér♥ts ♦♠♣♦s♥ts ♥tr♦♥qs ♥ ♣rés♦♥ tr ♣rt s ♠tér① rst♥t ♥♦r ♥ ♣s é♦♣♣♠♥t t r♣r♦tté s ♠srs s ér♥ts sts ♠tér①s♥ss ♦t ♥♦r êtr ♠é♦ré

rtérst♦♥ s s②stè♠s t♠♣s ré q srt♥t t♦r s ♠tér① ♥s ♥r♦♥♥♠♥t t②♣q ss été ♣rés♥té ♥ tt tès s s②stè♠s♥térés q s♥t r ♦♥t♦♥♥♠♥t sr strtr é♠ttr ♥rr♦♠térré♣tr ♠èr s ❬❱❪ ♦♥t ♠♦♥tré r ss sàs s éâts

①

♥ts ♣r r②♦♥♥♠♥t ♥s s ♦♠♣♦s♥t étr♦♥qs ①♣♦sés r②♦♥♥♠♥t♥ ♠ê♠ t♠♣s q P♦r r à ♣r♦è♠ tt tès ♣r♦♣♦s ♣♣r♦♥ s②stè♠ ré ♠tér ♦t ♥ ♦♣ rs ♦♣tqs q é♥t s s♥① ♠♥① rs étr♦♥q tr é♣♦rté ♦rs ♠♣ r②♦♥♥♠♥t ❯♥ ♣r♠r ♣r♦t♦t②♣ été ♦♥strt s rs ♦♣tqs éàtsés ❬r❪ ♥s s ♠♣s r②♦♥♥♠♥ts très rs t s ♣r♠rsréstts très ♣r♦♠ttrs s♥sté ♦rr ♠② ♦♥t été ♣rés♥tés ♥s tr

♥tért♦♥ ♥s s ①♣ér♥s t

♦♥s♦♥s

♥s ♣rt ♥ tt tès ♣tr qtr ♣trs s♠♦♥trs sét♦♥♥s t rt♥s ♦♠♠ ♣ts ♣♦r ♦s♠étr s t ♦s ♣♥ P❲ t P ♦♥t été ♥térés ♥s ♥ rtétr♦♥q tr ♥q ♥tért♦♥ s s♣♦sts st sé sr t qt♦s s ♦s♠ètrs ♣♥t êtr s ♠ê♠ ç♦♥ ♥t♦♥ ♥ ♦r♥t tr t q s qtr ♦♥t êtr tsés ♥ ♠ê♠ t♠♣s ♣♦r ♦r ♥ ♠srq♥ttt s ♠♣s r②♦♥♥♠♥t ♠①ts ♦♠♣①s

♥tért♦♥ ♦s♠ètrs s st ♣s r ♠sr ♦sté ♣r s s♣♦sts ♣t êtr té ♣r s ♠tér① q ♥t♦r♥t ♦♠♠ ♦tr P♦r tt r♥èr rs♦♥ ♥ ♦îtr s♣éq été ♦♥ç t s♦♥ ♦① étéé tst♦♥ ♦ ♦♥t r♦ ♦r t♦♥ ♥ ♣rtr ♥s tt tès s♦♥t ♣rés♥tés s ♣r♠rs tr① t♦♥ ①♣ér♠♥t ♦ s ♣r♦t♦♥s ❱ t s ♥tr♦♥s rétr ♥sttt ♥ ♥ ♦é♥ P♦r s ♣r♦t♦♥s ❱ ♣s été ♣♦ss é♠♦♥trr ♦♥ ♦r ♥tr s réstts s♠és t s ♠srs ①♣ér♠♥ts

Psrs sérs ♣trs ♣rés♥tés ♥ tt tès s♦♥t t♠♥t t♦r ♥ ♣s ♥stt♦♥ ♥s s ér♥ts ①♣ér♥

♦♥t♥ts

s♠é s ♠♦②♥s ♣♦r ♦s♠étr

s tr♥sst♦rs tsés ♦♠♠ ♦s♠ètr s s ♦s s♠ ♣♥ tsés ♥ ♣♦rst♦♥ rt ♦s♠ètrs sé sr ♣é♥♦♠è♥ ♠♥s♥ t♠é ♣

tq♠♥t s ♠♦②♥s ①♣ér♠♥t① t s ts rrt♦♥ P Pr♥♣① réstts ♥s rtérst♦♥ s ér♥ts ♣trs

♦s♠ètrs s ♦s s♠ ♣♥ tér① ①

♥tért♦♥ ♥s s ①♣ér♥s t ♦♥s♦♥s ①

♥tr♦t♦♥

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t r r♦♥ ♦r

t♦♥ s r♦♥ t ♠♥ tt♦rs ♦r ♥r② ♣②ss ①♣r♠♥ts t t

♥ rt♦♥ ♥r♦♥♠♥t ♥ rt♦♥ ♥r♦♥♠♥t

t♦♥ ♠ t t ♦t ♦♥③♥ ♦s ts ♥ ♥t ts s♣♠♥t ♠ ts

♦♥s♦♥

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s Pss ♦s♠trs

P♦②♠r♥♥ ♦s♠trs P ♦P♦t♦♠♥s♥t ♦s♠trs P ②r♦♥ Prssr ♦s♠trs P r♠♦♠♥s♥t ♦s♠trs r ♦s♠trs ② P ♦s♠trs r♦♠ ♦s♠tr ♠s

①

tt♦♥ ♦s rr♥t r♦♠ rrss s♦♥ tt♦rs

t ♦s♠trs t♦♥s♥s♥ t r♥sst♦rs s rsstt② ♦rr s ♣♥ ♦s ♣t② t♠t ♠♥s♥t ♠trs s

♦♥s♦♥

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts rrt♦♥ ts

P st rrt♦♥ ts t r rt♦r t st ♥tr♦♥ ♠ t ❯ P Pr♦t♦♥ t② t P ♠♠ s♦rs rt ❳② ♥rt♦r

sr♠♥t q♣♠♥t rtr③t♦♥ ♦ s♠♦♥t♦r ♦s♠trs rtr③t♦♥ ♦ ♠trs

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts Pr♦t♦♥ ♠ rtr③t♦♥ ♥ ♦s♠tr② ♥

tt♦♥ ♠sr♠♥ts ♠ ♣r♦♥ t ♦s♠tr ♠s ♠ ♣r♦♥ t ♠s ♠ ♣r♦♥ s♥

♦s♠tr② ♥ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦ ♦♥s♦♥

rtr③t♦♥ ♦ ♦s♠trs s rtr③t♦♥ ♣r♦r t

s r r♦♥s rs♣♦♥s ♥♥ s rs♣♦♥s t♦ ♥r② ♥tr♦♥s tt② ♦ t ♦s♠tr ♥♦r♠t♦♥ s♦r♦♥ ♥♥♥ sts

t♦♥ ♦ t ♦s♠trs ♦r t rtr③t♦♥ ♦ t

rt♦♥ rs ♥ ♦♣rt♦♥ ♣r♠trs ♥♥♥ ♦r ♥ s♣♠♥t ♠ ♥ r♦♥

rtr③t♦♥ ♦ t rt♦♥ rs ♥ ♦♣rt♦♥ ♣r♠trs ♥♥♥ ♦r ♥ s♣♠♥t ♠ ts ♥ r♦♥

♣♥ sss ♦r t ①♣r♠♥ts P♥ s♥ sts ♠♦ ♦ t ①♣r♠♥ts ♣♥ P♥ ①♣r♠♥t t♦♥ ♥ ♦♠♣rs♦♥ t

s♠t♦♥s

①

♦♥s♦♥

rtr③t♦♥ ♦ ♣♥ ♦s ♦♠♠r P❲ ♣♥ ♦s

♦♥s♦♥s r♦♠ ♣r♦s sts s♣♦♥s ♦ P❲ t♦ ♥tr♦♥ ♥ ♣r♦t♦♥ rrt♦♥ rt♦♥ rs ♦r P❲ s ♦♥tr♠ ♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦r P❲

s s♥stt② ♣♥ ♦s r♦♠ P

rt♦♥ rs ♦r P s ♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦r P s

♣♥ ♦s rt♦♥ rs ♦r s ♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦r s

♦♥s♦♥

♦s♠tr② ♦r t ①♣r♠♥ts ♠♣s s ♦r sts ♥stt② t♦ ❱ ♣r♦t♦♥s st ♦ ♥ ♥trt s♥s♦r ♦r s♣ ♣♣t♦♥s Pr♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r ♦r ♣♣t♦♥s

②st♠ sr♣t♦♥ ♥ ♣r♦r♠♥s t♦♥ r♥ss ♦ ♥trt s♥s♦rs ♦♣t ♦♠♣♦♥♥ts ♠tr ♥

t♠ ♠♦♥t♦r♥ t r s②st♠ ②♦t ♦ t s②st♠ Pr♦r♠♥s ♦ t r ♣r♦t♦t②♣

tr♦♥ tt♦♥ t ♠trs tr♦♥s♥st ♠trs ①♣r♠♥t ♣r♦r t♦ rtr③ ♥tr♦♥s♥st

♠trs rst rrt♦♥ tst ♦ ♥tr♦♥s♥st ♠trs ❱t♦♥ tsts ♦r ♥tr♦♥s♥st ♠trs

♦♥s♦♥

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t ①♣r♠♥t st♣ ♦r t tst

rrt♦♥ ♦♥t♦♥s t♣ ♦ t s ♥r tst

sts ♥ sss♦♥ ♦ t ♠sr♠♥ts rst rrt♦♥ ♥ ♦♥ rrt♦♥ ♥ sss♦♥ ♦ t rt♦ rs♣♦♥s rs♣♦♥s

♦♥s♦♥

①

♥trt♦♥ ♦ t rt♦♥ ♠♦♥t♦rs t t t♦♥ ♠♦♥t♦r♥ t t ①♣r♠♥ts

s♥ ♦ ♥ ♥trt s♥s♦r rrr ♦r ♥ ♠sr♠♥t

①♠♣ ♦ rt♦♥ ♠♦♥t♦r♥ s②st♠s t rt♦♥ ♠♦♥t♦r♥ s②st♠ t♦♥ ♠♦♥t♦r♥ ♥ t t♥♥ ♥ ①♣r♠♥t rs

♠♠r② ♦♥s♦♥

Pr♦r♠♥t s♣t♦♥ ♦r s tst ♣r♦r

P ❯❨ P

st ♦ rs

st ♦ ts

st ♦ ♣t♦♥s

♥♦♠♥ts

♦r♣②

♣tr

♥tr♦t♦♥

rt♦♥ ♦ t♦rs ♠♥ t♦ ①♣♥ ♦ t ♦r ♥ s♦r♠ ♣ss Prt P②ss t♦rs ♥ t♥♦♦ ♥s t r♦♣♥ r♥③t♦♥ ♦r r sr ♣rt rt♦rs ♥ ♥r② P②ss①♣r♠♥ts r t ♥ ♦rr t♦ s♦r ♥ s♥r ♣rts ♥ t♦ r② t♠♦s tt ①♣♥ t ♥trt♦♥s ♦ ts ♣rts P ♣r Pr♦t♦♥ ②♥r♦tr♦♥ ♥ t P r tr♦♥ P♦str♦♥ ♦rs t ♥ ♦tr rt♦rs r♦♥ t ♦r ♦ t s♦r② ♦ ♦ st ♦ ♣rts tt r ♣rt② t t♥r ♦ ♠♥ st♣ t♦rs ts rt♦♥ ♦r s♦♠qst♦♥s st r♠♥ ♦♣♥ ♥ ♥♦t t ♣rts tt r ♣rt ♣♣r♥ ♣rtr t s ♦s♦♥ s st ♥♦t ♥ tt s s ♦tr ♠ss♣rts tt ♥♦t ♣♣r ♣ t♦ t st ♥rs r ♥ P ♦s♦♥s

♥①t st♣ ♦ s tr♦r t ♦♥strt♦♥ ♥ ♦♠♠ss♦♥♥ ♦ t rr♦♥ ♦r rt♦r r t ♥rs ♥ssr② t♦ r②t ①st♥ ♦ t s ♦s♦♥ ♥ ♦tr ♣rts ts t♦ tt ♥ ♣rtss ♥ t♦ t ①♣r♠♥ts tt srr♦♥ t ♦r ♥trt♦♥ ♣♦♥ts r t t♦ ❱ ♠s ♦ t rt♦r ♦

♥ ts ①♣r♠♥ts r ♥♦t ♦♥② ♦♠♣① s ♦ t t♥♦♦② ♥♥ ♦rr t♦ tt ♣rts t s♦ s ♦ t ♣r♦tt♦♥ ♥ st② s②st♠s tt♠st ♥sr t rt② ♦ t ♠sr♠♥ts ♦r t♠ ♥ sr ♦ t q♣♠♥t♥ s ♦ ♥ts tt ♥ s ♦♠♣① ♠♥ ♠② ♣♣♥

♥ ♦ t♦s s②st♠s s t t♦♥ ♦♥t♦r♥ t♦♥ ♦♥t♦r♥ s②st♠s ♥st ♥ t ♠♥ s s ♥ t r♦s stt♦rs tt ♦♥stttts ①♣r♠♥ts s♥s♦rs ♣rs♥t ♥ ts tss r t ♦♥s tt s ♥♦r ♦ t ①♣r♠♥ts ♥ ♦♠ ♦ t♠ s♦ ♥st ♥ t t♥♥ ♥ ①♣r♠♥t rs r♥ s

t♦♥ ♦♥t♦r♥ q♣♠♥t ♦r t ①♣r♠♥ts r strt s②st♠s tt r ♥t♥ t♦ ♦r rt② ♦s t♦ t ♥trt♦♥ ♣♦♥ts s s r② r♦♠ t♠ ♥ t ♦tr tt♦r r♦♥s rt♦♥ ♥r♦♥♠♥t ♥♦♥tr♥ t st ♠sr♠♥t ♦t♦♥s ts r②♥ ♥ ♦♠♣♦st♦♥ ♥ ♥t♥st②♣♥♥ ♦♥ t ♣♦st♦♥ t♥ t ♦♠ ♦ t ①♣r♠♥t rt♦♥ ♥t ♥tr ♣rt ♦ t ①♣r♠♥ts r② ♥t♥s ♦ ×105 ② ♥ Φeq ♦♠♦r t♥ ×1014 cm−2 ♣r ②r ♥ ♦♠♥t ② r r♦♥s rt② ♣r♦② t ♦s♦♥s ♦ t ❱ ♣r♦t♦♥s ♥ t ♦tr tt♦r r♦♥s t s ♥st

♥tr♦t♦♥

♦♠♥t ② t s♦♥r② rt♦♥ ♥rt r♦♠ t ♥trt♦♥ ♦ t rr♦♥s t t ♠trs ♦ t stt♦rs t♠ss rt♦♥ ♠♥②♦♠♣♦s ② ♥tr♦♥s ♥ γr②s s ①♣t tr ♦r ts rs♦♥ t s♥s♦rs tt t♦ ♠♣♦② ♠st t♦ tst♥ ♦st ♥t♥st② rt♦♥ ♥r♦♥♠♥t t s♦ ♣r♦ s♥stt② t♦ ♠♦♥t♦r ♦ ♥t♥st② s r t ♦ s♦♠ ② ♥ Φeq ♥ t ♦rr ♦ ×108 cm−2 r ①♣t ♣r ②r

♠ ♦ t t♦♥ ♦♥t♦r♥ s ♠♥② t♦ r♦ss t ♣rt♦♥s ♦ ♦♥tr♦ s♠t♦♥s ♥ t♦ ssss t rt♦♥ ♥ ♠ ♥ ♠trs tt♦rs♥ tr♦♥ ♦♠♣♦♥♥ts r♥ ♦t ♥♦r♠ ♦♣rt♦♥ s s tr ♥ts ♦rt rst ♣r♣♦s t r② ♦ t ♦♥t r♦ ♠♦s ♦♣ t♦ ♣rt trt♦♥ ♥ ♥ ts ①♣r♠♥ts s ♥t♥ t♥ t♦r t♦ r♦rt rt♦♥ ♠♦♥t♦r♥ ♠sr♠♥ts r ♥ ♦r tr t♦♥ ♦r t s♦♥♣r♣♦s ♦s♠tr ♠sr♠♥ts ♥ ♣r♦ ♥t♦♥ ♦♥ ♠♥ts♦ r♣ t♦ r♥t t rt② ♦ t ♦r s②st♠ ♦r t♠

r♦♠ ♦ rs♦♥s t s tr♦r r tt ♦s♠tr ♠sr♠♥ts t♦ ♣r♦r♠ ♦r t t♠ t♦ q♥t② t rt♦♥ s ♥ tr♠s ♦ ♣rt♥ Φeq ♥ ♠−2 ♥ t ♥r② ♠♣rt t♦ t rrt ♠tr ♣♦s ♦s♥ ② rt♦♥ ♠♦♥t♦r♥ s♥s♦rs ♦r ♦s♠trs ♣② tr♦r ② r♦ ♥t ♠♦♥t♦r♥ ♦ t ♦ sr ♥♥ ♥r♦♥♠♥t ①♣t t t ①♣r♠♥ts

t②♣ ♦ s♥s♦rs ♥stt ♥ ts tss ♦r r s♦stt s♠♦♥t♦rs t♦♥s♥s♥ t ① ♠♦♥t♦r s♥s♦rs ♦r s ♥ ♣♥ s♦♥ ♦s s s ♣t② t♠t ♠♥s♥t trs st s♥s♦rs t ♦♠♠♦♥ rtrst tt t② ♥ ♠♣♦② t♦ ♣r♦r♠♦♥♥ r♠♦t ♠sr♠♥ts ♥ t② r ♠ ♦ ♠trs st t♦ ♠sr tt ♦ t rt♦♥ ♥ s♠♦♥t♦r ♦♠♣♦♥♥ts ♥ tt♦r q♣♠♥t ♥ tstss sr s♥s♦r s♠♣s ♥ rtr③ rrt ♥ r♦s rt♦♥ts ♥ tst ♥ t rt♦♥ r♥t♥st② ♠① r♦♥ tt s♠t t ①♣♦sr ♦♥t♦♥s tt t s♥s♦rs t t ①♣r♠♥ts♦r ts st ♣r♣♦s t rrt♦♥ ts t t Pr♦t♦♥ ②♥r♦tr♦♥ Prt♦r ♣② ♣r r♦ ♥ t r♠♦r ♦ ts tss ♦r r♦r trt ♦s♠tr rtr③t♦♥ s♦ ♣rs♥t r

rsts ♦ t rtr③t♦♥ tsts t t ♥②ss ♥ t ♦♥s♦♥s ①trt r ♣rs♥t ♥ ts ♦r ♥ r♦t t♦ st♦♥ ♦ st ♦ s ttt t ♣rs♥t stt♦trt ♥ ♣r♦♥ t♦ t ①♣r♠♥t rqr♠♥ts ♥ tr♠s ♦ rt♦♥ rs♣♦♥s ♥ ♠sr♠♥t rt② ♦r ts sts♥s♦rs t ss ♦ t ♥trt♦♥ t t ①♣r♠♥ts ♥ s♦ tt st② ♥ t ♦♥♣t♦♥ ♦ t ♣♥ ♥ t s♥s♦r rrrP st ♦r t ♥stt♦♥ ♥t♦ t

st② ♣rs♥t r s ♥ rr ♦t ♦r♥ t t r♦♣ ♦ t P②ss P ♣rt♠♥t ♥ ♦♦rt♦♥ t t r♦♣ ♦ t ♥ ♣♣♦rt ♣rt♠♥t ♥ t r♠♦r ♦ t ♦t♦r st♥t♣r♦r♠

♣tr srs s ♥tr♦t♦♥ t♦ t ♥ ts ①♣r♠♥ts ♥ ♥ ts ♣tr ts ♦t t rt♦♥ ♥

r♦♥♠♥t ①♣t t t rt♦r ♥ ♥ t stt♦r s②st♠s tt ♠♦♥t♦r r ♣rs♥t ♦r♦r t ♣♦ss ts t rt♦♥ ♥ ♦♥t tr♦♥s ♥ t ♣rt tt♦rs sss

♣tr s ♥ ♦r ♦t t r♥t ♦s♠tr t♥♦♦s ♠♣♦②r♦♥ ♣rt rt♦rs s ♦r ♥s t Pss s tt ♥ tstss ♦r r ② s t♦ ♦♠♣r ♥ t t ♠sr♠♥t ♣r♦r♠ tt t ♥s♦rs s t ♦♥s r sr ♥ t ♥ ts ♣tr s t② rt ♠♥ st ♦ ts tss ♦r

♣tr ♥ ♣tr r t t♦ t sr♣t♦♥ ♦ t r♥t rrt♦♥ts s t♦ tst t s♥s♦rs ♥ t ♦s♠tr② t t P rrt♦♥ t② ①♣r♠♥t ♣r♦rs ♥ ♠t♦s sr ♥ ts ♣tr ♥ t ♣r♦r♠rt♦♥ ♠♣♥s ♦ t♦ ssss t ♣rt ①s ♥ t ♥r② ♣♦st♦♥♥ t ♥r② ♣r♦t♦♥ ♠ ♦ t t② ♥ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦ t t② ♥ ♥ t r♦♥ ♥r♦♥♠♥t ♦ t t②

♣tr ♥ ts t rtr③t♦♥ ♦ t ♥ ♣♥ ♦♦s♠trs rs♣♦♥ss ♥ r ♣rts st ♥tr♦♥ s ♥ ♥ ♠①rt♦♥ ♥r♦♥♠♥ts r sss r ♥ t ♦r♦r stt② stst ♠♥s ♦ s♦r♦♥ ♥ s♦tr♠ ♥♥♥ t♥qs ♥ rr ♦tt t ♦ t♦ st t s tt st st t ♦♣rt♦♥ ♥ t ①♣r♠♥tsrt♦♥ s ♥ t s ♥ st t rtr③t♦♥ ♥t tr♠♥t♦♥ ♦ t s ② ♣r♠trs ♥ rr ♦t ♦r s♦♥② ♣tr ♣♥ sts t t ♣ ♦ ♦♥t r♦ s♠t♦♥♦ r s♦ rr ♦t

♣tr s ♥tr② t t♦ t ♦s♠trs rtr③t♦♥♦ ts ♠tr ♦r ♣♣t♦♥s s♣♥ r r♦♠ t ♠sr♠♥t ♦ t♠trs rs♣♦♥s ♥ t P ♠s ♥ ♥tr♦♥s ♦ r♥t ♥rs t♦ t ♦♣♠♥t ♦ r♥t ♥s ♦ ♦♥♥ s♥s♦rs s ♦♥ ts s♥st ♠tr ♥ts ♥ t ♠tt♦♥ ♦ t s ♦ ts s t t sss ♥t ♦r♦r t rst rtr③t♦♥ ♦ ♠trs t ♥♥ s♥stt②t♦ r♥t ♥r② ♥tr♦♥s s♦ ♣rs♥t

♥② ♦r r♥ t ♦♥s♦♥s ♥ ♣tr t t♦♥ ♦ t sts♥s♦rs ♥ rt♦♥ ♥r♦♥♠♥t t s♠r ♦♥t♦♥s s t ♣rs♥t ♥trt♦♥ ss ♥♦♥ t ♥stt♦♥ ♦ t st s♥s♦rs t t ♠♥ ♥ ①♣r♠♥ts s ♥st sss ♥ ♣tr

♣tr

rt♦♥ ♥r♦♥♠♥t ♥ ts

ts ♦♥ t q♣♠♥t

rt♦♥ ♥r♦♥♠♥t ♥♦♥tr t t ①♣r♠♥ts ♦ t r r♦♥ ♦r t r str♦♥② r♦♠ t ♦♥s ♥ t ①st♥ ♦s♠trt♥♦♦s r t②♣② s s♣ ♣♣t♦♥s ♠♥ rt♦♥ ♣r♦tt♦♥ t

♠① ①♣t t t ♦r ①♣r♠♥ts ♦t r♦♥ t r♥ ♦♠♣♦s ♦ ♥tr♦♥s ♣♦t♦♥s ♥ ♦t r ♥ ♥tr r♦♥s s♦♠♣① s ♥ s♠t ② ♦♥t r♦ ♦s ❬ ❪ s t♦ ♣rts ♥rt ② t ♣r♦t♦♥♣r♦t♦♥ ♦s♦♥s ♥ rt♦♥ ♣r♦ts ♦ ts♣rts t t stt♦r ♠trs ♦ t ①♣r♠♥ts t♠ss ♣r♦♣♦rt♦♥♦ t r♥t ♣rt s♣s ♥ t ♣♥ ♦♥ t st♥ ♥ ♦♥ t ♥t rs♣t t♦ t ♥trt♦♥ ♣♦♥t t rt♦♥ ♥r♦♥♠♥t ♥q ♥ stt♦r ♦♥sttt♥ t ①♣r♠♥ts ♦r ①♠♣ ♥ t ♥♣ ♠♦s♦ t tr♦♠♥t ♦r♠tr ♦ t ①♣r♠♥t ❬❪ t ♦t ♦♥③♥♦s ♦r ②r ♣r♦ s st♠t t♦ r ② ♥ t st r♦♥♥ s ①♣t t♦ ① 1014 ♣rt♠2 s rt♦♥ s r ♠ ♦r ♦♥sr ♥st t ♠♦♥ ♠rs ♦t♦♥ t t ①♣r♠♥t ❬❪♠t rt♦♥ ♦ss ♦ s♦♠ t♥s ♦ ♠② ♥ r♦♥ ♥s ♦ 108 ♣rt♠2

r ①♣t tr ♠♥ ♦♥r♥ rt t♦ rt♦♥ ♠ ♥ rt♦r ts s t♦ ♦

tt t ♥t ♥r② ♦ t ♣rts s rs ♥♥t♥t♦♥② ♥t♦ t q♣♠♥t♦r t s♦ ♥t tt rt♥ ♠♦♥t ♦ ♣rts ♦st r♦♠t ♠ ♥ ♥r ♦♣t♠♠ ♦♥t♦♥s ❬❪

t♦ ts ♥r② ♦sss tt♦rs s s ♠r♦tr♦♥ q♣♠♥t ♥ ♠trs t sr r♦♠ rt♦♥ ♠ ♥ ①♣♦s t♦ r♥t ♥s♦ rt♦♥ ♥r② ♣♦st♦♥ t♦ ♦♥③t♦♥ ♣r♦sss rs♣♦♥s ♦rt ♠t♦♥ ♦ r ♥ ♥st♦r ♠trs ♦♥ ♦① ♣rs♥t ♥ ♠r♦tr♦♥s rts ♥ tt♦rs ♥ t ts rs♣♦♥s ♦r ♥st♥ ♦r t♥ ♦ s tt♦rs s♥tt♦rs ♥ ♦♣t rs ♥r② ♣♦s ② ♣rts♣r♦♥ ts ♥ s♠♦♥t♦r r②sts ♥st t ♠♥ ♦♥r♥ ♥ t ♦ss♦ ♣r♦r♠♥s ♦ s♦♥ tt♦r s ♥② t ♠♦♥t ♦ ♥r② rs

r♦♥s r ♣rts ♥trt t str♦♥ ♦r s s ♣ π, µ ♥ t

r r♦♥ ♦r

r ②♦t ♦ t rt♦r

② t st r♦♥ ♦♠♣♦♥♥t ♣rs♥t ♥ t rs♣♦♥s ♦r ♥♥t t ♣♥♦♠♥ tt ♠② ♦♠♣r♦♠s t ♦♣rt♦♥ ♦ ♠♠♦rs ♥ ♦trt rts

♠ ♦ ts ♣tr s t♦ ♥tr♦ t ♥ ts ♥r② P②ss P①♣r♠♥ts ♥ t♦ sr ♥ t t rt♦♥ ♥r♦♥♠♥t ①♣t r♦♥ t♠♦r♦r ♥ ts ♣tr r r ♦♥ t rt♦♥ ts ♥ ② t r♥t♦♠♣♦♥♥ts ♦ t rt♦♥ ♦♥ tr♦♥s ♥ tt♦r s②st♠s ♥

r r♦♥ ♦r

r r♦♥ ♦r s ♣r♦t♦♥♣r♦t♦♥ ♣♣ ♦r ①♣t t♦ r trst ♠s r♥ ♥ t ①st♥ ♥rstrtrs ♣r♦s② s t ② tr tr♦♥ P♦str♦♥ P rt♦r ❬❪ s ♥ ♠♥ rt♣r♦t♦♥s r♥ ♥ ♥♣r♥t ♥tr♦♠ss ♥r② ♦ ❱ ♥ ♠♥♦st② ♦1034 cm−2s−1 r♥ ♣♣ r♥s s♦ rt ② ♦♥s ♦r PP♦s♦♥s t ♠①♠♠ ♥tr♦♠ss ♥r② ♣r ♣rt♣t♥ ♥♦♥ ♦ ❱ ♥ t ♠♥♦st② ♦r ts r♥s ♦ 1027 cm−2s−1 ♥ ♦rr t♦rt ♣rts t♦ s ♥rs t♥ t ♦♥♥s ♦ t ①st♥ P t♥♥♦ ♠ r♠r♥ t ♠♥ ss ♠♥t s②st♠ ♦♠♣♦s ♦ ♣♦♠♥ts t str♥t ♦ tt ♠♣♦② s♣r♦♥t♥ ♦s ♦♣rt♥ t rr♥t ♦ s♣r♦♥tt② t ts str♦♥ ♠♥t s t ♠♥ts♠st ♦♣rt t t s♣r ♠ ♦♥trr② t♦ t s ♦ t P ♥

❯♥t ♦ ♠sr ♦ t ♥♠r ♦ ♥ts ♣r s♦♥ ♥rt ② t ♥trt♦♥ ♦ t♦ ♣rt♠s

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t

tr♦♥s ♥ ♣♦str♦♥s r rt♥ ♥ t s♠ ♠ ♣♣ t rqrst♦ ♠ ♣♣s ♥ ♣r♦t♦♥s tr ♥ ♦♣♣♦st rt♦♥s

t♦ ♠s ♥trst ♥ ♦r ♣♦♥ts ♦ t r♥ ♥trt♦♥ P♦♥tsPs r t ♥r② ♣②ss ①♣r♠♥ts r ♦t ♠♥ ♦s ♦ts ①♣r♠♥ts r t s♦r② ♦ t s ♣rt ♥ t st② ♦ rr ♥tst ♥tr♦♠ss ♦s♦♥ ♥rs ❬❪ ♥ t ①♣r♠♥t ❬❪ ♦t ♥ P ♥ P rs♣t② r ♥r ♣r♣♦s tt♦rs♦♣t♠③ ♦r t ♦♣rt♦♥ r♥ t ♠♥♦st② ♣♣ r♥s ♥ t♦♥ t♦ t♠ t s t♦ ♦ ♠♥♦st② ①♣r♠♥ts ❬❪ ♦t ♥ P ♦r t ♣②ss♦ t ♠s♦♥ ♥ t ①♣r♠♥t ❬❪ ♦t ♥ P s ♦r ttt♦♥ ♦ ♣r♦t♦♥s r♦♠ st sttr♥ t s♠ ♥s t rs♣t t♦ t rt♦♥♦ t ♥♦♠♥ ♣r♠r② ♠s ♥② t s t ①♣r♠♥t ❬❪♦t ♥ P ♥ ♦♣t♠③ ♦r t st② ♦ PP ♦s♦♥s

s s♦♥ ♥ t ♠♥ s ♦♠♣♦s ♦ t ♦t♥ts ♥ ♦ts ♦t♥ts tr r t st♦♥s ♥♠ s r t ♠s r ♥t ♥ t♥srt♦♥ ♦♥s s tt r t ♣rts ♦ t r♥ t♥ t s tt ♦st ♦tt ♥trst♦♥s ♥ t ♥trt♦♥ ♣♦♥ts ♦r ♥ t t ♥srt♦♥ r♦♥s ♦♥sst♦ ♦♥ s♣rs♦♥ ♣♣rss♦rs ♦♥ strt st♦♥ ♥ s♦♥ ♥ ♥srt♦♥ ♠♥ts t ts t♦ ♦♥ ♦t ♠s ♥t♦ ts♠ ♠♣♣ ♦r t ♦s♦♥s ♦r♦r ♥ ♦rr t♦ t ♦ ttr♦♥ ♦st♦♥♥ t r♦♥ t ♠s r ♦s ② ♠♥s ♦ ♥♥r tr♣t ♠♥ts ♦r ♥srt♦♥s tt ♦♥t ♦st Ps r s ♦r t ♠♠♣ s②st♠ t ♠♥♥ s②st♠ ♦♠t♦♥ t ts s②st♠ t♦ rt t ♣rts ♥t ♥t♦♥ ♠♥s tt tr♥sr t ♣rts t ❱ ♦♠♥ r♦♠ t P♠♥ ♥t♦ t

❲ t ♥ ts ①♣r♠♥ts r♥ t ♣rts ♥rt t t Pst♦tr t t ♦♥s rs♥ r♦♠ ♦tr t②♣ ♦ ♥trt♦♥s ♦♦s tr ♥r②♥s t q♣♠♥t srr♦♥♥ t♠ ♠♦r rt♦♥ s♦rs t t rts t ♣rt ♣r♦t♦♥ r♦♠ ♣r♦t♦♥ ♥trt♦♥s ♦ ♠ ♦sss ♥ ♠s♥trt♦♥s

t♦♥ s r♦♥ t ♠♥

❲♥ t ♠s rt t st♦♣♣♥ ♦ ♥r② ♣r♦t♦♥s trrrt♦♥s ♥ t ♥ ♦ t t♦♠s ♦ t rs s ♥ t ♠ ♣♣ ♥ ♥ ♠trs srr♦♥♥ t s ♥t rt♦♥s ♣r♦ s♦♥r② ♦r♥r②♣rts s s ♥tr♦♥s ♣r♦t♦♥s ♥ ♣♦♥s s ♣r♦ss s t t ♦r♥ ♦ ♣r♦♠♣trt♦♥ ♥ t ♦♥t♥ ♥t t ♣rts ♦ ♥♦t s♥t ♥r② t♦ rtrtr ♥r rt♦♥s ♦r♦r t ♥ ♦ t str t♦♠s r♠♥t ♥rt r♥ ♦ ♦r ♠ss ♥st ♥ tt ② tr♦♥ ♣tr ♦r β♠ss♦♥ s t ♦rs ♥ t♠ s r②♥ r♦♠ ♠♥ts t♦ sr ②s ♥♥ t ♠ s ♦ s t t ♦r♥ ♦ t r♠♥♥t rt♦♥ ♥ t t♥♥❬❲❪

s ♥ ♦r ♦ strt♦♥ ♦ rt♦♥ ♦♥ t r♥ t♦♥♦s t♦ t ♠ r♦♥ s ①♣t t♦ ♦♠ r♦♠ t ♠s ♥trt♦♥s ②♦♦♦r ♣rts ♦ s♦♥② rt♦♥ ♠② s♦ ♦♠ r♦♠ ♦r r s

tt♦rs ♦r ♥r② ♣②ss ①♣r♠♥ts t t

r t♦♥ s ♦♥ t r♥ ♥ t ♣tr t ②♦♦♦r ♣rts ♦rrs♣♦♥ t♦ t r♦♥s ♥ t rt♦♥ s ♦♠♥t ② ♠s ♥trt♦♥s♦♦r r ♥st t st♦♥ ♦ t r♥ ♥ t ♣♦♥t♦sss r ♠♥ rs♣♦♥s♦ t rt♦♥ s

♦strt♦♥ ♦ t ♠ ♥♥ ♦r s ♦ ♠ ♦rts t♦ t② ♦rrt♦r♠♥ts

❲♥ t ♠♥ ♦♣rt♦♥ t ♠♥♦st② t ♠ ♦sss r①♣t t♦ ♦r t♥ 7 ♣r♦t♦♥ss ♠s ♥trt♦♥s r st♠t t♦ r♦♥ 2 ♣rts♠×s s t ♠♥ s♦r ♦ rt♦♥ r t s♦♥r② ♣rts ♥rt r♦♠ t ♣r♦t♦♥ ♦s♦♥s ♦ t ♠s r♦♥ 9 ♣rtssr♦r ♣♣r♦♥ t s r♦♠ t ♠ ♣♦♥t ♦sss strt t♦ ♠ ♥ ♥rs♥② ♠♣♦rt♥t ♦♥trt♦♥ r ♦♦r ♣rts ♦ ♣♦♥t ♦sss rs ♥♦t ♦♥② ② t ♣♣ ♦s♦♥s ♥ P ♥ P t s♦ ② ♥t♦♥ rr♦rs PP ② ♦♠t♦rs P P ♠ ♥str♠♥tt♦♥ ♦♣rt♦♥ P ♥ r♦♠t ♠♠♣ s②st♠ P s r ♦ t t♠ t ♦s rts ♦s t♦ tr②♦stts ♦ t ♠♥ ♠♥ts r ♦ t ♦rr ♦ ② ♣r ②r ♥ t s ②♣r ②r ♥ t r♦♥s ♥ ♠♦r t♥ ② ♥ t ❬ ②♥❪

tt♦rs ♦r ♥r② ♣②ss ①♣r♠♥ts t

t

♦r ①♣r♠♥ts r ♠ ♣ ♦ r♥t ♦♠♣♦♥♥ts stt♦rs s♦♠♣♦♥♥ts r s② ♣♦s s ♠♦st♦♥♥tr ②rs r♦♥ t Ps stt♦r s s♣③ ♥ tt♥ st ♦ ♣r♦♣rts ♦r ♥t ♣rt t②♣

trt♥ r♦♠ t P ♥ t ♥♥r♠♦st ♣rts ♦ t ①♣r♠♥ts r t tr♥s ② ♦♣rt ♥ str♦♥ ♠♥t ♥ ♦rr t♦ ♠sr ♣♦♥ts ♦♥ t ♥t

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t

♦♠♣t ♦ t ①♣r♠♥t t♦♥ ♦s r

r r♦♥ ① cm2s−1 tr♦♥ ① cm2s−1

r t♦♥ ♥s t ①♣r♠♥t ♦s ♠♣ s ♥tr♠♥ ♦r ②rs ♦♣rt♦♥ ♦ t ♠♥ r r♦♥s ♥ ♥tr♦♥ ①s ♥ t ♦r ♥♦r♠ ♦♣rt♦♥ ♦♥t♦♥s s t①t ❬❪

♣rt trt♦rs r♦♠ t ♠sr♠♥t ♦ t ♥♥ rs t s t♥ ♣♦ss t♦t t ♣rts r q ♥ ♠♦♠♥t♠ ♣

r ♣rts tt ♥ t tr♥ s ♣♦st tr ♥r② ♥ t♦r♠tr s tt r ♦t ♥ t ♦♦♥ tt♦r ②r ♦r♥ t♦ t t②♣♦ ♥trt♦♥ ♦ ♣rts t ♠ttr t ♦r♠trs r ♥ t♦ t♦rstr♦♠♥t ♦r r♦♥ P♦t♦♥s r tt ② t tr♦♠♥t ♦r♠tr ♥tr♦♥s r s♥ ② t ♥r② t② ♣♦st ♥ t r♦♥ ♦r♠trs r ♣rt trrss r ♠♦♥ts ♦ s♦rr stt♦rs t ♠♥♦r♥r② ♦sss ♥ s♠ ♥r s♣♠♥t s ♣rt s ♦♥sr s ♠♦♥♦♥s r ts ♥② ♥t ♥ t ♠♦♥ ♠rs tr ♥ ♣♥trt tr♦ t tt♦r s②st♠s s t②♣ ②♦t ♦ ♥ P ①♣r♠♥t s s ♦r①♠♣ ♥ t r♦ss st♦♥ s♦♥ ♥

♥ rt♦♥ ♥r♦♥♠♥t

rt♦♥ ♥r♦♥♠♥t ♦s t♦ t ♥trt♦♥ P♦♥ts Ps ♦ ♥ s♦♥ t♦ ①tr♠② ♦st ♣r♦ r♦♥ ①8 ♣♣ ♥st ♥ts♣r s♦♥ t ♠♥♦st② ♦ 34 cm−2s−1 ♥ ♦r t♦t r♦ss st♦♥ ♦ ♠

tt♦rs ♦r ♥r② ♣②ss ①♣r♠♥ts t t

♦♠♣t ♦ t ①♣r♠♥t r♦ssst♦♥ ♦ t ①♣r♠♥t

r ①♣r♠♥t t

♠♦♥t ♦ s♦♥r② ♣rts ♥ ♦s♦♥ ♣r♦ts ♥rt ♣♦st tr♥r② ♥ t ♠tr srr♦♥♥ t ♥trt♦♥ ♣♦♥t ♦♥③t♦♥ ♦r ♠ t② ♥♥ s♣♠♥t ♥ t ♠tr s ♦ q♥t② ts ♥r② ♦sss ❯♦♥t r♦ s♠t♦♥s ❬❪ r s t♦ t t s♦r ♦s ♥ t t♠♥trt ♣rt ① ♣r ♥t sr ♥ s♦♠ ss t s♠t ♣rt ♥s ♥ ♥♦r♠③ ♥ tr♠s ♦ t ♠ ♣r♦ ♥ s♠♦♥t♦r ♠trs ②♥tr♦♥s ♦ ♥ ♥r② ♦ ❱ Φeq s ①♣♥ tr ♥

♦ ♦t♥ ②rrs ♦r rt♦♥ sts t r♦♠♠♥ ss♠♣t♦♥ ❬P♦t❪s tt r♥ t rst ②r ♦ r ♦ t s♥ ♠♥♦st② ♥ ♥ tt♦ ♦♦♥ ②rs ♥ rs♣t② r♦♠ t ♦rt ②r ♦♥rs ♦♦♣rt t ♠♥♦st② ♦r t ♦ t♦♥ t ss♠ ♥♥ ♦♣rt♦♥ t♠♦ s ① t♦ ①7 s ∼ ②s ♥trt ♠♥♦st② s t st♠sr ♦r t t♠ rqr t♦ ♦t♥ ♣②ss s♦r② s s② ①♣rss ♥tr♠s ♦ ♥rs ♠t♦r♥ −1 st♥r ♣②ss ♣r♦r♠ s t♥ s♦♥ −1 ♦rrs♣♦♥s t♦ ①7 s t ♣ ♠♥♦st② q♦t ♥♠rs rq♥t t♦ r♦② ②rs ♦ ♦♣rt♦♥

♥ t s ♦ t ♦♠♣t ♠♦♥ ♦♥♦ ①♣r♠♥ts s t♦s ♠♣ tr −1 ♥ ♥ t ①♣t st rr♦♥ ♥ ♥tr♦♥ ①s r ♣♦tt rs♣t② ♥tr r♦♥ ♦ t ①♣r♠♥ts ①♣♦s rt② t♦ t ♣rt ① ♦♠♥ r♦♠ t ♥trt♦♥ r♦♥ ♥ t♦ ♥tr♦♥♦ ♠r♥ r♦♠ t ♦r♠trs ♦♥ ♥ t ♦tr ②rs ♦ t ①♣r♠♥tsts s♦♥ ♦♥trt♦♥ ♦♠s ♦♠♥♥t ts ♦r t r♥t stt♦rs t ♦ss ①♣t ♦r ②r ♦ ♥♦r♠ ♦♣rt♦♥ t t ♦srt♥ t ♦s ①♣t r♥ ♦r ♣②ss r♥ ♥ t s♠ t t ♥♥♥tr♦♥ ♥ r r♦♥ ♥s r r♣♦rt t s t♦ ♥♦t r tt t♥ ♥ ♦s ♥ r② ② sr ♦rrs ♦ ♠♥t ♥ ♠♦♥ ♦♥ t r♦♠♣♦♥♥t r t rs♣t t♦ t P ♦♥ ♦♥ t ③ rt♦♥ ♥ t ♥tr ♣rt

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t

P♦st♦♥ ♦s② ♦s rt ♦sr♥ t Φ② Φ②❬②❪ ❬②s❪ ❬②❪ ❬♥♠2❪ ❬♣♠2❪

P① ①5 ①−2 ①2 ①13 ①14

rr ①4 ①−3 ①1 ①13 ①13

①3 ①−4 1213 ♥ ①1 ①−6 ①−2 1314 <1213

①−2 ①−9 ①−5 1011 89

r♥ ①−3 ①−10 ①−6 <10 ♥r♥ ♥ ①−7 ①−3 <10 ♥

①♠♠ ♦s ♥ ♣rt ♥ st♠t♦♥s ♥ t r♥t stt♦rs ♦ ♥ st♥ ♦r tr♦♠♥t ♦r♠tr ♥ r♦♥ ♦r♠trrs♣t② ♥ ♥t② t rr ♥ t ♥♣ ♣rt ♦ t stt♦r s♠ ♣♣② ♦r t st♥s ♦r ❯ rr stt♦r

♦ t ①♣r♠♥t ♦♥ t ♠ ①s t♦s s r ♠♦st ♦♥st♥t ❬r❪♥ t ①♣r♠♥t ♦r♦ ♣♣rt s♦♥ ♥ ♠♦st

♦ t ♥r② r♦♠ ♣r♠r② ♣r♦t♦♥s s ♠♣ ♥ t♦ r♦♥s t ♦♠t♦r ♥t ♦rr ♦r♠tr tt r t♥ str♦♥ s♦rs ♦ s♦♥r② rt♦♥ st♦ s♦rs ②♦ ♦♦r ♥ t rt st♦♥ ♦ r ♦♠♣t ♥ t② ♥ s t ②rs ♦ ♥s ♠trs ♥ ♥ t♦ r tr rt♦♥♠ss♦♥s ♥ t ♦tr ♥ t ♠ ♠ s②st♠ ♠♣♣ t s♣♥st ♥t ♦ t ①♣r♠♥t ♥ s ♥ t ♦rr r♦♥ ♠♦r s♦r ♦ rt♦♥r♦♥s Pr♠r② ♣rts r♦♠ t P str t ♠♣♣ t r② s♦ ♥ss♦ t ♣r♦t ♠tr ♣t s r ♥ ② ts ♠♥s♠ t ♠ ♣♣ ♦♠s♥ ①t♥ ♥ rt♦♥ s♦r ♠♥t♥ t ♥tr♦r ♦ t ♦rr t② ts s♦♥ tt t ♠♥ ♠tr ♦♥trts ♠♦r t♥ ♦ t rt♦♥r♦♥s ♥ t ♠♦♥ s②st♠ ❯♥♦rt♥t② ①tr s♥ ♥ ts r♦♥ s ♥♦t♣♦ss t♦ ss ♦♥str♥ts ❬r❪

r♣♦rts t ♥♥ ♦ss ♥ Φeq ♦r t ♠♦st ♠♣♦rt♥t stt♦rs

♥ rt♦♥ ♥r♦♥♠♥t

♦r t r ♦♥ ♦r ①♣r♠♥t t t ♦♥t r♦ s♠t♦♥sr r♥ t♦ ♣rt ts rt♦♥ ♥r♦♥♠♥t ② s♥ t ♦♦♥ s♦r tr♠s ❬Ps❪

• Prt ♣r♦t♦♥ t t ♥trt♦♥ ♣♦♥ts r♥ t②♣ r♥♥♥ s♥r♦ t♣r♦t♦♥s ♠ ♥ ♦♥s ♦r♥ t t ①♣r♠♥t ♥ s♥♣♦rt ❬❪

• ♠ ♦ss t♦ ♠ ♠s♥t♦♥ P s ♦t ♥r t ♥t♦♥ ♣♦♥t r♦♠t P

• ♠s ♥trt♦♥s

tt♦rs ♦r ♥r② ♣②ss ①♣r♠♥ts t t

P♦st♦♥ ♦s tr♦♥ Φ r♦♥ Φ❬②❪ ❬ ❱eq ♥♠−2❪ ❬ ❱eq ♥♠−2❪

P① ①13 ①13

①13 ①12

①12 ①12

r ①−3 1011 ①9

①−5 ①9 89

>15 ❯ ①−5 911 810

♥♥ ♦s ♥ ♣rt ♥ st♠t♦♥s ♥ t r♥t stt♦rst ♠♥♦st② P① ♥ tr♥ stt♦rs ♦ ♦♥sttt t♥♥r tt♦r ♣rt ♦ t ①♣r♠♥t r st♥s ♦r q r♦♥ ♦r♠tr ♥ r t♦ r♦♥ ♦r♠trs ♥st ♥ r♥t ♦t♦♥s ❯ s♥st t r♦♥②♠ t♦ ♥t② t ♠♦♥ ♠rs stt♦r

rsts ♦ ts t♦♥s ♥ tr♠s ♦ ♥♥ ♦s ♥ t♦t ♣rt ♥ rr♣♦rt ♥ ❬❪ t s t♦ ♥♦t r tt t rt♦♥ s ①♣t♥ ts ①♣r♠♥t r ♠ ♦r t rs♣t t♦ t ♦♥s t ♦r ♥ s s t♦ t t tt t ♦♣rt♦♥ ♠♥♦st② r♥ ♣rt r♥s ♠ ♦r ♦♥ r♦♠ 1027 cm−2s−1 t♦ 1030 cm−2s−1

P♦st♦♥ ♦s ②r ΦTOT ②r P♦st♦♥ ♦s ②r Φeq ②r♥ ❬②❪ ❬♠−2❪ ♥ ❬②❪ ❬♠−2❪

P ①11 ❱ ①4 ①14

P ①10 ①3 ①12

P ①11 ①3 ①11

①9 ①10

❯ ①10 ❯ ①10

r♥ ①6 r♥

♦s ♥ ♥ st♠t♦♥s ♥ t r♥t stt♦rs ♦ ♥

♠r ♦♥srt♦♥s ♣♣② s♦ t♦ t s ♦ t ①♣r♠♥t ♥ ts st ♥♥ s ♣rs♥t ♥ ❬♦r❪ ♥ s♠t ss♠♥ ♥ r♠♥♦st② ♦ ①1032 cm−2 · s−1 ♥ r♦ssst♦♥ ♦r ♥st ♥ rt ♣r♦t♦♥♥ts ♦ ♠ ♥ ①7 ♥trt♦♥s ♥ 7 s♦♥s ♦ t t♥ ♣r ②r

♥ t ①♣t rt♦♥ ♦r ts ①♣r♠♥ts s ♦② ♠ ss♥t♥s s♦♠ ♦ t stt♦rs st t ♠♠ r♦♠ t ♠ r trt♦♥ ♥r♦♥♠♥t s st r② ♥t♥s s s ♦r ①♠♣ t s ♦ t ❱tt♦r t t ①♣r♠♥t r♦r t♦ rt♦♥ ♠ t s ①♣ttt r♣♠♥t ♦r ♣r ♦ s♦♠ ♦ ts tt♦r q♣♠♥ts rqrtr ②rs r♦♠ t rst ♦s♦♥ r♥s ❬♦❪

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t

rsts ♣rs♥t ♥ ts st♦♥ ♥ ♦t♥ t s♠t♦♥ ♦s s♦♥ rt♥ ♥♠r ♦ ss♠♣t♦♥s ♥ ♥rt♥ts ♦♠♥ r♦♠ r♦s s♦rs♦♠♣rs♦♥s tst t♥ r♥t rt♦♥ tr♥s♣♦rt ♦s ♥ ♥♠r♥ sts♦ t♦ ss♠ ♥ ♦r r② ♦ t rsts t♥ t♦r ♦r r♥♦ ♥rs s rt♦♥ s ♥rs ② ♦♣♣♦rt♥ st② t♦rs r t s♦r tst♥ ♥ ♦r t s♣t♦♥s ♦ tr♦♥ ♣rts ♥ s②st♠s ❬❪

t♦♥ ♠ t t

tt♦rs s♠♦♥t♦r ♦♠♣♦♥♥ts ♥ s t t ts rrt t ♠♥② r♥t ♥ ♦ ♣rts t ♥rs r♥♥ r♦♠ ❱ t♦ sr♥rs ♦ ❱ s ①♣♥ ♥ t ♣r♦s st♦♥s s s rrr t♦ s ♦♠♣①rt♦♥ ♥ ♦rr t♦ ♣r♠tr③ ts ♥r♦♥♠♥t t s ♦♥♥♥t t♦ st♥st♥ t r♥t ♦♥trt♦♥s t♦ ts ❬❲ ❲❪ ♥ t ♦♦♥ st♦♥s t r♥t ♦♠♣♦♥♥ts ♦ t rt♦♥ ss ♥ ♥t♦♥ ♦ trt ♦♥ tr♦♥ s ♦r♦r t ♦s♠tr q♥tts ♠♣♦② t♦ ♣r♠tr③t ♠① rt♦♥ s♦ ♥tr♦

♦t ♦♥③♥ ♦s ts

tr♦♠♥t ♦♠♣♦♥♥t s ♦♥sttt ♦ ♥r② ♣♦t♦♥s ♥ ♣rt ss tr♦♥s ♥ ♣♦str♦♥s rt♦♥ ♥ts ♦ ♦♥② ♥t♠trs srt♦♥s ♣♦s r ♠♦♥t ♦ tr ♥r② ♦♥③♥ t t♦♠s ♦ t ♠trs t②r ♥trt♥ t ♥rt♦♥ ♦ ♥ tr♦♥ ♥ ♣♦st②r ♦♥ s ♥r②♣♦st♦♥ s ♦♥♥t♦♥② tr♠ ♦s ♦t ♦♥③♥ ♦s ♦r ♥♠sr ♥ r② ② ② ♦rrs♣♦♥s t♦ t ♥r② ♦ ♦ rs ♥ ♦♠ttr

rt♦♥ t ♦ ts ♣rts ♦♥ tr♦♥ q♣♠♥t s rrr t♦ s sr ♠ ♥ s ♣r♦♣♦rt♦♥ t♦ t rs ♥ t s ♦r ①♠♣ t♣r♦t♦♥ ♥ ssq♥t tr♣♣♥ ♦ rs ♥ ♦① ♠s ♥ s sr♦s ♣r♦♠s♥ ♥ ♣♦r s ❬♦❪

♥ ♥t ts

♥ ♥t t P♥♦♠♥ ♦r ♦t s♦t rr♦rs ♥ ♥t ❯♣st ❯ ♥ t♣ ❯ s t ♥ ♦ stt ♦ st ♠♥t s ② t♠♣t ♦ ♥ ♥rt ♣rt tt ♣♦ss ♠♦♥t ♦ ♦♥③♥ ♥r② ♥ ts♥st ♦♠ ♦ t ♦♠♣♦♥♥t s t s ♥♦t strt ♥ ♥ ♦rrt② rrt♥ t t ♠♥t ♥ s♦♠ ss s ♦r t strtrst q♥tt② ♦ r ♣♦s ② ♦♥③t♦♥ r♥ ♥ ❯ ♥ ♦r t ♠♣♥♥ rt♥ r♦♥ ♦ t ♦♠♣♦♥♥t ♦♥ t ♦♥t♦♥ ♦ ♣rst tr♥sst♦rsstrtrs ♣rs♥t ♥ t t♣ t rr♥t ♦ ♥ t ♦♠♣♥ r♦♥ s♥♦t ♠t t t♣ ♥ ♦ ♥ strt r♥♦t s t s ♥ ♦sr ♦rP♦r tr♥sst♦rs ♥ t ts ♦t ♣♦r ♥ t♥♦♦s ❬♦❪

t①♠♦♥t♦rs

t♦♥ ♠ t t

♥ t s ♦ t r♦♥ s♦rs tt ♦♥ssts ♠♥② ♦ ♣♦♥s π±π0 ♣r♦t♦♥s ♥ ♥tr♦♥s ♠② ♥tt ♥r rt♦♥s t ♥r② ♦ t ♣r♠r② ♣rt s♥t② ♣t♦♥ ♣r♦sss ♥ trrs r t ♥ ♥ r r♠♥tst ❩ tt r s♦ ♦♥ ♦♥ s♦rt ♥t ♥ ♥s ♠trs ♥ts♥ ts t♦ t ♣♦st♦♥ ♦ r ♠♦♥t ♦ ♥r② ♥ s♠ ♦♠ s rqrt♦ ♥rt ❯s ♥ s ♦♥t♦♥s t s ♥ s♦♥ ❬❪ tt t rt ♥t ♥r♦♥♠♥t ♦♠♥t ② r♦♥s t ♥ ♥r② ♦ ❱

rt s ts ♣r♦♣♦rt♦♥ t♦ t ♥♠r ♦ ♣rts ♦ t ♥r② t♦♦ ❱ ♣r ♥t sr tt♥ ♦♥ t s Φ>20MeV

s♣♠♥t ♠ ts

♥tr♦♥ ♦♠♣♦♥♥t t ♠♦r ♥ ♥r ♥② ♥tr ♦r r ♣rt ttrrs ♠♦♠♥t♠ ♥s t♦ trt s♣rt② s t② r ststtr♥ r♦ss st♦♥s ♦♥ ♥ t ♥rs tr♦♥s ♦♥ t t t♦♠s ♦r②st♥ ♠trs s♦♥ ♥ ♦♦s rt♦♥ ♦ tr ♥r② s♣♥ ♣r♠r②t♦♠ ♦t ♦ ts tt st rst♥ ♥ s♦♥ ♥trstt ♥ t ♦r ♥② r♥Pr s ♣r ♠rt♥ tr♦ t ♠tr ♥ ts ♣r♦ t ♥ ♦ ♦r①t♥ ts ❬♦❪ ♥tr♦♥ ♥r② trs♦ ♦r ts t ♥ s♦♥ s ♦t ❱ ♠ ♥ r t ♣r♦r♠♥s ♦ r r♥ ♦ s♠♦♥t♦rs ♦♥ r♦♠ t ♣rt tt♦rs t♦ t r♦♣ s s♦r st ❬♦❪

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

E[MeV]

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

D(E

)/95

MeV

mb

neutrons: Griffin + Konobeyev + Huhtinen

neutrons

protons: Summers + Huhtinen

protons

pions: Huhtinen

pions

electrons: Summers

electrons

Displacement damage in Siliconfor neutrons, protons, pions and electrons

A. Vasilescu & G. Lindstroem

r s♣♠♥t ♠ ♥t♦♥s D(E) ♥♦r♠③ t♦ ❱♠ ♦r ♥tr♦♥s10−10 t♦ ❱ ❬r❪ t♦ ❱ ❬♦♥❪ ❱ t♦ ❱ ❬❪ ♣r♦t♦♥s❬ ♠ ❪ ♣♦♥s ❬❪ ♥ tr♦♥s ❬♠❪ t♦ t ♥♦r♠③t♦♥t♦ ❱♠ t ♦r♥t r♣rs♥ts t ♠ q♥t t♦ ❱ ♥tr♦♥s s t①t

rt♦♥ ♥r♦♥♠♥t ♥ ts ts ♦♥ t q♣♠♥t

♦ sr t ♦♥ s♠♦♥t♦rs s ② ♥tr♦♥s ♥ ♦tr st♣rts s rrr s s♣♠♥t ♠ ♥ t s s♥ ♣r♦♣♦rt♦♥ t♦ t t♦t♥♠r ♦ ♣rts tt♥ t s ♣r ♥t sr s q♥tt② s ♣rt♥ t s ♥t t t s②♠♦ Φ ♥ ♠sr ♥ ♣rts♠2 ♥♠♦♠♥t♠ tr♥sr t♦ t♦♠s s ♥♦ ♥ t s♣♠♥t ♠ t ststtr♥ t t②♣ ♥ t ♥r② ♦ t ♣r♠r② ♣rt r rt ♣r♠trs ♦r♥ rt sr♣t♦♥ ♦ s ♠♥s♠ ♦r♦r ♦r ♥tr♦♥s ♦ ❱ ♦♥s♦♥ ♥r rt♦♥s t ♣ ❬♥❪ ♥ t② s♦ t♦ t♥ ♥t♦ ♦♥t♦r ts t②♣ ♦ ♠ ♥ t♦ s t rt♦♥ ♠ ♣r♦ ② r♥t ♥♦ ♣rts ♦ r♦s ♥r② t rs♣t t♦ t rt♦♥ ♥ ♥s ♦sr♥ t ♠trs t s♦ ♦♥ ♦♥③♥ ♥r② ♦ss ②♣♦tss s ♥♥tr♦

s ss♠♣t♦♥ ♦ t ②♣♦tss s tt ♥② s♣♠♥t ♠ ♥ ♥ ♥ t ♠tr ss ♥r② t t ♠♦♥t ♦ ♥r② ♠♣rt ♥s♣♥ ♦s♦♥s t♦t t♥ ♥t♦ ♦♥t t s♣t strt♦♥ ♦ t ♥tr♦ s♣♠♥t ts ♥ t r♦s ♥♥♥ sq♥s t♥ ♣ tr t♥t ♠ ♥t ❬♦❪ ♥ ts ② t ♥ t ♥ s ①♣rss② t s♣♠♥t ♠ r♦ss st♦♥

s♦s t s♣♠♥t ♠ r♦ss st♦♥s ♦r ♥tr♦♥s ♣r♦t♦♥s ♣♦♥s♥ tr♦♥s ♥ ♥ ♥r② r♥ r♦♠ ❱ ♦♥ t♦ t♥t ♦ ❱ ❲t t ♣♦ t s♣♠♥t ♠ r♦ss st♦♥ D(E) t s ♥② ♣♦ss t♦ ♥ r♥sst♦r κ ♦♥ t♦ ♦♠♣r t ♠ ♥② ♦ r♥t rt♦♥ s♦rs tr♥t ♣rts ♥ ♥ ♥r② s♣tr φ(E)

t s ♦♠♠♦♥ ♣rt t♦ ♥ t r♥ss t♦r κ ♥ s ② tt t ♦♠♣rst ♠ ♣r♦ ② s♣ rrt♦♥ t♦ t ♠ ♦ ♥♣r♦ ② ♠♦♥♦♥rt ♥tr♦♥s ♦ ❱ ♥ t s♠ ♥

κ =

∫

D(E) φ(E) dE

D(En = 1MeV ) ·∫

φ(E) dE

.

r D(En = 1❱) s st t♦ ❱♠ ❬❪ q♥t ❱ ♥tr♦♥♥ Φeq ♥ ts t ②

Φeq = κ Φ = κ

∫

φ(E) dE

♥ t s ♠sr ♥ ❱ ♥tr♦♥ q♥t ♣rts♠2 ♦r s♠♣② ♠−2

♦♥s♦♥

♥ ts ♣tr ♥ ♦r ♦ t r♥t ♦♠♣♦♥♥ts ♦ t r r♦♥ ♦r ♣r♦t t s ♥ ♥ t ♣rtr ♠♣ss t♦ t ♦♠♣① rt♦♥ ♥r♦♥♠♥t tt ♥rt r♥ ts ♦♣rt♦♥ ♠① rt♦♥

s♦ ♠ ♥t♦♥ ♥ s♦ rrr t♦ s t s♣♠♥t ♥t ♥r② s t♦ ttr ♦r s♦♥ 100❱♠ = 2.144 ❱♠2/

♦♥s♦♥

♦♠♣♦s ♦ r♦ ♥rs γs e± ♥ ♣ π±,0 t s ♥ s♠t ② ♦♥t r♦♣rttr♥s♣♦rt ♦s ♦r♦r ts ♥t♥st② s ①♣t t♦ ♣♦st♦♥ ♥ t♠ ♣♥♥t ♦r r♥ ♦ ♦rrs ♦ ♠♥t s ♥r♦♥♠♥t ♥r ♥♦♥tr♦r ♥ ♣rt rt♦r ♠♥s t s ♥t♥st② r♣rs♥t ♥r ♦r tq♣♠♥ts ①♣♦s t♦ t r♦r t tr♦♥ ♥ t ♣rt tt♦rs t t rt♦r ♥ ♥s ts ♥r② P②ss P ①♣r♠♥ts srr♦♠ rt♦♥ ♠ ♦r t ②rs ♦ ♦♣rt♦♥

♦s♥ ♦♥ t s ♦ t P ①♣r♠♥ts ♦ t ♥ t ♥r② ♣♦st♦♥s ♥ t ♦♥③♥ ♥♥ ♦r s s ♥ t ♦t♦♥③♥ ♥♥ ♦r s♣♠♥t ♠r t ♠♥ ts tt ♥ t♦ ♦ss ♦ ♣r♦r♠♥s ♥ t♦ ♥ rt ♥♦ t r♥t ①♣r♠♥t tr♦♥ q♣♠♥ts r♦r ♥ t ♣rs♥t ♣trt ♥trt♦♥ ♠♥s♠s t s♠♦♥t♦r ♠trs s s ①♠♣s ♦ tr♥t rt♦♥ ♠ ts ♥ ♥

rt♦♥ ♠♦♥t♦r♥ ♥ s ♥ ♥r♦♥♠♥t r♣rs♥t ♥ tt s ♥ ♥ ts tss ♦r ❱r♦s ♦s♠tr t♥♦♦② ♥ s r ①st♥t ♥ ♥ ♦♣ ♥ t st ②rs ♦r r♥t ♥str ♥ rsr ♣♣t♦♥s♥ t ♥①t ♣tr ts t♥♦♦s r② sss t♦ ♥tr♦ t rt♦♥♠♦♥t♦r♥ s tt rtr③ ♥ t ♥ t ♦♦♥ ♦ ts tss♦r ♠♥ t♦ t ♥s ♦ t ①♣r♠♥ts

♣tr

r ♦ ♦s♠trs ♥ rt♦♥

♠♦♥t♦r♥ s

♥ ♣tr t s ♥ ♠♦♥strt tt t rt♦♥ ♥r♦♥♠♥t ♥rt r♥t ♦♣rt♦♥ r② ♥♥ ♦r t tr♦♥ q♣♠♥t ♥ tt♦rstt t♦ ♦♣rt ♥ t

♥ ♥ts r ♥st♥t♥♦s ts tt ♥ ♣♣r s s♦♦♥ s tr s rt♥ ♣rt ♠ r ♥ ♠ ♥ s♠♦♥t♦rs sr ♥ t♦♥ r ♥st ♠t ts tt ♥ rs♣♦♥s ♥ ♥♦r♠ ♦♣rt♦♥ ♦♥t♦♥s♦r ♦ss ♦ ♣r♦r♠♥ ♥ ♥ rt ♥ ♦ ①♣♦s ♦♠♣♦♥♥ts♦r♦r tr s rs ♦ ♥ts ♦r ♠♥t♦♥s tt ♠② ♣r♦ rt♦♥ rstsrtr ♥rs♥ t ♦ ♠♥t♦♥ ts

♦♠♣r♥s ♦♥t r♦ ♠♦s ♥ ♦♣ ♥ ♦rr t♦ ♣rt t rt♦♥ s s♦♥ ♥ t♦♥ ♥ t r② ♦ ts ♠♦s s♦♥st♥t② ♠♣r♦ t s ♠♣♦ss t♦ ② sr t rt♦♥ ♥ ♦♠♣①strtr t ♦r♦r t ♣②s ♠♦s s ♥ s♠t♦♥s t♦ sr♣rt ♥trt♦♥s s♣② t ♦♥s ♥♦♥ r② ♥r② ♣②ss ♣r♦sss♥t ♥ ② t ②t s ♦ ts rs♦♥s t rsts ♦ s♠t♦♥ r②s ♥t♥ t♦ ♣rs t♥ t st t♦r t♦

r♦♠ ♦ rs♦♥s t s tr♦r r tt ♦s♠tr ♠sr♠♥ts t♦ ♣r♦r♠ t♦ r♦ss t ♣rt♦♥ ♦ ♦♥t r♦ s♠t♦♥s ♥ t♦ sssst rt♦♥ ♥ ♠ ♥ ♠trs tt♦rs ♥ tr♦♥ ♦♠♣♦♥♥ts r♥♦t ♥♦r♠ ♦♣rt♦♥ s s tr ♥t s♥r♦s ♦r ts st ♣r♣♦s t♦s♠tr ♠sr♠♥t ♥ ♣r♦ ♥t♦♥ ♦♥ ♠♥t s♦ r♣ t♦ r♥t t rt② ♦ t ♦r s②st♠ ♦r t♠

♣r♣♦s ♦ ♦s♠tr② s t♦ q♥t② t rt♦♥ t♦ ♠sr t ♣rt♥ ♥♦r t ♥r② ♠♣rt t♦ t rrt ♠tr ♥② ♦s♠tr② ♠t♦sr ♥ t② ♥ ss s♥ ♠♥② r♥t rtr

♦r t ♣r♣♦ss ♦ ts ♦r t s s t♦ ss② t♠ ♥ t♦ t♦rs ♣ss ♦s♠trs ♦r t ♦s♠trs ♣♥♥ ♦♥ ♦ t ♦s♠tr ♥♦r♠t♦♥ sr ♦t Pss ♦s♠trs ♥ t♦ r♠♦ r♦♠ tr ♠sr♠♥t ♦t♦♥st♦ ♣r♦r♠ tr r♦t t ♦s♠trs ♥ r♠♦t② ss t② r♣♦st♦♥ ♥ t rt♦♥ t♦ ♦r♠tr② s t ♦♥② s♦t ♠t♦ t♦

Pss ♦s♠trs

♠sr t s♦r ♦s r♥t s♦♥r② ♦s♠tr ♠♥s ①st ♥ r s t ❬♦❪

♥② ♣ss ♦s♠trs ♥ r② rt t♦ rt♦♥ ♦ r♦s qts ♣rt t②♣ ♥ ♥r② ♥ ♠♣♦② ♦r r♦t♥ ♠sr♠♥ts ♦r ♦t♥t ①st♥t rt♦♥ rs r ♦♥② ♦r tssq♥t ♠trs ♥ s s ♦♣♣♦rt♥ rt♦♥s♣s t♦ tr♠♥ ♥ ♦rr t♦ ♦♥rt ts ♦s♠sr♠♥ts t♦ t ♥r② ♣♦st♦♥ ♥ ♠trs ♠♦r r♥t ♦r P ♣r♣♦ss 2 t ♦r s♦♠ ♦trs ♦s♠trs ♠♥② t t♥♦♦s t sst ♥ ts ♦r s♦stt s♠♦♥t♦rs ♥ ♣t② t♠t ♠♥s♥t♠trs ♥ ♣♣r♦♣rt rtr③t♦♥ s ♥ssr② ♦r tr s ♥ t ♦♠♣① ♥r♦♥♠♥t t s t♦ ♣♦♥t ♦t ♠♠t② tt t r ♠tr ♥ t ss ♦r t ♣r♣rt♦♥ ♦ ♦t ♣ss ♥ t ♦s♠tr s ♦r t♣r♣♦ss ♦ ts tss ♦r t ♠♥② sss ♥ t r♠♦r ♦ t♦♣♠♥t ♦ t ♦s♠tr s②st♠s

♦ ♦ ts ♣tr s t♦ ♥ ♦r ♦ t ①st♥ ♣ss ♦s♠tr②s②st♠s ♥ t♦ sr t t t♥♦♦s tt ♥ ♥stt ♥ t♦♦♥ ♦ ts tss ♦r t rt♦♥ ♠♦♥t♦r♥ t t ①♣r♠♥ts

Pss ♦s♠trs

♦♦♥ ♣rr♣s st t ♠♦st ♠♣♦rt♥t rtrsts ♦ r♦s t♥♦♦s♦ ♣ss ♦s♠trs ♦♠ ♦ ts t♥♦♦s ♥ ② ♠♣♦② ♥ ts♦r t♦ rtr③ t r♥t rt♦♥ s ♥ t♦ ♥♠r t ♠sr♠♥tsrr ♦t t t t rt♦♥ ♠♦♥t♦r♥ s t t ♥ ♦ t st♦♥t ♠♣♦rt♥t trs ♦ ♣ss ♦s♠trs t♦ s ♦r ♠sr♠♥ts rs♠♠r③ ♥

P♦②♠r♥♥ ♦s♠trs P

♥♥ s ♥ ♠♥♦ α♥♥ 3·2· t ♠ ♦♠♣♦st♦♥ qt ♦s t♦ tt ♦ tss ♠♦♥ t r s♣s ♥rt ♥ ♥♥ ②♦♥③♥ rt♦♥ t st r 3C s ♣r♦♠♥♥t t r♦♦♠ t♠♣rtr s ♣r♦♠♥♥t ♣ttr♥ ♥ ♠sr ② tr♦♥ s♣♥ rs♦♥♥ s♣tr♦♠tr ♦♥♥trt♦♥ ♦ ts r r ♠sr ② s♣tr♦♠tr②r♦s ♥r② t t s♦r ♦s ❬❲❪

Ps r ♣r♦ ♥ ♦r♠ ♦ s♠ s r t ♥♥ ♣♦r s ♠①t♦ ♣♦②♠r tt t s ♥r s ♦r ①♠♣s t P s♠♣s rr♥t②s t ♠♠ ♥ ♠tr ♦r ♠♠ ♥ ♥t s s♦♥ ♥ s rtrst ♠s t ♥♥ s② t♦ ♥srt ♥ ♣s t t♦ ss ♥♥ rs♣♦♥s s tss q♥t ♥ t r♥ ② t♦ ② t s ♥r②♥♣♥♥t ♦r ♠♠r②s ♦ ♥rs > ❱ ♥ ts ♥tr♦♥ s♥stt② rsr♦♠ ♦♥r② t♦ ♦t ♦r st ♥tr♦♥s t rs♣t t♦ ♠♠r②s ❬t❪ ♦ ♥ s ♠sr t ♠♥t t♠♣rtr ♥ st♥r ♠t②

♦♠t♠s ♦♥③t♦♥ ♠rs ♥ r ♦s♠trs s r s♦ ♦♥sr s s♦t ♦s♠tr② ♠t♦s ♥ r♦♥s s st♥rs

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♣rs♦♥ ♥ ♠sr♥ t ♦♥③♥ ♦s t s ♠t♦ s ♥ t ♦rr♦

♦P♦t♦♠♥s♥t ♦s♠trs P

♥r② rt♦♥ ♥s st r♦♣♦t♦♠♥s♥t ♥trs ♥ srtt♠♥♦♣♦s♣t ss ♠t ♣♦s♣♦rs♥ ♥ ①♣♦s t♦ ❯❱ t r♦♥ ♥♠ ♠♦♥t ♦ t ♣♦s♣♦rs♥ s rt t♦ t ♠♦♥t ♦ rt♦♥s♦r ♥ t ss t ♦t♣t ♥rss ♥r② t t ♦s ♣ t♦ ♦t ② t♥ t rt♦♥ r rrss t ♦t ② t♦ t ♥rs ♦ t♦♦rt♦♥ ♥ t ♦rrs♣♦♥♥ ss♦r♣t♦♥ ♦ t ss

s ♦s♠trs r s t ♥ ♦r♠ ♦ s♠ tr♥s♣r♥t ②♥rs ♦ ♠♠ ♥t ♥ ♦ ♦t ♠♠ ♠tr s rs♣♦♥s ♦ s s♦s ♠sr♠♥ts ♥ r♦ ♦s r♥ r♦♠ ② t♦ ② ♦r t② ♣rs♥t r ♦rst♠t♦♥ ♥ t ♠sr ♦s ♦r ♦♥r② ♠♠s < ❱ rrs♣♦♥s t♦ st ♥tr♦♥s s ♦t t rs♣t t ♠♠r② ♦♥s ♠ ♥♥ t ♦rr ♦ ♣r♥t ♦r tr ♠♦♥ts s ♥ ♠sr ♦r P r♦♦♠t♠♣rtr t♠♣rtr ♥♥♥ ♦ P ♥ s t♦ rs t ♦s♠tr♥♦r♠t♦♥ ♦♥ tr rt③t♦♥

♣rs♦♥ ♥ ♠sr♥ t ♦♥③♥ ♦s t s ♠t♦ s ♦♥ t♦rr ♦ ♦r ♦ss ♣ t♦ s♦♠ ♥r ♦ ② t r ♦ss t rrs ♦r♦ t rt♦♥ r ♠s t ♠sr♠♥t ♥rt♥ts r ♦r ♦ss ♥ t② r♥ ♦ ♦r♦♠ ts ♣r♦♠ P rr s ♦♥ ❯❱ t s♦r♣t♦♥♠t♦ s ♥r ♦♣♠♥t t ❬❪

②r♦♥ Prssr ♦s♠trs P

②r♦♥ s ♦r♠ ♥ ♦s r♦♠ t rrt ♣♦②t②♥ P P ♠s ♦ s♦♠t♥s ♦ ♠r♦♥ t♥ss r ts r♦ ♥ ss ♣s ♦ ♦t × ♠ s s♦♥♥ ♦s s tr♠♥ ② r♥ t ♣s ♥ ♥♦♥ ♦♠ ♥♠sr♥ t ♣rssr ♦ t ♦ ②r♦♥ t ♦♥st♥t t♠♣rtr ❲t tst♥q t s ♣♦ss t♦ ♣r♦r♠ ♠sr♠♥t ♥ t r♥ ② ② t♥ ♥rt♥t② ♦ ♦t

r♠♦♠♥s♥t ♦s♠trs

r♠♦♠♥s♥t ♦s♠trs r ♥♦r♥ r②sts ①t♥ ♦♥♥trt♦♥♦ tr♣♣♥ ♥trs ♥ t ♣ t♥ ♥ ♥ ♦♥t♦♥ ♥s tr♦♥s rt r♦♠ t ♥ t♦ t ♦♥t♦♥ ♥ ② t ♥♥t ♦♥③♥ rt♦♥♥ r t♥ ♣tr t ♦♥ ♦ t tr♣♣♥ ♥trs ♦s ♥ s♦ tr♣♣ ♥ ♥♥♦♦s ♣r♦ss ♠tr ♥t♦♥s s ♥ ♥trt♥ tt♦r ♥ t♥♠r ♦ tr♣♣ tr♦♥s ♥ ♦s s ♣r♦♣♦rt♦♥ ♦♥ t ♥♠r ♦ tr♦♥♦♣rs ♦r♠ ② t rt♦♥ ①♣♦sr

tr t ①♣♦sr t tr♣♣ rrrs ♥ ♠sr ② t♥ t ♥ rt♥ t♠♣rtr tr♠♥ ② t ♥r② s ♦ t tr♣s t tr♣♣tr♦♥s ♥ ♣ ♣ ♥♦ tr♠ ♥r② s♦ tt t② r r①t t♦ t

Pss ♦s♠trs

P P ♥ P r♦♠ ❬❪

r ♦♠ ♣ss ♦s♠trs s t

♦♥t♦♥ ♥ s♦ rt tr♦♥s ♠rt t♦ ♥r tr♣♣ ♦ r t②♥ r♦♠♥ t t ♠ss♦♥ ♦ ♣♦t♦♥ tr♥t② t ♦s r rst② ♠② ♠rt t♦ tr♣♣ tr♦♥ ♥ tr r♦♠♥t♦♥ s♦ rsts ♥ rt♣♦t♦♥ ❬❪

♠tt ♣♦t♦♥s r ♥ t s r♦♥ ♦ t tr♦♠♥t s♣tr♠ ♥tr t♦t ♥♠r s ♥ ♥t♦♥ ♦ t ♦r♥ ♥♠r ♦ tr♦♥♦ ♣rs rt② t rt♦♥ rrs r s♥ ② t♥ t ♦s♠tr ♥ r♥t t ♦t♣t ♣♦t♦♠t♣r t ② s r♦r s ♥t♦♥ ♦ ts♠♣ t♠♣rtr ♥ ♦ r ❬r❪

♥ ♦♠♠♦♥ t②♣ ♦ ♠tr s t tr ♠♦♥ts ♦ ♥ s s② ♣r♦ ♥ s♠ ♣ts ♦ ×× ♠♠3 s s♦♥ ♥ s♥tr t♠ ♦♥t♥s 6 ♦s♠trs r s♥st t♦ s♦ ♥tr♦♥s ♥♥α rt♦♥ rs♣♦♥s t♦ ♥tr♦♥s ♥ ♥♥ ② s♥ t♠ ♥r♥ 6 ♦r s♣♣rss ② s♥ t♠ ♦♥sst♥ ♥tr② ♦ 7 ♠♦st ♥♥ t r♦♦♠ t♠♣rtr ♠s t ♠sr♠♥ts t ts s r② rt♥ t r♥ µ② ② t♥ ♥ rr♦r ♦

r ♦s♠trs

rr♦s s♣t ♦s♠tr s② r s s ♦♥ t ♠ ♣r♦ss ♦♦①t♦♥ ♦ rr♦s ♦♥s ♥ q♦s s♦t♦♥ t♦ rr ♦♥s ② ♦♥③♥rt♦♥s ♠t♦ ♥ s ♦r rt s♦r ♦s tr♠♥t♦♥ s♥s♣tr♦♠tr ♠sr♠♥ts ♦ t rr♦♥ ♦♥♥trt♦♥ t ♥♠ ♥t ♥t ♣ ♦ t s♦r♣t♦♥ s♣tr♠ ♥ t♦t ts ♠t♦ s qt t♦s t♦s tss q♥t ♠sr♠♥ts ♦ t ♦s ♥ t r♥ ② t♦ ② t♥ r② ♦ ♣r♥t ♦r ts rs♦♥ ts ♠t♦ s r♦♥③ s st♥r

② P ♦s♠trs

s ♣r♦r ♠s s ♦ t rt♦♥♦♦rt♦♥ ♣r♦♣rt② ♦ ♦♠♠r P♦②♠t②♠tr②t P ♦r P①s ♥ t ♦r♠ ♦ sts ❯♣♦♥ rrt♦♥ t♦ ♦ss ♥ ①ss ♦ ② t ♠tr r♥ t♦ t ♦r♠t♦♥ ♦ ♥

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♠ ♦♥rt♦♥ strt t ②r ②♥♠ t♦♥t②♣ t♥ss r♥ rs♣♦♥s

❳ ②♣ tr ②rs ②♦ µ♠ ② ❱ γ♣♦②str

t ②r r µ♠ ② > ❱ γ♦♥ sstrt ♣♦②str > ❱

♥♠ ❯❱

♠t②r r × µ♠ ② > ❱ γ♣♦②str > ❱

rtrsts ♦ t r♦♠ ♠s

s♦r♣t♦♥ ♥ ♥ t s r♦♥ ♦ t s♣tr♠ r♥♥ ♥ ♠sr♥ tr♠s ♦ ♦♣t ♥st② s♥ ♦♥♥t♦♥ ♥st♦♠tr

♥ rt♦♥ r rt♥ t ♥ ts♦r♣t♦♥ t♦ ♦s s stst ♠tr ♥ s ♦r ♦s♠tr② ♥ t r♥ t♦ ② ♠sr♠♥tsrr ♦t t s s ♥ ♦♥ t♦ str♦♥② ♥♥ ② t♠♣rtr♠t② ♥ t ①♣♦sr ❯♥ss ♦rrt♦♥s r ♣♦ss t ♣rs♦♥ ♦ ts ♠t♦s r♦♥

r♦♠ ♦s♠tr ♠s

r♦♠ r♦r♦♠ ♦s♠tr② ♠s r s♦♣♥ ♠ ♠ s ♦r t♠sr♠♥t ♦ s♦r ♦s ♥ t ♠♣♣♥ ♦ rt♦♥ s s ♠s ♦♣ st♥t ♥ rtrst ♦♦r ♣♦♥ ①♣♦sr t♦ ♦♥③♥ rt♦♥ ♥ ♦♠♣r♦rss② rr ♥ ♣r♦♣♦rt♦♥ t♦ s♦r ♦s

t ♦♠♣♦♥♥t ♥ ts ♠ s ♠r♦r②st♥ rt♦♥ s♥st♠♦♥♦♠r t②♥ tt s s♣rs ♥ t♥ ♠tr① ♥ ♦t ♦♥t♦ ♣♦②str♠ s ❲♥ t t ♠♦♥♦♠r ♦♠♣♦♥♥t s ①♣♦s t♦ ♦♥③♥ rt♦♥ ♣♦②♠r③t♦♥ rt♦♥ s ♥tt rst♥ ♥ t ♣r♦t♦♥ ♦ ② ♣♦②♠r ♣♦②t②♥ ♠♦♥t ♦ ♣♦②♠r ♣r♦ ♥ ts t ♥t♥st② ♦ t ♦♦r♥ s ♣r♦♣♦rt♦♥ t♦ t ♠♦♥t ♦ ♥r② s♦r ♥ t t ②r str♦ t ♠sr♠♥t ♦ t ♦♦r ♥ ♣r♦ ♣♦♥ ①♣♦sr t♦ rt♦♥ ts ♣♦ss t♦ q♥t② t s♦r ♦s ❬❪

r t②♣s ♦ ♠s ♥ t s♥st ♠♠ s ♦t t r♥t sstrt ②rs ♦ r♦s ♠trs r ② ♥tr♥t♦♥ ♣t② Pr♦ts P♥♦♦s ♦s♠tr ♠s ❳ ②♣ ♥ ♥ s ♥ ts♦r ♥ tr ♠♥ rtrsts r s♠♠r③ ♥

r♦♠ ❳ ②♣ ♠ s s♥ t♥ ♦♥ tr♥s♣r♥t ♠ sstrt♥ ♦♥ ♦♣q t ♠ sstrt tr♥s♣r♥t ♣♦②str sstrt ♦♥t♥s ②♦ ② ♥ ♣r♣♦s ♦ t ②♦ ② s t♦ ♥♥ t s ♦♥trst ♦ tr♦♠t ♥s tt ♦r ♥ t ♠ s ①♣♦s t♦ rt♦♥ s♦♥ ♣r♣♦ss t♦ ♣r♦tt t t ②r ♥st ①♣♦sr ② ❯❱ ♥ t ♥ tr② ♥t ♠ t♦ ♠♦r t♦r♥t ♦ ♥ ♥ ♥ t t s trs ♠ ts ♠

Pss ♦s♠trs

r rt♦♥ ♥r② ♥

59♦♥γ60♦ tr♠ 197♥γ198 ♣tr♠ 115♥♥♥115m♥ ❱

58♥♣58♦ ❱ 32♥♣32P ❱

27♥α24 ❱ 59♦♥♥58♦ ❱

12♥♥11 > ❱ ♠♥59♦♥♥57♦ > ❱

♥ ♥r rt♦♥s s ♦r ♥tr♦♥♥ ♠sr♠♥ts

st ♦r ♠ ♣r♦♥ ♣♣t♦♥s ♠s r♦♠ ♥ r ♥st ♦♠♣t② tr♥s♣r♥t ♠

♥ t t ②r s ♦t ♦♥ t♥ tr♥s♣r♥t ♣♦②str ②rs ② ♦♣ rtrst ♦♦r tr ①♣♦sr tt ♥ ♠sr ② ♠♥s ♦ tr♥s♠ss♦♥ ♥st♦♠tr t t ♦ ♥♠ ♥t ♦♦r ♥st② s ts s t♦♠sr t s♦r ♦s r♥ rrt♦♥ ♥ r♥t rt♦♥ s

♦♣t ♥st② ♦ ♦t ♠ t②♣s ♥rss t t♠ r♥ strt♦♥ sst♥ rs tr rrt♦♥ ❬❪ s ♠s ♦ ♦s ♠sr♠♥ts t ♥r② ♦ ♣r♥t t ♣♣r♦♣rt ♥t ♦r t r♦t s ♦s♥ ♥ ♦rrt♦♥s ♦ t ts♦r♥ ♥rs tr rrt♦♥ r r② t♥ ♥t♦♦♥t ❬❪

s ♦s♠tr ♠s ♥ ② s ♥ ts ♦r t♦ rt t r♥trt♦♥ ♥r♦♥♠♥ts ♠♣♦② ♦r ♦r tr t③t♦♥ t ♠ tsr t r rt ♥ ♣tr t rt♦♥ rr ♦t s♥ r ss♦ts ♥st♦♠tr ♥ t ❱ ♣r♦t♦♥ ♠ tt t② ♣rs♥t ①♠♣s ♦ ♦ ts ♠s r s ♥ ttr♠♥t♦♥ ♦ t ♣r♦ ♦ t s♠ ♣r♦t♦♥ ♠ s♦ ♥ tr

tt♦♥ ♦s

s ♠t♦ ♦ s♦t ♣rt ♥ ♠sr♠♥ts s s ♦♥ ♥r rt♦♥stt t♦ t ♦r♠t♦♥ ♦ r♦♥s ♥ r♦s ♣rt② ♠trs ♦ ♥ t tr ♣rt ①♣♦sr t ♠♦♥ts ♦ ♥rt ♥s ♥ tr♠♥ ② ♠♥s ♦ γs♣tr♦s♦♣② ♥②ss

♦r ♥tr♦♥s t ♥γ ♥♣ ♥α ♥①♥ ♥r rt♦♥s ♥ st ♥♦r♥ t t ①♣t ♥tr♦♥ s♣tr♠ ♥ t rrt♦♥ t♠ ♥ ♦s♦ r♦s ♠tr r s ♦r ts ♥ ♦ ♠sr♠♥t r t ♥ s♣ sst t rs♣t t♦ t ♥tr♦♥① ♥t♥st② ♥ rrt♦♥ t♠ t♦♥♦ t s♣ tts ♥ ♥ t ♠trs ♣r♦ t♥ ♥♦r♠t♦♥ ♦t t♥tr♦♥ ① ♥ t r♥t ♥r② r♥s ♥ ts t♦♥ t rrt♦♥ t♠

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

r♦ssst♦♥ ♦♣

r ♣♥ ♣rt tt♦r ♦ strtr t p+ rr♥ r♦♥ t t rtt ♦♥ssts ♥ p+ − i(ν) ♥t♦♥ ♠t tr ❬♦ ❲❪

♥ t s ♦ t r♥t s♦t♦♣s ♠st t♥ ♥t♦ ♦♥t t♦ t ts♣ tt② t strt♦♥ ♥tr♦♥ r♦ssst♦♥ rs ♥ ♥♦♥ ♦♥② t♦ ♦♠♣t t s♣ ♦ t ♥tr♦♥ s♣tr♠ ♥r ♥stt♦♥ ❬♦❪ ♣rs♦♥ ♦ ts ♠t♦ s ♦ ♦t ♠♥ ♥r rt♦♥s s ♦r ♥tr♦♥♥ ♠sr♠♥ts r st ♥ ♦r r ♣rts ♥ ♠sr♠♥tst ♦ ♦♥srt♦♥ s♦ ♣♣s ♥ t♦♥ t rt♦♥ ♦ ♥trst ♦r t♠sr♠♥t ♦ t ❱ ♣r♦t♦♥ ♥ ♥

rr♥t r♦♠ rrss s♦♥ tt♦rs

♦♥ ♣rt tt♦rs r rrs s ♣♥ ♦s t r② rsstt②sr Ω·♠ ♥t②♣ ♦ s② µ♠ t♥ss

r rt♦♥ rs ♦r ♣♥ ♦s t t ts ♦ t P rt♦rsr♠♥ts ♣r♦r♠ tr ♥♥♥ ♦r ♠♥ t

rrt♦♥ ♦ s s ♣r♦ ♥rt♦♥r♦♠♥t♦♥ ♥trs ♥ t

Pss ♦s♠trs

s♦♥ ♥ t♦ ♥ ♣r♦♣♦rt♦♥ ♥rs ♦ t rr♥t t s ♣t ② ♣t t s ♥ ♠♦♥strt tt t ♥rs ♦ t rr♥ts ♥♣♥♥t r♦♠ t ♠♣rt② ♦♥t♥t ♦ t s♦♥ s ♠tr ❬♦❪ ② ♥ s s ♣r♦♣♦rt♦♥ ♠ ♦♥tr ♦r r♥ ♦ r♥t ♣rts ♥♣rt ♥rs r s t♥ ♦t t rtr ♦♠♣① ♥♥♥ ♦r ❬♦❪

♦r ♦s♠tr ♣r♣♦ss s② s♠ Pstrtrs t ♥ t r ♥ t♦rr ♦ t♦ ♠2 ♣r♦tt ② ♦♥ ♦r sr rr♥s ♥st rr♥ts rs s s♦♥ ♥

♥ ts ♦r µ♠ t ♣♥ tt♦r tst strtrs ♣r♦ ② r♦tr♦♥s t② t ♥ t r ♦ ♠2 ♥ ♣r♦tt ♦♥ t r♦♥t s ② rr♥ ♥ s ♦ rt t♠ t tt♦rs r ①♣♦s t♦ t r♥t rt♦♥ s t ♠♥t t♠♣rtr ♦t t♦t s♥ t♠ trrrt♦♥ t s r ♥♥ ♦r ♠♥ t ♥ t rr♥t t ♣t♦♥ s ♠sr ♦♥ ♦rt♦r② tst♥ ♥ ♥♦r♠③ t♦ ❬♦❪ rsts r ♣rs♥t ♥ ♥ ♠♦♥strt tt ts s ♥ s♦r r② Φeq r♥ ♣r♦ tt t ♥♥♥ s ♣r♦r♠ r②

r

♦♦s♠

trs

♥rt♦

♥♠♦♥t♦

r♥

s

♦s♠tr P P P r P r♦♠

②♥♠ 5 −1 6 4 7 −5 1 ①2 4 −1 2

r♥ ② ss q♥t

γr②s ♥r② ♥rst♠t♦♥ ♦rst♠t♦♥ ♥ ♦rst♠t♦♥ ♦rst♠t♦♥ ♥♥♦♥ ♥

♣♥♥ t <❱ t < ❱ t < ❱ t < ❱

tr♦♥s s♥st② ♦ s♥st② ♦ 7 ♥♦♥

♥r② t ❱ tr♠ 6 tr♠

♣♥♥ t ❱ st

t ❱

♥ ♥♦♥ t ♦r ♥ ♥ ♥♦♥ ♠♣♦rt♥t ♦

♥ ♠t② ♠♦♥ts t t s♥st rrs

♦ t s♥st ♥♥♥

♦t P ♠♥s♥ Prssr ♠♥s♥ ♣tr♦ ♣t ♥st♦♠tr②

♠t♦ ❯❱ t t♥ ♣♦t♦♠tr② s♦r♣t♦♥

♥ts ♦r♥ rs ♦♦ ♦r r② rs s s ♣ ♥ r② s②

♦ss st♥r s② t♦ r t♦ r

s♥ts t ♥♦t s♥st ♦ ♦s t t♦ s♥st t♦

r♦t ♥ t♦ ♦ ♦ss r♥ ♣r♣r t♠♣rtr

② r♥ ♥ ♠t②

♠♠r② ♦ t ♣r♦♣rts ♦ ♣ss ♦s♠trs s ♦r ♠sr♠♥ts ♦♦♠ ♠♣rtr

t ♦s♠trs

r Pr♥♣ ♦ ♦s♠tr s♠t r♦ssst♦♥ ♦ t s♥s♦r r ♥rt♦♥ ♥ t ♦① ②r ❬❪ tr♦♥♦ ♣rs ♥rt♦♥ ❬❪ tr♦♥♦ ♣rsr♦♠♥t♦♥ ❬❪ ♦s tr♥s♣♦rt ❬❪ ♦s tr♣♣♥ r ♦♦r ❬❪ ♥tr stts② ♣ ♦♦r

t ♦s♠trs

t♦♥s♥s♥ t r♥sst♦rs s

Pr♥♣ ♦ ♦♣rt♦♥

t♦♥s♥s♥ s s r ♣♥♥ tr♥sst♦rs tt r st♦ ♠sr t ♦♥③♥ ♦s ♣ ♦ r ♥ t ♥st♥ s♦♥ ♦① 2②r ♦ t tr♥sst♦r tt tr♦r ♦♥sttt t s♥st ♣rt ♦ t ❬♦♦❪ s♠t r♦ssst♦♥ ♦ ♦s♠tr s s♦♥ ♥ s r ♥trt♥ ♦s♠trs ② r s② s r rr ♠sr♠♥ts♦ ♥trt ♦ss r rqr t♥ ♠t ♦♠s ❬♦♥❪

♦♥③♥ rt♦♥ rts tr♦♥♦ ♣rs tr♦♦t t ♦ ♦① ♦♠ ♣♥♥ ♣♦♥ t tr ♥s t ♦① ox t ♥r② ♥ tt②♣ ♦ rt♦♥ s♦♠ ♣rs ♥rt r♦♠♥ t♥ ♣♦s♦♥ t ♣r♦t② Pr t♦ tr ♠♦t② µe ♠2·❱−1·s−1 tr♦♥s s♣r♦♠♥t♦♥s r r♣② s♣t ♦t ♦ t ♦① ②r t t ♦♥tt ♥♦♦s ♠♦ ♥st s♦② t♦r t s♦♥ sstrt t♦ t ♠♦t② µh

−8 ♠2·❱−1·s−1 tr♥s♣♦rt ♦ t ♦s t♦rs t t♦ ♥ t sr s ♥ t♠ ♣♥♥ ♦♥ t t♠♣rtr t ♣♣ tr ♥ t♣r♦ss♥ ♦ t ♦① ②r ❬❪

♦s ♠② t♥ tr♣♣ ② ♣r①st♥ ♦ tr♣s ♥rt r♥ t♣r♦ss♥ ♦ t ❬♠❪ ♥ ♦t ♥ ♥rr♦ r♦♥ ♦s t♦ t ♥trt♥ s♦♥ ♥ t 2 tr♣♣♥ ♣r♦t② Pt ♠2 ♥ ♥ ♥ t♣♥s ♦♥ t ♣r♦ss♥ ♦♥t♦♥s ♦ t ♦① ②r ♥ t ♣tr r♦ssst♦♥♦r ♦s tt s ♥t♦♥ ♦ t tr ♥ t ♥st♦r ox

r♦r s rst ♦ rrt♦♥ ♣♦st r ot ♦♣s ♥ t t ♦①♥r t s♦♥ ♥ ♥t♦ ♦♥t t ♣r♠trs ♥tr♦ ♦r ts r ♥

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

rtt♥ s ❬♦ r ❪

Qot = q · g · tox · Pnr(Eox, E) · Pt(process, Eox) · D

r q s t tr♦♥ r ①14 ♠−3·②−1 s t tr♦♥♦ ♣rs ♥rt♦♥ rt ♥ t ♦① ♦t♥ s♥ t ♣r♠trs ♦ tox s t ♦①t♥ss Pnr(Eox, E) = 1 − Pr(Eox, E) s t ♣r♦t② ♦ tr♦♥♦ ♣rs t♦ s♣ r♦♠♥t♦♥ ♥ ② s t ♦s s♦r ♥ t ♦① ②r

s♠♣ ♠♦ sr ♥ q s ♥ ♦♥st♥t tr ox s♣♣ t♦ t ♦① ②r t t tr♦ r♥ rrt♦♥ ❱G 6= ❱ ♦s♠trs ♥ s ♠♦ ♣♦st t s s t ♠♦st ♦r s t♦ ♥rs ♦tr♣♣♥ s t tr s rt r♦♠ t ♠t t♦ t s♠♦♥t♦r s♦tt ot s st♦r ♥r t s♠♦♥t♦r♦① ♥tr ♦r ox ♦♥t♥♦s②♦rs ts r♥ t ♦♣rt♦♥ ♥t t ♦s♠tr rs t strt♦♥♥ t ♣r♦♥ t r ♣ t ♥rs♥ tr ♥ t tr♣♣♥r♦♥ ♦ t ♦① rs t ♥ t rst ♦ t ♥st♦r r t tr♦♥♦♣rs r ♥rt s t s ts t♦ strt♦♥ ♦ t rs♣♦♥s s ttr♦♥♦ ♣rs r ♥♦ ♦♥r s♣rt

s ♥ t s ♦ ts ♦r t ♦s♠trs r ♦t♥ ①♣♦s t♦ rt♦♥t♦t s♥ t♠ ❱G ❱ ♦s♠tr s ♥ ③r♦ s ♠♦ ❬♦❪ ♥ s ♦♥t♦♥ t ♣r♦t② ♦r ♦s t♦ s♣ t r♦♠♥t♦♥ s r② s♠ ss♥t ♦tr♣♣♥ ♠♥s ts r s♥stt② ♥ tt♥ ♦♥③♥ rt♦♥s♥ t ♦tr ♥ ts ♦♥t♦♥ s ♥t♦s ♦r ♣♣t♦♥s r t s ♥t♦ ♠sr ♦ss strt♦♥ s r tr ♥ t♦ ♦ ♦♠♣① rtr② ♥①tr♥ ♣♦r s♣♣②

r♦♠ t ♠r♦s♦♣ ♣♦♥t ♦ ♥ s r ♥s tr sr② s♠ t stt♦♥ s ♠♦r ♦♠♣t t rs♣t t♦ t ♠♦ ♣rs♥t ♦r ♠♥s♠s s s ♦ s♦♥ ♥ s♣r ts t♦ t♥ ♥t♦♦♥t t♦ ♦t♥ q ❬❪ ♦r♦r rs t r tr♣♣♥ ♥ t r♦♥♦s t♦ t s♦♥ sstrt s sts ♦r s ♦①s ♥♠ r♦♠ t♥tr t s♦♥ ❬♦❪ ♥ t s ♦ ♥s ♥st♦rs t tr♣♣♥ r♦♥ s♥♦t ♥ ♠♦♥strt t♦ ♥r t tr♦s ♦ tr♣s ♥ ts strttr♦♦t t 2 ♦♠ t s ♦♥sq♥ rtr rs ♦ t s♥stt② t♦ ot ♥♥♦t r ♥②♠♦r r♦♠ q t ♠♥ts sr♦r t s ♠♦ ♥ q♥ttt② ♣♣ s♦ t♦ t ♥s s

♣ ♦ st r ♥ t 2 ot s ♥♦t t ♦♥② ♣♥♦♠♥♦♥ tt♦rs ♦♥ s ①♣♦s t♦ ♦♥③♥ rt♦♥ ♥ t ♥tr r♦♥ t♥2 ♦tr tr♣♣♥ ♥trs r sts r♥ t ♣r♦ss♥ ♦ t s♦♥ ♦①tr rs ♥ tr♦r st♦r ♥ ts ♦t♦♥ ♥tr stt rs ♣♥ t s ♦ ♣ tr♥sst♦rs ts rs r ♣♦sts ♥ t♦ t ♦♥s tr♣♣♥ t 2 it s r stts ♥ ♥ rt ♦♥tt t t ♥r②♥s♠♦♥t♦r r♦♥ r tr② t ♥ ♥ rs♣♦♥s ♦ sr ♥stt②♠♥s♠s s sss ♥ t♦♥

♥tr stts r s② tr② t♥t ♦r rrt♦♥ ♥ t② r trr② rt♦♥ ①♣♦sr ♦r r ♥t♦♥ ♣♥♦♠♥ r♦r t② ♦♣ r♦♠ s♦♥s t♦ t♦s♥ ♦ s♦♥s tr rrt♦♥ ①t♥t ♦ t it ♣ ♣r♦ s

t ♦s♠trs

r t♦♥♥ ♥s ♥ ♦s♠trs st ♦ t tr♥sst♦r D❱GS rtrst r ②①s s r ♣♦tt ♥ ♦rt♠ s r rt ♦r trs♦ ♦t st

② ♣♥♥t ♦♥ t ♦① ♣r♦ss♥ ♦♥t♦♥s ♥tr stt ♥st② r♦ts r r♥ rrt♦♥ ♥ s s ♣♣ t♦ t tr♥sst♦r t ♥ st ♠♣♦rt♥t s♦ ♥ ♥s ♦♥t♦♥s

s♠♠r③s r♦♠ t♦ t st♣s ♥♦ ♥ t ♣♦st♦♥ tr♥s♣♦rt ♥ tr♣♣♥ ♦ rs ♥ t ♦r♥ ♥r② ♣ ♦ t s♦♥ ♦① ♥st♦rs t s ♥ sr ♥ ts st♦♥

s♣♦♥s ♥r rrt♦♥ s♥stt② ♥ ②♥♠ r♥

♦t ♣♦st rs ot ♥ it ♥rt ② rrt♦♥ ♥ t t ♦① ♥ tt 2 ♥tr rs♣t② t♦ st ♦ t tr♥sst♦r D r♥ rr♥t❱GS t ♦t rtrst r t♦rs ♠♦r ♥t ♦ts s s♦♥ ♥ tr♥sst♦r trs♦ ♦t ❱T s ♥ s t ♥trst♦♥ ♦ t♥r ♣rt ♦ t r

√ID s ❱GS t t ❱G ①s ♥ ts t♦ q♥tts r

♣♦tt ♥ ♥r s s q♥tt② s♦ sts ♥r rrt♦♥ ② ♥ ♠♦♥t ∆❱T

♦♦♥ t qt♦♥ ❬r r❪

VT = VT,0 −Qot + Qit

Cox

= VT,0 + ∆VT

r ❱T,0 s t ♦ ❱T ♦r rrt♦♥ ♥ ox s t t ②r ♣t♥ ♥tr r it ♠♦r♦r rs t s♦♣ ♦ t ♥r ♣rt ♦ t D❱GS

r t♦ rt♦♥ ♦ t rrr ♠♦t② µ ♥ t tr♥sst♦r ♥♥ ❬❩♣❪ ss♦♥ ② t r r ♦

r♦r ∆❱T s t ♠sr ♦s♠tr ♣r♠tr ♥ t s ♣rt② ♦t♥ r♥ ♦r tr rrt♦♥ s♥ t s ♠sr♠♥t ♦♥rt♦♥ s♦♥♥ ❲t s r♦t rt t ♠sr q♥tt② s ♥♦t ❱T tt

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♣♣rs ♥ q t ♥ q♥t ♦♥ ♥ s

VGS = VT −√

ID0

β

r D0 s ♦♥st♥t rr♥t ♦r tr♦♦t t tr♥sst♦r ♥ t s s ss♦♥ ♥ ♣r♠tr β s ♥♦♥ s t tr♥s♦♥t♥ ♣r♠tr♥ s ♦♥st♥t q t♦ β = 1

2· µ0 · Cox · W

L r µ0 s t sr ♠♦t② ♦

t Cox t ♣t♥ ♦ t t ♦① ♥ ❲ s t tr♥sst♦r s♣trt♦ ❬③❪ t s ♦♠♠♦♥ ♣rt t♦ t ∆❱GS r ♦t r♦♠ q t ts♠ ② ♦ ∆❱T trs♦ ♦t st ♦ ♦ ♦♥s♦♥s t♦ ♣rs♥t t t ♥ ts ♦r t s ♥♦♠♥tr ♣t ♥ t ♦s♠tr♣r♠tr ♥t s ∆❱th t♦ ♥t♥ t st ♦ ❱GS ♦r ♦♥st♥t r♦trr♥t

s s♦♥ ♥ t♦♥ t ♣r♦ss♥ ♦♥t♦♥s ♦ t s♦♥ ♦① ♥ t s♣♣ r♥ rrt♦♥ r t t♦ ♣r♠trs tt ♣② ♥♠♥t r♦ ♥ t♦tr♣♣♥ ♣r♦t② Pt ♣r♠tr ♥ ts ♥ ♠①♠③♥ t s♥stt②

❲ s♦ r② s♥ tt ♥ t s ♦ s s ♥t♥ t r♥st② t t ♥tr t ot s st♦r r② ♦s t♦ 2 ♥tr rtst ∆❱T ♥ ts rtt♥ t s tr♦stt ♦♥srt♦♥s ② trt♥ ts♥st ♦① ②r ♥ t s♠ s♦♥ s ♣r♣ts ♣t♦r

∆VT =tox

ǫ · ǫ0

· Qot

r ǫ ♥ ǫo r t ♠ ♣r♠ttt② ♥ t tr ♦♥st♥t ♦r t ♦①rs♣t② ♥ Qot s t t♦t r tr♣♣ ♣r ♥t sr tr rrt♦♥ ♥ ♥rr♦ ②r ♦s t♦ t s♠♦♥t♦r ♥tr s ♦ P

q tr♦r s♦s tt t s♥stt② ♥ rtr ♥rs ♦r sr♦rrs ♦ ♠♥ts ❬r❪ ② ♠♥tr♥ s t t ♦① ②rs

rs♣♦♥s ♣♥ ♦♥ t s ♣♣ ♦♥ t t ❱G t rs♣t t♦ tsstrt ♣♦♥ rrt♦♥ ♥ t ♦tr ♥ ♦r ♦①s ♣r♦ ♥ s♠ ♣r♦ss♥♦♥t♦♥s t s trs♦ ♦t st s ♥t♦♥ ♦ t rt♦♥ ♦s ∆❱th♥ ♣t ♥r ♦r sr ♦s s ② ♥♥ t ♣♣ tr ♥ t♥st♦r ♦r ① ❱G t s♥stt② ♦ t t♦ rt♦♥ ♥ s ts♦♣ ♦ t ♥r ♣rt ♦ t ∆❱th s ♦s r ♥ s♦ r ② sr ♦rr♦ ♠♥t ② r②♥ t ♦① t♥ss ② ♥♥ t ♦① t♥ss r♦♠ µ♠ t♦ µ♠ s♥stt② ♥rs ♦ ♠♦r t♥ t♦r s ♥ ♦♥ ♦r s①♣♦s t ❱G ❱ ❬♦ ❪ r♦r ①♣♦s♥ t♦ rt♦♥ st♥ ♦① tox ∼ µ♠ t s ♣♦ss t♦ ♦r t ♥r rs♣♦♥s♦s r♥s ♣ t♦ s♦♠ ② t s♥stts ♥ t ♦rr ♦ ♠❱② ❬r❪

♥ t ♥s ♠♦ ③r♦ s ♠♦ t ♥r r♦♥ ♥② ①t♥s ♦r r② ♥rr♦ ♦s r♥ ❬❪ ♥ ts s t ①♣t rs♣♦♥s ♦ t ♦t st∆❱th s ttr r♣rs♥t ② ♣♦r

∆Vth = a × Db

t ♦s♠trs

r ♥ r ①♣r♠♥t ♣r♠trs ❯s② t s ♥♦t ♣♦ss t♦ ♥ s ♦r ♥ r tr♦♦t r ♦s r♥ ♥ s ss ♣rs ♦ ♥ r ♥ ♦r r♥t ♦s r♥s ♦r s♠ ♦ss s s② ♦s t♦ ♦♥ ♦r ♦ss ♠ s♠r s r ♦♥ Pr♠tr ♥ t ♦♥t♥s sr ♦♥st♥t ♣r♠trs s s ♦① t♥ss ♥♠r ♥ r♦ssst♦♥ ♦ ♦tr♣s ♥t t ♦① s r② s♦♥ ♥ q ②♣ s♥stts ♥ t ♦rr ♦ ♠❱② ♥ ♦t♥ t ♥s t ♦①s ♦ s♦♠ µ♠ t♥ss

♥♦tr ♣♦sst② t♦ ♠♣r♦ t ♦s♠tr rs♣♦♥s s rr♥t② ♥r sts ♥ t ♦♥sst ♥ s♥ sr tr♥sst♦rs ♥ srs ♦♥rt♦♥ ❬♦♥ ♦♥ ♦♥ ♦♥ r❪ t s ♥ s♦♥ tt st♥ ♥ tr♥sst♦rs t s♦r ♦ t ♥ ♦♥♥t t♦ t r♥ ♦ t ♥ ♥ s♦ ♦♥t ♦t♥ rt♦♥ rs♣♦♥s s ♠♦r t♥ ♥ t♠s t ♦♥ ♦ t s♥ ♦r st ♦ tr♥sst♦rs ♥ ❱G ❱ s♥stts ♦ ♠❱② ♥ r

♥♥ ♦ rt♦♥ t②♣ ♥ ♥r②

r r sr ②s ♥ t rs♣♦♥s ♦ t s ♥ s♥st t♦ trt♦♥ t②♣ ♥ ♥r②

• ♥tr♥ ♦s ♥♥♠♥t s ♣♥♦♠♥♦♥ s t♦ t ♣rs♥ ♦ ❩♠trs ♥ t ♠t③t♦♥ ♦ t t ♥ t sstrt ♥ ♥ ♦tr ♣rt ♦t ❬r❪ s t rss s t ♥st♦r t♥ss ♥rss ♥t s ♥ ♦♥ t♦ t st♥r rs♣♦♥s ② ss t♥ ♦r♦♥r② ❱ ❳r②s ❬r❪

• ♦♠♥t♦♥ ♦ tr♦♥♦ ♣rs t♥ t ♦① ②r s ♦♥trt♦♥r♥ t trs♦ ♦t st ♦ t s ♦r ♥ ♥r② ♣♦st♦♥ ♦s s ①♣t t♦ s♥♥t ♠♥② ♥ t s ♦ ♥s ♦s♠trs t t ♦① ①♣♦s t♦ rt♦♥ ♥ ♥r ♥r② r♥sr ❬ P❪

♥ ③r♦ s ♠♦ t tr r♦ss t ♦① ②r s ♦♥② t♦ t♦r♥t♦♥ ♣♦t♥t ♥ ts ♥t♥st② rss t ♥rs♥ ♦① t♥ss ❬❪ tr♦♥♦ ♣rs ♣r♦ ② ② ♦♥③♥ rt♦♥s α♣r♦t♦♥s ♥ ♥② ♥ ♦ ♥♠♠ ♦♥③♥ Prt P ♥ ♥♦t s♥t②s♣rt ② t ①st♥ tr r② s♣ t♦ r♦♠♥t♦♥ ❬❪ s rsts t ♥♠r ♦ ♦s ♦r tr♣♣♥ s r s ♥ tr♥ t rs♣♦♥s

• ①tr♥ ♦s ♥♥♠♥t s ♣♥♦♠♥♦♥ s t♦ sttr tr♦♥s ♣r♦ ② t ♥trt♦♥ ♦ t rt♦♥ t ❩ ♠trs ♦ t♥st♥♥ ♦r tt ♠② ♣rt ♦ t ♦♠♣♦st♦♥ ♦ t ♦s♠tr ♥♣st♦♥♣♥ ❬♦s❪ ♥ ♥tr♦♥ ♥r♦♥♠♥t s♦ t ♣rs♥ ♦ ♦❩

♥r ♥r② r♥sr s q t♦ t ♥r② r ♣rt ♦ss t st♥ r♦♠ ts ♣t ♥ ♣♥trt♥ t ♠ttr s s② ♥t ♥ ❱µ♠ ♥ s tr♠ ♦♠♠♦♥②♠♣♦② ♥ rt♦♥ ♦♦② ♥ ♥r ♣②ss ♦r t s♠ q♥tt② t tr♠ t♦♣♣♥ P♦r s♥st ♠♦st ♦t♥ s

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

P♦②t②♥ ♥ s♠r ♣♦②♠rs ♠trs ♥ rt t♦ t ♣r♦t♦♥ ♦ ♣r♦t♦♥ r♦s ♦s ♥♥♠♥t t♦rs r♦♠ ♥tr♦♥s t♦ ♦t ♦♥r② ♣♦t♦♥s ♥ rstr ❬r♦ ❪ r♦r t ♣♥ rqr ♦r s ♣♥ ♣♦♥ ♣♣t♦♥ ♦r t ♦s♠trs ♥t♥

tr♦♥s ♥ s♦ ♥trt rt② t t ♦① ②r ♦ t s ♥r②♣♦st♦♥ ② ♥tr♦♥s ♥ s♦♥ ♦① ♥ t ♥ ♦♠♣r t t ♦♥♣♦s ② ♦♥③t♦♥ r♦♠ r ♣rts ♥ ♠♠r②s t ♥rs ♦r t♥♦t ❱ ♥tr♦♥s tr♥sr ♦♥② ♥ q♥tt② ♦ ♥r② t♦ s♦♥r② ♣rts t rs♣t t♦ ♣♦t♦♥s ♥ r ♣rts s s s♦♥ ♥ rt ♥r② rs ♥ 2 ♥ tr♠s ♦ ❬♣②×cm2❪ s ♣♦tt rss t♣rts ♥r② ♥tr♦♥ r s sr ♦rr ♦ ♠♥t ♦ t ♦trs tr ♥rs > ❱ t r♥ t♥ ♥tr♦♥s ♥ ♠♠r② s rt♦ ♦t ♦♥ ♦rr ♦ ♠♥t s ♦ t ♦♥trt♦♥ ♦ t ♥r② ♣♦st♦♥r♦♠ ♥r rt♦♥ r♠♥ts s♠ ♣♣♥ t♥ ♥tr♦♥ ♥ ♣r♦t♦♥s t♦r r ♥r② s & ❱

♥ ♥tr♦♥s tr♥sr tr ♥r② t♦ r s♦♥rs t ♥r② ♣♦st♦♥♥ 2 ♦♥③t♦♥ ♣r♦sss ts ♣ ♦r t ♣r♦ s♦♥rs s② ♦♥③t♦♥ ♥sts ♥ r ♠♦st ② rs♣♦♥s ♦ ♥♥ r♦♠♥t♦♥ ts s♥ ♠sr ♣♦♥ ♥tr♦♥ rrt♦♥ ♦ s rst tsr t rs♣t t♦ t ♦♥ ♠sr tr ①♣♦sr t♦ rt ♦♥③♥ ♣rts ♦r♠♠r②s ♦r ts rs♦♥s s ♦s♠trs r ♥t♥ t♦ s ♥♦ts♥stt♦ ♥tr♦♥s ♦r tr ♣♣t♦♥ t t st② ♦t t♦ t rs♣♦♥s ♦ s t♦ ♥s ♦ st ♥tr♦♥s r ♣rs♥t ♥ ♣tr

♦r t ♣r♣♦ss ♦ ts ♦r t r♦♠♥t♦♥ ♥ t ①tr♥ ♦s ♥♥♠♥t♣♥♦♠♥ st ♦ ♥ r♦♥③ s ♠♥ sss s s t♦ t ♦♠♣♦st♦♥ ♦ t rt♦♥ t t sr ♥ ♣tr ♥r② ♠①rt♦♥ t ♦♠♥♥t ♥tr♦♥ ♦♠♣♦♥♥t ♥ s♦♠ ♦t♦♥s

r♦r t r♦♠♥t♦♥ t♥ t 2 ②r s ♥ t♥ ♥t♦ ♦♥t ♥t st♦♥ ♦ t s♥s♦rs t t ①♣r♠♥ts t ①tr♥ ♦s♥♥♠♥t ♣♥♦♠♥ ♥ ♦♥sr r♥ t sts ♦ st s♥s♦r♣♥ s t♦ ss ② sss ♥ t ♦♦♥ ♣tr ♥♣tr

♥stt② ts ♥ ♠t♥ t♦rs ♥ t ♦s ♠sr♠♥t

♠♥ ts ♠t♥ t ♠sr♠♥t r② ♥ t ♦st ♠sr ♦st s ♥ ♥t ♥ t ♥♥♥ ♦ t tr♣♣ r t ♣ ♦ ♥tr stts t rt♠ ♥stt② t t♠♣rtr ♣♥♥ ♥ ttr♦♥ ♥♦s

• ♥♥♥ ♦ t tr♣♣ r s ♣♥♦♠♥♦♥ ♦♠♣r♦♠s♥ t ♦♥tr♠ stt② s t♦ t ♥tr③t♦♥ ♦ t r ♥ t 2 ②r♥♥t♦♥ ♦ t tr♣♣ ♦s ② rt tr♦♥ t♥♥♥ r♦♠ t ♥r②s♦♥ ②r ♥t♦ t ♥st♦r ❬♦❪

t ♦s♠trs

r ♦♥③♥ ♥ s♦♥ ♦① t ♦r ♥tr♦♥ ♣r♦t♦♥s ♥♠♠r②s ♥tr♦♥ ♥ ♠♠r② t r r♦♠ ❬❪ ♥ ❬❪ rs♣t② ♣r♦t♦♥ t ♥ t ② ♠♥s ♦ t s♦tr ❬❪ ss♠♥t ♦♠♣♦st♦♥ ♦ t 2 t♦ w ♦①②♥ ♥ w s♦♥ s ♥st② st ♦♥ r♣♦rt ♥

s ♠♥s♠ tt s s② s ♥ t ♣♦strrt♦♥ ♦r t♦ rt♦♥ ♦ ∆❱th ♥ ♥t♦♥ ♦ t t♠ ♦rs t ♥♥♥ s♦♦rs r♥ rrt♦♥ ♥ t ♥ ♥tr♦ s♦♠ ♠tt♦♥s ♥ t t③t♦♥♦ t s s t r② ♦ ♦srts

♥♥♥ s ♣♥♥t ♦♥ t t s r♥ ♥ tr rrt♦♥ ❬❪ ♥♣r♦ss♥ ♦♥t♦♥s ♦ t ♦① ❬ ❪ ♥ t ♦① t♥ss ♥♥♥rs rst② s tox ♥rss ♥ ♥ t t♠♣rtr ❬❪ t♠♣rtr ts ♦♥ t ♥♥♥ ♦r rs ♥ ♥ ♥rs tr♠ ♠ss♦♥ ♦♦s r♦♠ t tr♣♥trs t 2 ♥ ♥ ♥ t♦ ♥ ♥♥ ♥♥♥ t t♠♣rtr s ttr ♣♥♦♠♥♦♥ ♥ ♦♥sr s rtr♠tt♦♥ ♥ t s ♦ s t r t♠♣rtrs

• ♥tr stts ♣ s ①♣♥ ♥ t♦♥ ♥tr stts ♦♥t♥t♦ ♦r♠ t t 2 ♥tr tr rrt♦♥ ♣r♦♥ ♥ ♥rs ♥t trs♦ ♦t st ∆❱th ❬ ❪ ♣♥♥ ♦♥ ts rt ♠♥t t ♥tr ♣ ♥ tr♦r ♦sr tr rrt♦♥ tr t♦r♠t♦♥ ♦ ♥tr stt s s♥♥t s ♣♦strrt♦♥ trs♦ ♦tr♦t s s♦♠t♠s rrr t♦ s rrs ♥♥♥

• t♠ ♥stt② trs♦ ♦t ♦ s ♠② rt tt♠ t♦ rrr♥♠♥t ♦ rs ♦r♠ r♥ ♣r♦ss♥ ♦r rrt♦♥s ♠♥s♠ s♦ rt♣ ❬♠ ♦❪ s ♥ ①♣♥ ②s♦♠ t♦rs t t ①st♥ ♦ s♦ ♥tr stts ♦rr sttsbt

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♥ t ♦① ②r r② ♥r t 2 ♥tr ❬ ❪ rstr♣♣ ♥ ts stts r r② s♥st t♦ ♥s ♥ t t ♣♦t♥t ♣r♦ tr♥s♥t s♣ ♦ r tt ♥ tr♥ ♣r♦ rt ♣ t t ♥st♥ttt t s ss ② t r♦t s②st♠ ♦♥

rt♣ rss t t♠ tr tr♥♥ t ♦♥ s ♦rrstts strt s ♦rt♠ ♥t♦♥ ♦ t♠ ♥t rt ♦ rt♣ ss② ss t♥ ♠❱ ♣r ♦ t♠ ♠sr ♥ s♦♥s ♥ t ♥rss t♥rs♥ ♦① t♥ss ♦r♦r t rt♣ ♠♣t ♥rss str♦♥② s ♥t♦♥ ♦ rrt♦♥ t♦ t ♥rt♦♥ ♦ ♥ ♦rr stts ♦r t②♥♠s ♦ ts rt t ♥ ♦♠♠♦t ② t s♥ ♦ t r♦trt

• ♠♣rtr ♣♥♥ ∆❱th ♥s t t♠♣rtr ♥② rt♦♥♦ t trs♦ ♦t s ts t s♠ ♦ tt t♦ rrt♦♥ ♥ tt t♦ t♠♣rtr rt♦♥s t♠♣rtr s♥stt② ♦ ∆❱th ♥rss s tox

♥rss ♥ ♣♥s s♦ ♦♥ t ♦♣♥ D ♥ t s♠♦♥t♦r ②r♦r s♦ ts ts ♥ ♦♠♠♦t ② s♥ r♥t ♠sr♠♥t♣r♦rs tt sr ♥ t ♥ t ♦♦♥ t♦♥

• tr♦♥ ♥♦s ♦♠ t♦rs ❬r❪ ♥t② t s♥t♦♥♦s rt♦ s ♠t♥ t♦r t♦ t ♠♥♠♠ ♠sr ♦s s ss s r♥t s♣②♦r r② s♥stt② s t♦s t♦ r ts ♥♦s r ♦r①♠♣ t♦ ♥rs t t r ♥ t ♦ ♦ t ♦① ②r

t♠♣rtr ♣♥♥

r r tr ♠♦r ②s t♦ r t t ♦ t♠♣rtr ♦♥ t trs♦♦t ❬r❪

rst ♦♥ ♥♦s stt♥ t r♥ rr♥t t t ♣♦♥t r ♠♥♠♠ t ♦t♠♣rtr tt♦♥s s ①♣t t ♠♣rtr ♦♥t Tc = ∂V/∂T s❩r♦ s ♣♦♥t s t ❩ ♦r ♣♦♥t ❬ ❱t ♠❪ ♠t♦ rs ♦♥ t ♠t ♥t♦♥ ♦ t t♠♣rtr rts ♦ trs♦♦t ♥ ♦ ♥♥ ♠♦t② ♦r s♣ t♠♣rtr r♥ ❬ r❪

s♦♥ ♠t♦ ss r♥t ♠sr♠♥t ♦ t♦ s s♠t♥♦s② ❬ ♦❪ ♦s♠tr ♦♥ssts ♦ t♦ ♥t s ♦♥ t s♠♣ ♦♣rt♥ t t♦ r♥t ♣♦st t ss ❬♦❪ s♦ tt t ♠sr r♥ t♥ t trs♦ ♦ts ♦ t t♦ s♥s♦rs s r♣rs♥tt ♦t s♦r ♦s ♥ t ♠♥t ♦ ts r♥ ♣r ♥t ♦s s ♦♥st♥t ♥♥♣♥♥t r♦♠ t♠♣rtr rt♦♥s

tr ② ♥♦s ssss♠♥t ♥ strt♦♥ ♦ t rt ♦♥trt♦♥ ♦t♠♣rtr tt♦♥s t♦ t qr t ❬❪ s s ♥ ♦♥ tr ②tt♥ t t♠♣rtr ♦♥t ♥ strt♥ t t♠♣rtr tt♦♥s ♦r ②♠♦♥ t t♠♣rtr ♣♥♥ s ♦♥ ♣r♠trs ♦t♥ r♦♠ ♦rt♦r②①♣r♠♥ts

t ♦s♠trs

rsstt② ♦rr s ♣♥ ♦s

♦rr s ♦♣rt♦♥ ♦ ♣♥ ♦s

♣♥ ♦ s ♣♥ ♥t♦♥ t ♦♣♥ ♣r♦ t♦r s♦ tt ♥ ♥tr♥s ②rt r♦♥ ♦r s s s♥ t♥ ♣ ②r ♥ ♥ ♥ ②r s s♦♥ ♥ ♥ ♣rt ♦r t r♦♥ s ♣♣r♦①♠t ② tr rsstt②♣ ②r ♦r rsstt② ♥ ②r s ♦ ♦ ♦♣♥ ♥ t ♥tr♥s r♦♥ ♠♦st♦ t ♣♦t♥t r♦♣ r♦ss ts r♦♥ ❬③❪

♣♥ ♦ s ♣♣t♦♥s ♥ ♠r♦ tr♥s♠ss♦♥ s ♦ ts ♦♥st♥t ♣t♦♥ ②r ♣t♥ ♥ t ♣♦sst② t♦ ♥ ♣♦rs ♦r♦r♣♥ ♦s ♥ s s r tt♥t♦r ② ♦♥tr♦♥ t rsst♥ ttrs ♣♣r♦①♠t② ♥r② t t ♦rr rr♥t ❬③❪

❲♥ ♣♥ ♦ ♦ st ❲ s s ♥ ♦rr ♦♥t♦♥s ♦s r ♥t r♦♠ t ♣+ ♦♥tt ♥ tr♦♥s r ♥t r♦♠ t ♥+♦♥tt ♥ ts♦♥t♦♥s t t♦t ♦t r♦♣ r♦ss t ♦ s t s♠ ♦ t ♦t r♦♣s r♦ss♦t t t♦ ♥t♦♥s t♦t ♥t♦♥ ♦t ❱Fj ♥ t s ❱Fb

VF = VFj + VFb

♥ ♦ ♥t♦♥ ♦♥t♦♥s ♦ rr♥t ♥sts t rrrs ♥st② ♣♥s♥r② ♦♥ t rr♥t ♥st② ♥ t s r♦r t ♦♥tt② ♥rss ♣r♦♣♦rt♦♥② t♦ t rr♥t ♦t r♦ss t s ❱Fb s ts ♥♣♥♥t ♦♥ ts rr♥t ♥ ♣♥s ♦♥② ♦♥ t ❲ rt♦ ♥ ♦♥ t ♠♦t② rt♦ µn/µp

√D · τ s t s♦♥ ♥t r s t s♦♥ ♦♥t ♥ τ t t♠

♦ ♦t r rrrs µn ♥ µp r t ♠♦t② ♦ tr♦♥s ♥ ♦s ♥ s♦♥rs♣t② ❱Fj ♥r ts ♦♥t♦♥s s t s ♥t♦♥ ♦ qt♦♥ ♥ trr♥t ♦ s ♠♥② t♦ tr♦♥♦ r♦♠♥t♦♥ ♣r♦sss

JFj ∝ eqVFj

2κT

r q s t tr♦♥ r κ t ♦t③♠♥♥s ♦♥st♥t ♥ s t t♠♣rtr♥ ♥t♦♥ ♦♥t♦♥s t rrrs ♥st② ♦♥ t s s ♣♥♥t ♦♥ t

sqr ♦ t ♥♠r ♦ t ♥t rrrs ❯♥r ts r♠st♥s ❱Fb ♣♥s♦♥ t sqr r♦♦t ♦ t rr♥t ♥st② ♦♥ ♦♥ t rt♦ ❲ s s ♦♥ t ♦♣♥♥ t ♥t ♦ t ♦♥tt r♦♥ ❱Fj ♥r ts ♦♥t♦♥s s ♥♣♥♥t ♦♥ ts ♦♣♥ ♥ ♦♥ t rrr t♠ ♥ rs s

JFj ∝ eqVFj

κT

♣♥ ♦s ♦r ♥r r♦♥ rrt♦♥

t♦r② ♦ t ♣♥ ♦s rs♣♦♥s t♦ ♥tr♦♥s s ♥t② st ② rt③ ♥rst♦♥ ♥ ❬❪ rs♣♦♥s s tr♠♥ ♦r s t s ♠♥tr r♦♠ ♦ rsstt② s♦♥ ≤ Ω·♠ ♥trt♦♥ ♦ ♣rts t t

♥t rrr ♥st② ♥ ♣ ♠ ♦r t♥ t ♦♣♥ ♦♥♥trt♦♥ ♦ t ♥tr♥s r♦♥ ♥ ≈♣ ≪ ♥i

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

r ♠ ♦ ♦rr s ♣♥ ♦ st♥ ♦rrs♣♦♥s t♦ t♥tr♥s s t♥ss ❲

♦ ♥rt st ts ♥ t s♦♥ tt t s r♦♠♥t♦♥ sts tt t t ♦ r♥ t ♠♥♦rt② rrr r♦♠♥t♦♥ t♠ ♥ t ♦♥tt② ♦ t s♦♥ rst♥ ♣♥♥ ♦ t ♠♥♦rt② rrr t♠ τ ♦♥ t♣rt ♥ s ♥ ②

1

τ=

1

τ0

+ Kτ · Φ

r τ0 s t ♥t ♠♥♦rt② rrr t♠ Φ t ♣rt ♥ ♥ τ st ♠♥♦rt②rrr t♠ ♠ ♦♥st♥t ♥t♦♥ ♦ ♣rt t②♣ ♣rt ♥r②♥t s♦♥ ♠tr ♥t♦♥ ♥ t♠♣rtr ②♣ τ s s ♥ tr♥ ♦ −5−6 ♠2·s−1 ❬♣ s❪

❯♥r ♦♥t♦♥s ♦ ♦♥tr♠t ♥t♦♥ s♠ rr♥ts ♥ r t t♦ t s ❲ s s♠ ♦♠♣r t♦ t s♦♥ ♥t ♦ t r rrrs ❲rt♦ ≤ ♦ ♦t t ♦r ♣rt s♥stt② s ♥t s t ♥t♦♥♦t ❱Fj ♣r♦♠♥ts ♥ rss t rs♥ τ ♦r r ❲ rt♦♥st t ♦t s♥stt② t♦ ♣rts s ♣♦st t♦ t s ♦t ❱Fb tt♥rs t t rs♥ ♦ t s♦♥ ♥t ♦r ① rt♦ ❲ t ♦ts♥stt② t♦ ♣rt ♥ s t ② r♥tt♥ t q ♦♥t♥♥ t①♣rss♦♥s ♦ ♥t♦♥s ♥ s ♦ts ♥ ♦ ♥t♦♥ ♦♥t♦♥s t s ts♣♦ss t♦ ♥

∆VF

∆Φ∼ Kτ · τ ∼ Kτ · W 2

❯♥r ♦♥t♦♥s ♦ ♥t♦♥ r rr♥ts s♥ t t♦t ♥t♦♥ ♦t❱Fj s ♥♣♥♥t ♦ rrr t♠ ♥t ♣rt s♥stt② s ♥♦t ♦♥ t♦t ♦t r♦♣ r♦ss t ♦ s ♦♠♥t ② t ♥ ♥ ❱Fb ♥ t ♣rts♥stt② s ♣♦st ♦r s ♦ ❲ ❬♥t❪ ♥ s s r♣t♥ t ♦sr t♦♥ ♥ s ♦ ♥t♦♥ ♦♥t♦♥s ♦r ① rt♦ ❲ t♦t s♥stt② t♦ ♣rt ♥ s

∆VF

∆Φ∼ Kτ · τ 3/2 ∼ Kτ · W 3

r♦♠ t ♦ stt♠♥ts t s ♣♦ss t♦ ♦♥ tt ♦r ♦ rsstt② s♦♥♦

• ♥ ♦♥t♦♥ ♦ ♥t♦♥ ♥♣♥♥t② ♦ t ❲ rt♦ ♦ t ♦ t♣rt s♥stt② s ②s ♣♦st t♦ t rs ♦ t ♥rs♥ Φ

t ♦s♠trs

s r♦t rt rr♥t ♣s s♣

r ♣♥ s♦♥ ♦ ♦rr rr♥t r♦t

♦r t t ♦ t rr♥t t♥ t ♥t♦♥ ♦ t♦ t t♦ ♥ ♥♥ s♦♠ ♦ t ♣rt♥ ts

• ♥ ♦♥t♦♥ ♦ ♦♥tr♠t ♥t♦♥ ♥ ♦r ❲ rt♦ ♦♥ss♥s♦rs t ♣rt s♥stt② s ♥ ②s ♣♦st ♦r ♦r♥ tq τ rss q② t t ♥♥♥ ♦ t rrt♦♥ ♦♠♥ s♠♥ ♠♦st ♦♥st♥t ♦r r ♣rt ♥s ♦rr ♦t ❱F strtstr♦r t♦ r♦ t ♥rs♥ ♣rt Φ t q② rs strt♦♥ ♥ ts ♦♥t♦♥ t s ♥ ♥ ❱F s ts ♣r♦ ♦♥② ♦r ♦ Φ r♥ ♣t♦ ♦t 11 ♣rtscm2

ts ♥♦ ♦♥sr ♣♥ ♦s t s ♠♥tr r♦♠ rsstt②s♦♥ > Ω·♠ ❬♦s❪ ♥ ts s ♥ ♥ ♦♥t♦♥s ♦ ♦♥tr♠t ♥t♦♥t ♦♥♥trt♦♥ ♦ rrrs ♥ t s r♦♥ t ♥ ♥ rsstt② s ♥t♦♥ ♦ t ♣rt ♥ ♠st t♥ ♥t♦ ♦♥t ♣♥♥ ♦ ts♦♥ rsstt② ♦♥ t ♣rt ♥ ♦t♥ ② r s ♥ ②

ρ = ρ0 · eΦ/Kρ

r ρ0 s t ♥t qr♠ rsstt② ♦ s♦♥ ♦r rrt♦♥ Φ t ♣rt♥ ♥ t ♦♥t ρ ♦r♥ t♦ r s t♥ ♥ cm−2 ♦r r♥t s♦♥ ♠trs

trt♥ r♦♠ s♦♥ ♠tr t rsstt② t s s♦ ♣♦ss t♦ ①t♥ t♦ ②♥♠ r♥ ♦♠♣♥st♥ t ❱F strt♦♥ ② s♥ t ♥rs♥ rsstt② ♦ t s r♥ rrt♦♥ ♦r♥ t♦ t ♠ ♦ rst♥t rt♦♥rs♣♦♥s tr♦r ♥r ♥rs ♦ t ♦s ♦rr ♦t ♦r r♦q♥t ♣rt ♥ r♥

♦♥♥ t s r tt t s♥stt② ♦ t ♣♥ ♦s t♦ ♣rts rrt♦♥♥ ♦♥t♦♥ ♦ ♦♥tr♠t ♥t♦♥ ♥ tr♠♥ t t ♠♥tr ♦t ♦s ♥ ♥ ♥rs ♠♥ ♦s t ♥tr♥s s ♥ s♥rsstt② s♦♥ t r ♥t rrr t♠

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♣♥ ♦s r♦t ♣r♦t♦♦s ♥ ♠t♦s

r♦t ♦ t ❱F ♥ ♣♥ ♦ s ♣r♦r♠ ② ♥t♥ ♦rr rr♥ttr♦♦t t ♦♦♥ t s♠ ♣rs♥t ♥ ♥♠r ♦ t♦rs sr r♦t s②st♠s ♥ ♠t♦s ♦r ♣♥ ♦s♠tr ♦s s ♦♥ s ♠t♦

s♠ t ❬s❪ sr rr s ♦♥ ♦♥st♥t rr♥t♥rt♦r s♠♣ ♥ ♦ rt ♥ ♥ ♥♦ t♦ t ♦♥rtr t s♣② ♦♥st♥t rr♥t s♦r s st t♦ ♠ ♦t r♦ss t ♦ s ♠srs♥ s♥ ♠s ♣s ♦ ♠ r♥ t ♦rr s ♦t s ♣trt t s♠♣ ♥ ♦ rt stt② ♦ ± ♠❱ s ♦t♥ t ts rr♦r t ♦rs ♦ sr ②s

rr t ❬❪ ♥stt rr s srs ♦ tr t♦ ♠s rt♦♥ ♣ss ♦ ♠ ♦r t② ♦♥ tt ts ♠t♦ st♥ ♦ t ♦ t t ♦♥sq♥t ♥♥♥ ♦ t rt♦♥ ♥ ts② tr♦r ♦♣ rr tt ♠♣♦② s♥ ♠s rt♦♥ ♠ ♣s

tr t♦rs ❬♥t❪ ♥ rr ♣t♦♥s ♦♥t ①♣r♠♥ts ♠♦r ♠t rtr③♥ s♦♥ ♠ r♦ss st♦♥s ♠♣♦② ♦♥st♥t rr♥t ♥♦♥♣sr♦t rts t rr♥ts ♦ ♣ t♦ ♠ ♥ s ♦ s ♠

♥ ❬r❪ t s ♥ ♣r♦♥ tt t r♦t ♦ t ♦rr s ♦t t♥ r② t♥ ♠❱ ♥ s② s♥ ♣s rr♥t s♦r ♦r rsstt② ♣♥ ♦ t r② r s ❲ ∼ ♠♠ s♥ ♣s rr♥ts♦r ♥ ♣ tt♦r rt t s s♦♥ tt s ♣♦ss t r♦t ♦ t ♣♥♦s t t② ② ♦

♥ t rr♥s t ♠♥♠③t♦♥ ♦ t t♥ ♦ t ♦ s ♥ ♣rs♥ts t ♠♥ ss r♥ t r♦t ♦ ♣ ♦ t t♠♣rtr ♥rs r♥ t♦s r♦t s ♠♣♦rt♥t ♦r t♦ rs♦♥s

• ♥② ♥♥♥ s ♦

• ♥s ♥ t ♦rr s ♦t ♦ t ♦ t♦ tr♠ ts ♦♥ s♦♥♦♥tt② r ♦

♦ stt♠♥t ♥ s♦ r t s♠♣ t♦♥ ♦r rrt♦♥t t②♣ ♦t r♦♣ r♦ss t s ♦ ♣♥ ♦ t ♣♣r♦①♠t ♠♥s♦♥s♦ ×× ♠♠3 s ♥ t ♦rr ♦ ❱ ♥ t s s♣♣ t ♠s ♦rr rr♥t♣s ♦ ♠ t ♣♦r ss♣t ♥ t s ♦ t ♦ s st♠t s ❲ V × I r ❱ s t ♦t r♦♣ r♦ss t s st♦♥ ♥ s t rr♥t t♥t r ♣♦r ss♣t ♦ ♦ t ♦rr ♦ ♠❲ r♦♠ ts t ♥r②♣♦st♦♥ r♥ t r♦t ♦ t ♦ ♥ t s♥ t s♠♣ qt♦♥♦r ♠s ♣s ♥t

Q = P × t ≃ 3 × 10−5J

♦ ss♠♥ s♣ t ♣t② ♦ c = 0.7 Jg−1 −1 ♦r s♦♥ ρ = 2.33 g/cm3♥ ♠ss ♦r t ♦ ♦ ♣♣r♦①♠t② ♠ t s ♣♦ss t♦ t ♦r ♥ tt r♥ t r♦t ② t t♠♣rtr ♥rs ♦

∆T =Q

c × m= 0.015

t ♦s♠trs

♣t♥ t ♦ t♦♥ tr rrt♦♥ ss♠♥ t ♦t r♦♣ r♦sst ♥rss ♣ t♦ ❱ ♦r ♥ rrt♦♥ ♣ t♦ Φeq ①12 cm−2 t s② t♦s tt t t♠♣rtr ♥s ♦ ♥rs ♣ t♦ r♦r tt♠♣rtr ♥ t ♣♥ ♦ ♦ ♥② t♦ rs ② ♠♦r t♥ r♥t r♦t ② ♣♥ t rr♥t ♣s s ♦ s ♠s ♥ t ♦tr ♥ ♦♥ ts♠ ①rs ♦r rr♥t ♣s ♦ s t s ♣♦ss t♦ st♠t tt t t♠♣rtr♥rss ♥ t ♦ ♦ ♦t r♥ t r♦t ♦ ♥ rrt ♦

rts ♦ ♣♥ ♦s♠tr ♦s

♠♥ rs ♦ ♠rt ♦ t ♣♥ ♦s♠tr ♦s ♥ r♣♦rt r ♦s ♥t ♥ r♥t rts ② r♦s t♦rs ❬♦s r ♣Pr♦ ♦r s❪

• s♠♣ r♦t

• s♣t rs♦t♦♥

• r♥ ♦ rs♣♦♥s

• r s♥stt②

• rs♣♦♥s ♥♣♥♥t ♦ ♦r♥tt♦♥

• ♦srt ♥♣♥♥t

• s♠ rs♣♦♥s rt♦♥ t♥ t ♦ s rqr t s♥stt②♥ ♠ ♠♦r ♥♦r♠ ② ♣rrrt♦♥ t st ♥tr♦♥s t♦ ♥ ♦11 cm−2 ♦♦ ② r t♠♣rtr ♥♥♥ ♣r♦ s r♣♦rt ♥ ❬♦s❪

• s ♠② rs

• r♠♦t r♦r② s♥ rr♥t ♥♥♥ s ♣r♦♣♦s ♥ ❬♦s❪ ♥t♦r rrt s

• ♠♥s♠ ♦ rs♣♦♥s ♥t t♦ t ♠ ♥ tr♦♥ s

♣♥ ♦s t♠♣rtr ♣♥♥

t♠♣rtr ♣♥♥ ♦ ♣♥ ♦ s t rst ♦ t♦ s♣rt ♣♥♦♠♥t ♣♦st t♠♣rtr ♦♥t ♦ rsst♥ ♦ t ♥tr♥s s♦♥ ♥ t ♥tt♠♣rtr ♦♥t ♦ t ♣♥ ♥t♦♥s t♠♣rtr ♣♥♥ ♦ t ♣♥♦s s ♠♦r ♣r♦♠ s tr s ♥♦ rt ② ♦ r♥tt♥ t♥ ♥s♥ ♠♣♥ s ② ♣rt ①♣♦sr ♥ ♥ s ② t♠♣rtr ❬❪

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

♣♥ ♦s rr♥t♣s ♥②ss

❲♥ sqr rr♥t ♣s s ♥t tr♦ ♣♥ ♦ ♥ t ♦rr rt♦♥t ♦t ♥rt r♦ss t ♦ s ♥♦t s♠♣ sqr t rtr ♦♠♣①♦r♠ s tr st♥t r♦♥s s♣ ♥ t ♠♣t ♦ ♦ tsr♦♥s ♣r♦ ♥♦r♠t♦♥ rr♥ ♣r♠trs s s ts ♠♣♥♥ t ♠♥♦rt② r rrr t♠s ♥ rt rt② t♦ t ♥♥t♥tr♦♥ ♥ t②♣ ♦ ♦t♣t ♦r♠ s s♦♥ ♥

①♣♦♥♥t ♦r ♥ t ♥♥♥ s t♦ t ♦♥tt② ♠♦t♦♥♣r♦ss rsts ♥ ♦r♥ t ♦rr rsst♥ ♦ t ♣♥ ♦ s tr rrr ♥st② ♥ t s ♥rs

st② stt r♦♥ tt ♦♦s ♦rrs♣♦♥s t♦ ♦♥st♥t ♠♣♥ ts ts ♦t tt ♥s ♥ ♣r♦♣♦rt♦♥ t t ♣rt ① ♥ s ♠srs ♦ s♥ t♠ rqr t♦ r st② tt ♦t ♣♥s ♦♥t rsstt② ♦ t ♥tr♥s s♦♥ ♥ t ♦♠tr② s sts t ♦r♠t ♦♥ t ♥trr♦t♦♥ ♣s rt♦♥ ♥ t ♣♦r r t♦ t

s s♦♦♥ s t rr♥t tr♦ t s ♥trr♣t t st② stt ♦tr♦♣s t♦ ♦r q t♦ t ♦t r♦♣ r♦ss t ♥t♦♥s ♦ t s♦♣ ♦ ts ♣♦rt♦♥ ♦ t ♦r♠ s rt t♦ t t♠ ♦ t rrrrs ♥ t s♦♥ r②st ♣r♦♣rt② ♥♦♥ t♦ t ② s♦r♣t♦♥ ♦♣rt ♥ t rst♥ ♠ t♦ t tt s ♠② s s ♥ tr♥t♣♣r♦ t♦ r t t s ①tr♠② ♦ s♥stt②

s tr r sr ②s t♦ r t ♦ t t ♦rr ♦t r♦♣ r♦sst ♦ ♦r t r s♥stt② ❬❪

♣t② t♠t ♠♥s♥t ♠trs s

Pr♥♣ ♦ ♦♣rt♦♥

♣t② t♠t ♠♥s♥ ♣♥♦♠♥ rsts r♦♠ ♣r♦sss ♥♦♥t r♦♠♥t♦♥ ♦ tr♣♣ r tr rrt♦♥ r♣♣♥ ♣♥♦♠♥ ♥ sr s♠r t♦ t ♦♥s tt ♦r ♥ t ♦① ②r ♦ tr♥sst♦r s s♥ ♥ ♥ t r s tr♣♣ ts r♦♠♥t♦♥ ♠② trrst♠t ② r♥t ♠♥s ♦r ①♠♣ t ♠trs ♥ t t♦ ♦tt ♠♥s♥t s♥ s s t s ♦ t ♦s♠trs sr ♥ t♦♥ ♥♦tr st♠t♦♥ ♠t♦ s t ♦♣t ♦♥ ② s♥ t ♠tr t♥ ♣♣r♦♣rt ♥t s s t s s ♥ t s ♦ t ♠trs t♦♣r♦ t ♥r② ♥ ♦r r r♦♠♥t♦♥

♠trs r ♥♣ ♥st♦rs ♥ rt♥ ♥♠r ♦ ♥r② s ts ♥ ♥tr♦ ② ♦♣♥ t ♠tr r♥ ♣r♦ss♥ ♣♥♥♦♥ tr ♣♦st♦♥ ♥ t ♥st♦r ♥♣ ts ts ♥ t r♦ ♦ tr♣ s t② ♦s t♦ t ♦♥t♦♥ ♥ ♦r t② ♥ t s r♦♠♥t♦♥ ♥trs t②r ♦t ♥ t ♠ ♦ t ♥♣ ❬s❪

t ♦s♠trs

r ♣rt♥ ♣r♥♣ ♦ ♥ ♦s♠tr s ♠♥s♠ ♦ t ♦♣t②st♠t ♠♥s♥ r♠ s ♦r ts ♦r

♦♥③♥ rt♦♥ rts ♥ t ♠tr r ♠♦♥t ♦ tr♦♥♦ ♣rs♦s♥ ♦r tt♥t♦♥ ♦♥ t tr♦♥s t t ♦ t ♦♥③t♦♥ s t♦ ①t t♠ t♦t ♦♥t♦♥ ♥ ♦ t ♠tr s ♥t ② ♥ ♦♠ ♦ ts rtr♦♥s r ♣r♦♠♣t② r♦♠♥ s♦♠ ♦trs r♠♥ tr♣♣ ♦♥ ♦③ tstr♣ s ♦r ♦♥ t♠ ♣r♦ ♣♥♥ ♦♥ t t♠♣rtr ♥ t tt♦♥♥r② ♦ t tr♣s tt♦♥ ♥r② ♦ tr♣ s ♥ s t r♥ t♥t ♥r② ♦ t tr♣♣♥ ♥tr ♥ t ♥r② ♦ t ♦♥t♦♥ ♥

♦♣t st♠t♦♥ ♦ t ♠tr t ♣r♦♣r ♥t ♣r♦t♥ t ♥ssr② tt♦♥ ♥r② t♦ rs t tr♣♣ r ♥ r t tr♦♥s ♥ tr♣♣ ♥ ♦r ♣tr ② r♦♠♥t♦♥ ♥tr tt ♦♠s ♥st❲♥ t r♦♠♥t♦♥ ♥tr ♥② ♦♠s t♦ ts ♥♠♥t stt ssq♥t rt r♦♠♥t♦♥ ♠② ♦sr s s♦♥ ♥ ♥t②♥t ♠♦♥t ♦ ♠tt t ♠s t ♣♦ss t♦ t t ♥r② s♦r ② t♦s♠tr

r ♠s ♦ ♠trs ♥ ♥t s ♠tt♥ ♣t② t♠t♠♥s♥ ② r ② tr ♠ ♥ ♦♣t ♣r♦♣rts ♥ ♥♦t ♦ t♠r ♣♣r♦♣rt ♦r ♥ ♣♣t♦♥ ♥ ♦s♠tr② ♥tr♥s t② t♦ tr♣ rs♦r ♦♥ t♠ ♣r♦s ♥ t ♥② ♦ t ♠♥s♥ r t ♠♦r rtr♦♥ ♦rst♥ ♠trs s ♥② s str♦♥② ♣♥♥t ♦♥ t ♦♣♥ts ♥ tr♦♥♥trt♦♥ ♥♦tr ♠♣♦rt♥t rtr♦♥ t♦ ♦s ♠trs s t s♣rt♦♥♦ t st♠t♦♥ ♥ t ♠ss♦♥ s♣tr ♥ ♦r♣ ♥ t t♦ s♣tr ♠s tt s♦♠t♠s ♠♣♦ss t♦ sr♠♥t t ♠ss♦♥ r♦♠ t st♠t♦♥

rrt♦♣ ♥ ss r ♥ ♦trs ♥ ♥t ② t r♠♥ ♣②sst ♥r s ♥t ♣♦s♣♦rs ② ①t ♦t r♠♦♠♥s♥ ♥ ♣r♦♣rts Pr♠r② ♦t t♦ ♥rrs ♦♥rs♦♥t② r tr st ♥t♥s② ♦r ♣♣t♦♥s ♥ rt♦♥ ♦s♠tr② ♥ ts ♦r ♠trs s ♦♥ tr♦♥t♠ s r ♣r♦ss t t tr♦♥ ♥ t♦♥s sr ♦rt♦r② ♦ t ❯♥rst② ♦♥t♣r r♥ ♥ s s

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

r r♠ rtrst s♣tr t♠t♦♥ s♣tr♠ ♠ss♦♥ s♣tr♠

♦♥♣r r s ♦♣ t s♠ ♦♥♥trt♦♥s ♦ r♠ ♥ ♠r♠♠♣rts ♦ t ♥t♥ srs rrrts r♠ tt♦r s ♥tr♦♥ t ♠tr t♦ t ♠♥s♥t ♠ss♦♥ ♥ t s ♣rt ♦ t tr♦♠♥ts♣tr♠ ♠r♠ ♦tt♦r s ♥st s t♦ ♥ t st♠t♦♥ s♣tr♠ ♥ t ♥rr r♦♥ ♥♠ s ♠s t ♣♦ss t♦ r ♠♥♠♠ ♠sr ♦s ♥ t r♥ ♦ µ② ♥ s♦s ♥ ♦ strt♦♥tr ①♣♦sr t♦ ♦t ② ♥sr♥ ♦rrs ♦ ♠♥t ②♥♠ r♥ ❬s❪ rtrst st♠t♦♥ s♣tr♠ ♦ t r♠ s ♣♦tt ♥ ♦♣t♠♠ st♠t♦♥ ♥t r♦♥ µ♠ ♦♣t st♠t♦♥ rststs ♦♠♣t② ♥♣♥♥t ♥ s② t♦ sr♠♥t r♦♠ t ♠ss♦♥ s♣tr♠ tt♥st r♥s r♦♠ ♥♠ t♦ ♥♠ s s♦♥ ♥ ❬s s❪

sr♠♥t♦♥ t♥ t st♠t♦♥ ♥ ♠ss♦♥ s♣tr ♥ t r♦♠sr♠♥t r♥ r t t♦ ♠♥ rtrsts tt st♥s ♠trsr♦♠ t ♦trs ♦♥ t ♠rt ♦r ♦s♠tr② ♣r♣♦ss α23 t♦r♦r t s♥ ♦ r♥ tr ♥ t ♦ r ♥trt② ♦s ♥② r♦♠♥t♦♥ ♣r♦sss sr ♦r ♥ t s ♦ t ♦♥♦① s s tr ♠ t ♠tr s♥st t♦ ♥② t②♣ ♦♦♥③t♦♥ rs t♥ t t♦t ♥② ♣♥♥ ♦♥ rt♦♥ t②♣ ♥ ♥r② s♠ ♥tr♦♥ r♦ss st♦♥s ♦ t r ♦r ♥tr♦♥s ♥ r♦ ♥r② r♥ ♠s s♦t s♥stt② t♦ ♥tr♦♥s r② ♦ q♥ttt t♦♥ ♦ t ♥tr♦♥ s♥stt② ♥ tr ♥ ts ♦r ♥ ♣tr ♦ trs ♠ tr♦rt ♦♥t♣r ♦♦ ♥t ♦r t ♦s♠tr② t t ①♣r♠♥ts

♠tt♦♥s ♥ ♦s♠tr② ♥ ♥st ♦♠ t♦ ♠sr rt♦♥s t r② ♥ ts s q♥♥ ts ♦ t ♠tt ♠♥s♥ ♥ r♣♦rt ♥trtr ❬♦♦❪ r♠②st♠t ♥ ts ♥ ♥② rs♣♦♥s ♦ ♦ss ♦ tr♣♣ r tt ♥ ♥ rr♦rs ♥ t ♦s ♠sr♠♥t ♣r♦r♠ t ♠trs ❬❱❪ r tr♣♣♥ ♣r♦t② 1

τ ♦♦s ♥ rr♥s

♦ s ♥t ♥ q r ❬s−1❪ s t rq♥② t♦r κ s t ♦t③♠♥♥

t ♦s♠trs

r ②♣ s♣ ♦ ♥ s♥ s r♦r t ♣♦t♦s♥s♦r ② ♠♥s ♦ ♥♦s♦s♦♣ st♠t♦♥ s ♥ ♣r♦ t

♦♥st♥t φ ❬❱❪ s t tt♦♥ ♥r② ♦ t tr♣ ♥ s t r♦♦♠ t♠♣rtr

1

τ= A · e− φ

κ·T

q s tr♦r t t ♦ t t♠♣rtr ♦♥ t tr♣♣ r r t t♠♣rtr t ♦r t r st♦r t♠ ♦ t rs ♥ t tr♣s s t rts t ♣♦sst② t♦ rst t ♠tr ♦r ts t③t♦♥② ♠♥s ♦ tr♠ ② ♣r♠♥r② t♦♥ ♦ t ♥ ♦ t s ♠trs ♣rs♥t r ♥ ♣tr

s♥

r♣rs♥ts t t②♣ s♣ ♦ ♥ s♥ ♦ ♠tr ①♣♦s t♦ ♠② ♦s ♥ t s ♣rs♥t ♥ t ♣tr t st♠t♦♥ r ♣r♦ ② ♥ t ♠ss♦♥ ♦ st ♦♥ ♠s tr t ♥♥♥ ♦ t qst♦♥ s♥ s♦ q ♠♥s♥t ♠ss♦♥ ♦♦ ② ② ♣r♦ ♦♥ s♦♥ t♠s ② ♦ t s♥ ♥ s② ♠♦ ② ♦♥sr♥ s♠♣ rt♦♥rt qt♦♥ ♣r♦♥ ♥ ①♣♦♥♥t s♦t♦♥

t ♥♦ ♦♥sr rrt ♠tr ♥ rs ♥ tr♣♣r♥ t rrt♦♥ ♣r♦ss ♥♠r ♦ rs ♣♥s ♦♥ t ♦s s♦ tt ❯♥r ♦♥st♥t st♠t♦♥ ① t s♥ t s ♦sr ♥ ♥t♦♥♦ t t♠ t t s♣ ♦ ♥ t rs♣♦♥s ♦ t t♦ st♠t♦♥s ♦t♥ t♥ ♥♥♦s♦♥s t rs♥ t♠ ♦ t ♠♥s♥ ♥ ♦♥sr s♥ t s t♥ rs♦♥ t♦ ss♠ tt t ♣ ♦ t s♥ s ♦t♥♦r t ② ♦ t s♥ s t♥ ♠♦ t ♥ ①♣♦♥♥t

S(t) = K · N(D) · F · e−σ·F ·t

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

r s ♦♥st♥t tt ♣♥s ♦♥ ♦t t ♠tr ♥ t r♦t ♠t♦ σ st r♦ss st♦♥ ♦ t st♠t tr♣♣♥ ♣r♦ss t♠ ♦♥st♥t ♦ t ②s t♥ ♣r② ♣♥♥t ♦♥ t st♠t♦♥ ① ♥t♥st② s t s t♥ ♥ ②

τ =1

σ · F

r♦♠ q s t♥ st ♣♦ss t♦ s tt t t t ♣ ♦ t s♥s ♥ ②

Speak = K · N(D) · F

♥ s rt② ♣r♦♣♦rt♦♥ t♦ t ♦s s ♦♥ s t st♠t♦♥ ① r♠♥s♦♥st♥t ② ♥trt♥ q t s ♥② ♣♦ss t♦ t t ①♣rss♦♥ ♦r t♥trt s♥

Sintegrated =

∫

∞

0

S(t) · dt =K

σ· N(D)

♥ ② q s ♥♦ ♦♥r ♣♥♥t ♦♥ t st♠t♦♥ ① t♦♥② ♣r♦♣♦rt♦♥ t♦ t t♦t ♠♦♥t ♦ r tr♣♣ t♥ t ♠tr s ♦♥sq♥ t ♦s s♦r ② t ♥ ♠sr r♦♠ ♦t t ♣ ♦ t s♥ ♥ t ♥trt ♠♥s♥ ♥ t ♦♥ ♥ t ♠sr♠♥t♦ t ♣ s ♣rt s t ♦♥② rqrs t qst♦♥ ♦ s♥ ♥st ♦ ♦ r ♥ t ♦tr ♥ t ♣ ♣♥s ♦♥ t ♥t♥st② ♦t st♠t♦♥ ❬❱ s❪ ♦♥st♥t st♠t♦♥ t ♠ ts t ♠♥♦♥str♥t t♦ r♥t r ♠sr♠♥ts t ♠sr♠♥ts ♣rs♥t ♥ ts♦r r ts ♦t♥ ② ♠sr♥ t ♣ ♦ t ♠♥s♥t s♥

♦s♠tr② s②st♠s s ♦♥

trs ♦ t ♠trs sr ♥ t ♣r♥ st♦♥s ♥ ①♣♦t♥ ♠♥② ♣♣t♦♥ tt ♦s r♦♠ t r♦r♣② ♠♥str ♣♣t♦♥sr t s s② s♣ ♥ ♦r♠ ♦ ♣ss ♦s♠tr ♠s t♦ t ♦♣♠♥t♦ ♦♥♥ ♥ rt♠ ♦s♠tr② s②st♠s s♣ ♥ ♥r ♣♣t♦♥s r♦rr♥t st♠t♦♥ s♦rs ♥ ♣♦t♦tt♦rs ♥ s ♥ ♥t♦♥ ♦ ts♥stt② ♥ ②♥♠ r♥ rqr t s♣ ♥ t ♣♦r ♦♥str♥ts t

♥ ts st♦♥ ♦♥② t ♣♣t♦♥ ♣r♥♣s ♦ rt ♥trst ♦r ts ♦r sr ♠♦r ①st st ♦ ♣♣t♦♥ ♥ ♦♥ ♥ ❬s PP♦ ❱ r❪ ♥ rr♥s tr♥

• ♦s rt♦r♣② t ♠s ♠s s ♦r ♦s ♠♣♣♥ r µ♠t ②r ♦ ♠tr ssr♥ ♣r♥t ♦♥ ♣t♦♥ ♦ s t ♦♥ s♦♥ ♥ ② ①♣♦s♥ s ♠s t♦ ♣rt ♠ t rs t tr♣♣♦♥ ts sr ♣r♦♣♦rt♦♥② t♦ t ♠ ♣rt ♥t♥st② ❬s P❪ tr♠ ①♣♦sr t rrt ♦ ♥ r♦t s♥ s♦stt sr ♠♦ ♦t µ♠ ♥t ♦s ♦♥ t ♥ ② ♣♦st♦♥♥ t ♠ ♦♥ ❳❨ st ❬P♦❪ sr ♠ s t♥ st♣♣ ♦r t ♦ ♥ t t♦ ①s♥ t ♠tt ♠♥s♥t s♥ s ♦t ② ♠♥s ♦ ♣♦t♦♠t♣rt s♥ s ♥② t③ ♥ r♦r t♦ t ♠♣ ♦ t ♠tt

t ♦s♠trs

r ♦s♠tr② s②st♠s s ♦♥ ♠s ♦r ♦s ♠♣s ♥s♦r ♦r s♣♣♣t♦♥s

♠♥s♥ rss ❳ ♥ ❨①s tt r♣rs♥ts t s♣t ♦s strt♦♥tr r♥ t ♠tr ♥ ♦♠♣t② rst ② ♦rs ♥♥♥ t ♠s r s ♥ ts ♦r t♦ rtr③ t ♣r♦t♦♥ ♠ ♦t t② t s r s♣t rs♦t♦♥ s str♦♥②♣♥♥t ♦♥ t ♠♥s♦♥ ♦ t sr s♣♦t s ♦r t r♦t ♥ ♦♥ t ♠r♥rt② ❲t t tst ♥ t t ❯♥rst② ♦♥t♣r t s♣♦ss t♦ ♦t♥ ♠♣s ♦ t ♣r♦t♦♥ ♠ t µ♠ rs♦t♦♥

• ♥trt s♥s♦r ♦r s♣ ♣♣t♦♥s s s♥s♦r s s♥♥ ② tt t♥ ②r s rt② s♥ t♥ t ♥ s ♣♦t♦♦ ❲t ts ♣r♥♣ t s ♣♦ss t♦ rt♦♥ s♥s♦rs♦r P♠♦♥t t ♦♥ s♦♥ ♥ t s③ tt ts ♥ sr ♦♠ ♣♦r ♦♥s♠♣t♦♥ ♦ s s♥s♦r s ♠t t♦ t rr♥t♥ t♦ s t r♥ st♠t♦♥ s ①tr♥ rtr② ♥t♦ ♦♣rt t s♥s♦r ♦♥ssts ♦♥② ♦ ♥ ♦♣rt♦♥ ♠♣r tt ♦♥rts trr♥t r ② t ♣♦t♦♦ ♥t♦ ♦t s♥ s t♥ ♠♣ ♥t③ ♦t s♦r trr ② ♦ ♥♣t s s♦ ♥ t♦ ♦♣rtt st♠t♦♥ s♦r ❬❱ ❱❪

s♥s♦r ♦♣ t t ❯♥rst② ♦♥t♣r ♥s s♦ rt♦♥r♥♥ s♦t♦♥ tt ♦♥sst t♦t ♦♦♣ t♦ ♥rss ♦ t ♦rr ♦t rr♥t ♥ t t ♥rs♥ ♣rt ♥ s s t♦ ♦♥ s♥ t t ♠ss♦♥ rs ♦r t♠ t♦ s♣♠♥t♠ ♥rr ♠ss♦♥ s ♣t ♦♥st♥t ② ♠sr♥ t s♥ s♦♥♣♦t♦♦ st ♥st ♥ ♣r t♦ t ♦♥ s ♦r t r♦t

♦ r ts ♥s♦r s ♦♥ ♦♥ t ♥tr♥t♦♥ ♣ tt♦♥ s ♣rt ♦t P ♠♦ s♥ ② t ♥ t s ♥ ♥trt ♥ srstt ①♣r♠♥ts ♥ ♥ ♦ts ♦r ts s♥s♦r t t t ♦ t♦ ♣r♦ ts t③t♦♥ ♥ tP ①♣r♠♥ts t

• ♠♦t ♥♥ ♦s♠tr② s♥ ♦♣t rs ♥ t s ♦ t ♥trts♥s♦r ♦t t ♥ t tr♦♥s ♦r t r♦t r ①♣♦s t♦ rt♦♥

r ♦ ♦s♠trs ♥ rt♦♥ ♠♦♥t♦r♥ s

Pr♦♣rt② 2 r

t♦♠ ♥♠r ❩❩eff t♦♠♦r t ♥st② ❬ ♠−3❪ t♦♠s ❬×1022 ♠−3❪ r②st strtr ♠♦♥ r♦s tt ♦♥st♥t ❬❪ t♥ ♣♦♥t ❬❪ > r♠ ①♣♥s♦♥ ♦♥t ❬10−6K−1❪ r♠ ♦♥tt② ❬Wm−1K−1❪

tr ♦♥st♥t ǫ ♥ ♣ ❬❱❪ ♥r② t♦ rt ♣r ❬❱❪ t♦♥ ♥t ❬♠❪ r ♠♥♠♠ ♦♥③♥♥r② ♦ss ❬❱ −1♠2❪

tr♦♥ ♠♦t② ❬cm2V −1s−1❪ ♦ ♠♦t② ❬cm2V −1s−1❪ 1×108 ♥tr♥s rrr ♥st② ni [cm−3] 1.5×1010 ♥tr♥s rsstt② ❬Ω · cm❪ 2.3×105 > 1016

s ♣r♦♣rts ♦ ♦♥ ♦♥ ♦① ♥ tr♦♥t♠ t r♦♦♠ t♠♣rtr ❬③ r♦ ♦ s ❪

t ♣r♦♠ ♦ t rt♦♥ ♥ ♠ s s♣♣♦s② ♥ rss ts ♥♦t ②s ♣♦ss ♦r ♣rt t♦ s s♥s♦r ♥trt♥ ♦t t ♥t r♥ rtr② rs♦♥ ♥ tr s ♦ r② rs rt♥r♦♥♠♥t ♦r t ♥sst② t♦ ♠♥♠③ t s③ ♦ t s♥s♦r ♥ s♦♠ sst s ♦ ♦♥ s ♥t t ♠sr♠♥t ♣♦♥t ♥ s♦ ♣r♦♠ ♦rtr♦♠♥t ♦♠♣tt②

♦ r t s s♥s r♦♠t♦ t ♠tr t s ♦ ♦♣t rs♥ ♣r♦ t s♦t♦♥ ♦ t ♦ ♣r♦♠s ♥ ♣♣t♦♥ ♦ s s②st♠♥ t rt♠ ♠♦♥t♦r♥ ♦ t ♦s r t♦ t♠♦r r♥ ♥♥tr ♣rt ♦ r♣② trt♠♥t s♦♥ ♣♣t♦♥ ♥ s♦ t♠sr♠♥t ♦ r② ♦ss ♥ t ♥r♦♥♠♥t ♦ t ①♣r♠♥ts sst ♣♣t♦♥ s ♥ t ♥ t r♠♦r ♦ ts tss ♥ t ♣rs♥t ♥ ♣tr

♦♥s♦♥

♦♥s♦♥

♣r♣♦s ♦ ♦s♠tr② s t♦ q♥t② t rt♦♥ ♥ t♦ ♠sr t ♣rt ♥ ♥♦r t ♥r② ♠♣rt t♦ t ①♣♦s ♠trs rt ♦s♠tr②♠sr♠♥ts r tr♦r ♠♣♦rt♥t s♣② ♥ t s ♦ t ①♣r♠♥ts♥ ♦rr t♦

• ♣r♦ r♦ss t ♣rt♦♥ ♦ t ♦♥t r♦ ♠♦s tr r②s ♠t ② t ♦♠♣① ♦♠trs tt t♦ ♠♦ t♦ sr t ♠♥ ♥ ② t ♥♦ ♦ t ♣②ss ♦ r② ♥r② ♣rt♣r♦sss

• ssss t ♦♥tr♠ rt♦♥ ♠ t t ♠ t♦ r♥t t rt② ♦t tt♦r s②st♠s ♦r t ②rs ♦ t ♦♣rt♦♥

r t②♣s ♦ Pss ♦s♠trs r ①st♥t ♥ ♥ sr ♥ t rst♣rt ♦ ts ♣tr ② r ② s s♣② ♥ t ♣r♦s ♥rt♦♥ ♦ rt♦r ♠♥s ♦r r♦t♥ ♠sr♠♥ts ♦r ts rs♦♥ ♥ ♠♣♦rt♥t♠♦♥t ♦ t rr♥ tr rt♦♥ ♥ rt♦♥ ♦ r♦s qts sr② ♥ trtr

t♦ Pss ♦s♠trs ♠♣♦② t t tr t③t♦♥ rs t♦ ♠t s ♦ t ♦ r♠♥♥♥t rt♦♥ ♥ rt♥ ♦t♦♥ ♥st ①♣r♠♥ts t r♠♦ ♥ s ♦ t ♠♣♦sst② t♦ r rt♥ ♠sr♠♥t ♣♦st♦♥s ♦ ♥trst t ss ♦r♦r t t tt tss ♥ ♦t♥ rt t♦ ♠sr t ♥r② ♣♦st♦♥ ♥ tssq♥t♠trs ♠s rt ♣♣t♦♥ ♦ t ♣r♦r♠ ♠sr♠♥t t♦ t t♦♥♦ t ♠ ♥ tr♦♥s ♥ s♠♦♥t♦r s t

t ♦s♠trs s♠♦♥t♦r s♥s♦rs ♥ ♠trs ♣r♦ s♦t♦♥t♦ t ♦ ♣r♦♠s ♦♥ t♦ ♦♦ ♥ rt♠ ♦♥♥ t ♦t♦♥ ♦ trt♦♥ rtrsts ♦ ts s♦♥ t♦r② ♦ s ♥ sr♥ ts ♥ t s♦♥ ♣rt ♦ ts ♣tr t s ♠♣♦rt♥t r t♦ ♣♦♥t ♦t tt s♦♠♦ ts t t♥♦♦s ♣r♦ ♥trt ♠sr♠♥ts ♦r t♠ s ♦ tr♣t② t♦ st♦r t ♦s♠tr ♥♦r♠t♦♥ ♥ st ② ♦♠ ♦ ts s♥s♦r ♥ ts s t t s♠ s♦♥ ♦ Pss ♦s♠tr t t ♥t tt tr♣②s ♠♥s♦♥ ♥ rr♥ t ♣♣r♦♣rt ♣s t♦ ♦♠♣r ♦s♠r t rs♣t t ♠♦rt② ♦ t sr ♣ss s

♦r ♥tr♥ ♥ t s♣ sss ♦♥r♥♥ t t ♦s♠trs t t ①♣r♠♥ts ♣rs♥t ♥ t ♣trs t ①♣r♠♥t q♣♠♥t s ♦r trtr③t♦♥ ♦ s s sr ♥ t ♥①t ♣tr ♦♠ ♦t ①♣r♠♥t ts sr tr ♥ t P ♣② ♣r r♦ ♥ ts tss ♦r s ♦ tr s♠rt② t t rt♦♥ ♥r♦♥♠♥t rtr③t♦♥ ♦ t t ♦s♠trs ♥ ts rt♦♥s t s ♣♦ss ♦♥② tr tr rt rt♦♥ ② s♥ ♥♣♥♥t ♦s♠tr♠♥s s rt♦♥ sss tr♦r sss ♥ ♣tr

♣tr

①♣r♠♥t q♣♠♥t ♦r rt♦♥

s♥s♦r sts

rrt♦♥ ts

P st rrt♦♥ ts t

♦ st② rt♦♥ ♠ ♥ s♠♦♥t♦rs ♥ tr♦♥ s t ❬♦❪s♥ tr rrt♦♥ ts r ♦♣rt ♥ t st ①♣r♠♥t r ♦t Pr♦t♦♥②♥r♦tr♦♥ P rt♦r ❬ ❪ t② ♥♠ ♦t ♥ t P ♠♥ ♦s rrt♦♥ ①♣r♠♥ts t t ❱ ❱ ♣r♠r② ♣r♦t♦♥ ♠ ♥ t s♠ ♠♥ t t② ♦♥st t♦ rr② ♦t rrt♦♥s ♥ ♠① ♥tr♦♥r ♣rtsγr② t② ♦t t t ♥ ♦ t P ♠ ♥ ♦s ♥② rrt♦♥①♣r♠♥ts ♥ ♠① ♥tr♦♥γr② ♥r♦♥♠♥t ♣r♦ ♥ t② ♦r ♠st♦♣♣r

♥ t ♠♥ t ♣r♠r② ❱ ♣r♦t♦♥ ♠ ♦ t P rt♦r s rtt♦ t rrt♦♥ r r t t② ♥♠ r♠♦t ♦♥tr♦ stts②st♠ s ♦t ♥ ts ③♦♥ t ♣r♦t♦♥ rsts r r r♥ t s s♣r② ♦ t P ♠♥ ♥ s♣s ♦ ♦t ♠s s♦ ①trt♦♥ t ♠①♠♠ ♠ ♥t♥st② ♦ ①11 ♣r♦t♦♥s ♣r s♣ ♦s♥s♥♥♥ s②st♠ ss t♦ s♣r ♦t t ♠ ♥ ♦rr t♦ ♣r♦ ♥ ♥♦r♠ rrt♦♥ s♣♦t ♦r sr tt ♥ r② r♦♠ t♦ ♠2 ❬❪ ♥♥ ts t♦ ♣r♠trs ♣r♦t♦♥①s r♦♠ ①11 cm−2h−1 t♦ ①13 cm−2h−1 ♥

stt ♠♦s ♦♥ r ♥s ♠t ♦♥t ♦ ♥t ♦ ♦t ♠ ♥ ♦s tr♥s♣♦rt ♦ t s♠♣s t♦ rrt rt② r♦♠ t ♦♥t♥ r♦♦♠♥t♦ t rrt♦♥ r ♦♥t s ♥srt ♥t♦ rt♦♥ s♥ ♦♥sttt♦ ♦♥rt ♦s s s♦♥ ♥ ♥ t rrt♦♥ ♦t♦♥ t♦ rs t

r ♦ rt♦♥ ♦ r ♣rt s ♦t♥ ①♣rss s♦ s ts ♠♦♠♥t♠ ♥ t ♥t ♥r② ❬❱❪ ♦ ♣rt ♦ rst ♠ss ❬❱❪ ♥ ♠♦♠♥t♠ P ❬❱❪ t s ttE =

√P 2 + M2 − M ♥ t s ♦ ♣r♦t♦♥s ❱ ❬❪

rrt♦♥ ts

r P st rrt♦♥ ts ②♦t ♦ t t② ②♦t ♦ t t②

♥tr♦♥ sttr♥ t♦ ♣r♥t ♠r s♦rr ♦ ♠ s ♥ ♥srtt♥ t stt ♣♦st♦♥ ♥ t ♦♦♥ r♦♥ ♠ st♦♣♣r ♠♥s♥t sr♥t ♠r s s t♦ s♣② t ♠ s♣♦t ♥ ♦♥r② ♠ss♦♥ ♠r ❬r❪ ♣r♦s ♠sr♠♥t ♦ t t♦t ♠ ♥t♥st② r♥ rrt♦♥s

rt♦♥ ♥r♦♥♠♥t ♥rt ♥ t r r♦♥ t rrt♦♥ ♣♦st♦♥ ② t ♥trt♦♥ ♦ t ❱ ♣r♦t♦♥ ♠ t t ♠ st♦♣♣r s s♦ ♦t♥s t♦ ♣r♦r♠ rrt♦♥ tsts ♥ ts r ♥♠ s ♦rt ♠① ♣rt s t♥ s♠♣s t♦ rrt tr r st ♥♣♦st♦♥s ♥t ② ♠♥s ♦ t♦ ♦♦r♥ts t st♥ r♦♠ t ♠st♦♣♣r♠sr ♦♥ t ♣r♦t♦♥ ♠ ❩ ♥ t r st♥ r♦♠ t ♠ ①sr

r ♦♥t r♦ s♠t♦♥s ♥ ♣r♦r♠ ❬r❪ t♦ tr♠♥ t s♣tr ♦♠♣♦st♦♥ ♦ ts ♥r♦♥♠♥t ♥ ts ♥t♥st② ② ♥ t ②♠♥s ♦ tt♦♥ ♦ ♠sr♠♥ts ❬❪ s♦s t ♣rt s♣trs♠t ♦r ❩ ♠ ♥ r ♠ ♥ ♥ 5 ♣r♦t♦♥s r s♥t t♦rt ♠st♦♣♣r ♥ ts ♣♦st♦♥ t ♥r♦♥♠♥t s ♦♠♥t ② sttr ♥tr♦♥s ♥ ♣♦t♦♥s ♦ ♥r② r♦♥ s♦♠ t♥s ♦ ❱ ♦r ♥rs r t♥ ❱ t ♦♥trt♦♥ ♦ r r♦♥s strt t♦ s♦ ♠♣♦rt♥t

♥② s♦s t r strt♦♥ ♦ t sttr ♣rts ♦r❩ ♠ ② ♣♥ t s♠♣s ♠tr ② r♦♠ t ♠ ①s ♥tr♦♥ ①s♦ ♦t 7 cm−2 ♣r ♣r♦t♦♥ s♣ ♥ r t ♥rs♥ st♥s r♦♠ t♠ ♠♣ r ❩ s ♥tr♦♥ ①s s ♦ s 6 cm−2 ♣r ♣r♦t♦♥ s♣ ♥ ♥st ♦t♥

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts

r t② t t P st Prt s♣tr s♠t ♦r 5

♥♦♠♥ ♣r♠r② ♣r♦t♦♥s strt♦♥ ♦ sttr ♣rts t st♥ ♦ ♠ r♦♠ t ♠r s♦rr r♦♠ ♦tt♦♠ t♦ t♦♣ ♣r♦t♦♥s ♥t ♣♦♥s ♣♦st ♣♦♥s♠♠s ♥ ♥tr♦♥s ♣♦t s rrr t♦ ♣r♠r② ♠ ♥t♥st② ♦ ×1011 ♣r♦t♦♥s

s♦s t ②♦t ♦ t rrt♦♥ ③♦♥ ♦t t t ♥ ♦ t ♠♥ rrt♦♥ s ♣r♦r♠ ♥ t② t s♦♥r② ♣rts ♣r♦② t ♣r♠r② ❱ ♣r♦t♦♥ ♠ tr r♦ss♥ trt ♦♥sttt ♦ ♠ ♦r♦♥ ♥ ♠ ♦ ❬❪

s ♦r t t② ♠♦t♦r③ stt s②st♠ ♦s tr♥s♣♦rt ♦ t s♠♣s r♦♠ t ♦♥t♥ r♦♦♠ t♦ t rrt♦♥ t② ♥ r♦ s♣tr♠ ♦♥tr♦♥s γr②s ♥ r r♦♥s s ♣r♦ s♦s t t②♣ s♣tr♠ ♦t♥ ② ♦♥t r♦ s♠t♦♥s t t ❯ ♦ ❬s❪ ♥ t tr ♠♥s♦♥ ♣rt ♣r♦ ♥s t rrt♦♥ t② s s♦♥ s♦♥r② ♣rts ♥t♥st② ♥ t t② s♦♥ ♥ s ♥♠sr ② ♠♥s ♦ tt♦♥ ♦ ♦s

❲t t r♠♦t ♦♥tr♦ stt s②st♠ t s ♣♦ss t♦ st t ♣♦st♦♥ ♦ ts♠♣s ♥ t rt ♦♦r♥t ❩ t rs♣t t♦ t ♠ ①s ♣♥♥ ♦♥ t♣♦st♦♥ ❩ t rt♦ ♦ r r♦♥s ♥ t ❱ ♥r② r♥ t♦ ♥tr♦♥s ♥ γ ♥ ♦s♥ t s ts ♣♦ss t♦ ♣r♦r♠ rrt♦♥s ♥ ♣r γ♥tr♦♥ ♥r♦♥♠♥tt ♣♦st♦♥s r r♦♠ t ♠ ①s t②♣② ❩ ♠ ♦r ♥ rr♦♥ rrt♦♥ ♥r♦♥♠♥t tt ttr r♣rs♥ts t ♦♥ ①♣t ♦r t ♥♥r tt♦rs ♦t ①♣r♠♥ts t ♣♦st♦♥s ♦s t♦ t ♠ ①s t②♣② ❩ ♠

♣r♦t♦♥ rsts r ♥ t ♠♥ t s♠ t♠strtr st♦s ♦ t ♠♥ t s tr♦r ♣♦ss t♦ r ❱ ♥tr♦♥ q♥t①s r♦♠ ①12 cm−2h−1 t♦ ①12 cm−2h−1 ♣♥♥ ♦t ♦♥ t ♥♠r ♦ s♣sr ② t P ♥ t st♥ ♦ t s♠♣ r♦♠ t ♠ ①s s ♥ t s ♦ ♣r♦s ♥② ♠sr♠♥t ♦ t ♣r♠r② ♣r♦t♦♥ ♠ ♥t♥st②tt ts t trt

rrt♦♥ ts

♣rt s♣tr t ❩ ♠ ♣rt ♣r♦ ♥ ♥t♦♥ ♦ ❩

r t② ♦♠♣♦st♦♥ t ♠ r♦♠ t ♠ ①s ♥♦r♠③ t♦ ♦♥ ♠♣♥♥ ❱ ♣r♦t♦♥ ♦♥r② ♣rt ♣r♦ ♥ t ♦ t② ♥ ♥t♦♥ ♦ ❩ ♥ ① tr♠♥ ② ♠♥s ♦ tt♦♥ ♦s t♥q

r rt♦r t

t♦r sr ♥tr t t ♦③ t♥ ♥sttt ♥ ♥ ♦♥s ♥ ①♣r♠♥t ♥r rt♦r ♦ t②♣ ❬❪ s ♥tr♦♥ s♣tr♠ ♦ ts t② tr♠♥ ② ♠sr♥ t tt♦♥ ♦ ♦s ♦r♥t ♠trs s s♦♥ ♥ ❬r❪

♥ ts t② rrt♦♥s r ♣r♦r♠ ② ♣♥ t s♠♣s ♥t♦ t rt♦r ♦rtr♦ t♦ rrt♦♥ ♥♥s t rr r♦ss st♦♥ ♦ ♠ ♠tr♥ t t ♥ ♣t r♦ss st♦♥ ♦ × ♠ tt ♦♣② r♦ ♣♦st♦♥s♥ ♥trs t rt♦r ♦r r♦♠ ♦ ♥tr♦♥ ① r t♦ t s♠♣s s♥r② ♣r♦♣♦rt♦♥ t♦ t rt♦r ♦♣rt♥ ♣♦r tt r♥s r♦♠ ❲ t♦ ❲ ♦rrs♣♦♥♥ ❱ ♥tr♦♥ q♥t ① t t ♥ ♦ t ♥♥ s ♦×109 cm−2s−1 t rt♦r ♣♦r ♦ ❲ ♥ t ♥♥ t ♥tr♦♥ ① s♦t t♦r r t rs♣t t♦ t ♦♥ ♠sr ♥ t ♥♥

♥ t r♠♦r ♦ ts tss srs ♦ rt♦♥ ♠sr♠♥ts ♦ t♦tr♠♥ tt t r② ♦ t ♥tr♦♥ ① r t♦ t s♠♣s ♥r st② sttr t♥ ± ♥ ♦t ♥ ♥♥s ♦r♦r srs ♦ ①♣r♠♥t♠sr♠♥ts ♥ rr ♦t ♥ ♦rr t♦ tr♠♥ t ss♦t t♦ s ♥tr♦♥ ①

s♦s t rt ♦srt ♣r♦ r♦r ♦♥ t rrt♦♥ ♥♥ ♥ t ①①s t st♥ s ♠sr r♦♠ t ♥tr ♦ t rt♦r ♦r ♠sr♠♥ts ♣rs♥t ♥ t ♣tr ♥ r♦r t t rt♦r ♦ ② ♠sr♥ t ♣♦t♦rr♥t ♥rt ♥s rrs s s♦♥ tt♦rs s♠ ♦ss ♦r ♠sr♠♥ts ♣rs♥t ♥ ♦ P r♦♠ t ♠♥s♦♥s♦ t ♠♣♦② ♦ t s t♥ ♣♦ss t♦ ♦♥rt t ♦ ♠♥t♦♥ rr♥t ♥t♦♦♥③♥ ♦s ♥ s♦♥ ❬♥❪ s♦♥ ♦srt ♠sr♠♥t ♣r♦r♠ t ♦s♠trs s s♦ s♦♥ ♥ ♦s ♣r♦s ♠sr t ts t♦

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts

r r rt♦r t r♦ssst♦♥ ♦ t rt♦r t② ♦r♠③ ♥tr♦♥ ① s♣tr♠ t ❲ ♥♦r♠③t♦♥ s ♥ ♦♥ ♥ ② tt∫ 20MeV100keV Φ(E)dE r Φ(E) s t ♥tr♦♥ ①

♥♣♥♥t ♠♥s s♦ t♦ ♥ r♠♥t ♦r ss t♥ ± ♥ t ①♣r♠♥t ♦♥t♦♥s ♠♥t♦♥ ♦ t ♦srt ♠sr s t r

♠♥♥t ♦♥ t♦ t tt♦♥ ♦ t rt♦r strtr s ♦♥trt♦♥ t♦ t ♣♥s ♦♥ t ♣♦r t t rt♦r s ♥ r♥ ♦r ts st♦♥ ♦r ①♠♣ tr ② ♦ r♥♥♥ t rt♦r t ❲ r♠♥♥t ♦srt ♦ ②s s♥ rstr tr r♥♥♥ t t ♠♥♠♠ rt♦r ♣♦r t ♦srt s♥ ♠sr t♦ r ♦ t♦r ♣t ♠sr♠♥ts t rt♦r ♦♥ t t ♣rs♥ ♦ ♥tr♦♥s r♦♠ t ♥r rt♦♥ s♦ ♥tr♦♥ ♦♥trt♦♥t♦ t ♦ ♦t s ♠sr♠♥ts tr♦r sst ②s t♦ rtt ♦srt ♥ t rrt♦♥ ♥♥s ♦ t rt♦r ♦r t s♠♣ rrt♦♥sstrt

st ♥tr♦♥ ♠ t ❯

♥t♥st② ♥tr♦♥ ♠ t t ②♦tr♦♥ sr ♥tr ♦ tt♦ ❯♥rst② ♦ ♦♥ ❯ ♥ ♠ s s♦♥r② ♠ s♦♥ t ♥r rt♦♥ 9♥10 ❱ ♣r♠r② tr♦♥ ♠ ♦ t ❯s♦r♦♥♦s ②♦tr♦♥ tt ts t r②♠ trt s s t♦ ♥rt ♥tr♦♥ t ♥ ♥r② s♣tr♠ r♥♥ r♦♠ ♦t t♦ ❱ ♥ ♠①♠♠ tt s t ❱ ❬❪ tr♠♥ ♣rt ♦ t ♠♥ tt ♦sts t r②♠ trt♥ t s♠♣s ♦r s s♦♥ ♥

tr♦♥ ♥s ♦ ♥s t ♥ t r♣tt♦♥ ♣r♦ ♦ ♦t ♥s r♠♥ t ♥tr♦♥ ♠ qs♦♥t♥♦s ♥ t♠ s♠♣s t♦ rrt ♥ ♣♦st♦♥ t r♥t st♥s r♦♠ t trt ♥ ♦rr t♦ t r♥t ♥tr♦♥①s t st♥ ♦ ♠ r♦♠ t trt ♦r ①♠♣ t♦t ♥tr♦♥ ① ♦×1010 cm−2s−1 ♥ ♦t♥ r t rrt♦♥ s♣♦t t ♠ ♥t♥st② rss♠♦♦t② ② ♦t ♥ tr♠s ♦ ♥ t ♦♥t♠♥t♦♥ ♦ t ♠ t

rrt♦♥ ts

r ♠♥♥t ♦srt ♣r♦ ♥ t ♥♥ ♦ t r rt♦rt ♠sr♠♥ts ♥ rr ♦t ② ♠♥s ♦ rrs s s♦♥ tt♦rs♠♣t② ♠rrs ♥ ♦s♠trs ♠rrs

♠♠ r②s r♦♠ ♥tr♦♥ ♥trt♦♥s t t ♠tr ♦ t trs srr♦♥♥ ttrt s ♥ ♠sr t♦ ❬r❪

P Pr♦t♦♥ t② t P

♣r♠r② ♣r♦t♦♥ ♠ ♦r t ♥r② Pr♦t♦♥ rrt♦♥ t② P ♦t P rrr ♥sttt P ♥ ❱♥ t③r♥ s r t♦ t tst r r♦♠t ❱ ♥rt♦r ② ♣ss♥ tr♦ st ♦ ①♥ ♦♣♣rr♣t♦s ♣r♠r② rr ♥ ♦rr t♦ r ts ♥r② ♥ ts ♥t♥st② tr t♣r♠r② rr t ♣r♦t♦♥ ♠①♠♠ ♥r② s q t♦ ❱ ♥ t ♠①♠♠rr♥t s rstrt t♦ ♦t ♥ ♥ ♦rr t♦ ♠t t r tt♦♥ ♥ t ①♣r♠♥tr

P ①♣r♠♥t st♣ ♦♥ssts ♦ ♦ ♥r② rr tt ♦s t♦ rtrst t ♣r♦t♦♥ ♥r② ♦♥ ♥t ♦t ❱ ♠ ♦♠t♦rs ♥ ♠♦♥t♦r♥ s♦♥③t♦♥ ♠r ♥ r ♠r s s♦♥ ♥ rrt♦♥s r s②rr ♦t ♥ r ♣♥ t s♠♣s ♦♥ ♠♦ ①② t tt ♠♦♥ts s♠♣s♦r ♣r♣♥r② t♦ t ♠ rt♦♥

♠①♠♠ ① r t ❱ s ♦ ×108 ♣r♦t♦♥s♠2×s ♦r♥ rrt♦♥ r ♦ ♠ ♠tr P t② s ♣rrt t r② ♥ t ①♦s tr♠♥t♦♥ ttr t♥ ♦♥t♠♥t♦♥ t♦ t♥tr♦♥ r♦♥ t t rrt♦♥ ♣♦st♦♥ s t t♦ ss t♥ −4

♥tr♦♥s♣r♦t♦♥♠2 rrt♦♥ s ♦♥tr♦ tr♦ st ♦ srs ♥ Ps t qst♦♥

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts

r rrt♦♥ ts t ❯ ♥ P st ♥tr♦♥s ♠♥ t❯ ♠ ♥r② Pr♦t♦♥ rrt♦♥ t② t P t③r♥

s②st♠ s②st♠ ♠♦♥t♦rs ♣r♦t♦♥ ① ♥ ♦s rt ts t t♦t ♣♦st♦s ♥ ♦♥tr♦s t ♣♦st♦♥ ♦ t s♠♣ s s ♠ ♦s ♣r♠trs t s♦♦s t stt♥ ♦ t ♠ ♥r② ② ♥♥ t ②♦t ♦ t P ♦ ♥r②rr ❬❪

♠♠ s♦rs

s st ♥ ts tss ♦r ♥ rrt t r♥t ♠♠s♦rs ♣♥♥ ♦♥ t ♦srt ♥s ♥ t s♦rs t② rtr rsr♣t♦♥ ♦ t t② t t P❯ t② t ♦ ② r♥♥ t ♠♠ rrt♦r ♦ t ❯♥rst② ♦♥t♣r ♦♥t♣r r♥ ♥

♠♠ rrt♦♥ t② s ♥st ♥ tst ③♦♥ ♦r♠r ❳ ♠t t P ❲st r ♥ r r ♥r② ♣rt tt♦rs r①♣♦s t♦ ♣rt ♠ ♥ t ♣rs♥ ♦ ♥ st r♦♥ ♦ ♠♠r②s s s ♦♥ t t ♠ ♦ s♠t♥ t r♦♥ ♦♥t♦♥s tt t♥stt tt♦rs sr ♥ tr ♦♣rt♥ ♥r♦♥♠♥t t t

♠♠ rrt♦r s ♦s ♥ rt♥r ♦♥t♥r ♠♠ ♥ ♠♠ s s♦♥ ♥ ♠♦r t ♥ s s♦r ♥ s♦ s ♦♣t ♣rt ♠ s sr ♦ t t ♥ s ♦♥ t♦ ♣r♦r♠ ♣r♠♠ rrt♦♥s s♦r s s♦ q♣♣ t st ♦ tt♥t♦♥ trstt ♥ st ♣ t♦ rs t ♦srt t ♠♥t s r♦t 137ss♦r ♠ts ❱ ♣♦t♦♥ ♥ ♦ t ②s t ♦ ②rs

tr t s♠♥t♥ ♦ t ❳ ♠♥ r♥ t ♦♠♥ rrt♦♥ ♠♠s♦r♣rt ♠ s ♥♦ ♦♥r ♦♣rt♦♥

rrt♦♥ ts

r rrt♦♥ s♦rs t ❱rt t ♦ t s♦r s♦♥ t trs❬❪ r♦ t s♦r t ♦r ♥ tt s t t♦ ♣ t s♦r ♥ rrt♦♥ ♣♦st♦♥❬❪ rt♦♥ ♠♦♥t♦r ❬❪ s♦r ♥♦s♥ ❬❪ ♦s♥ ♦ t s♦r ❬❪ ♥ t ♦♥rts♥ ❬❪ rt ❳r② ♠♥ ♥ ts ♥t

♥ str♥t ♦ q ♠sr t r ♦s rt ♥ tst② t♦t s♥ ♥② tr s ♦ ♦t ♠② t ♠tr st♥ r♦♠ ts♦r ♥ ♣t♠r ❬♦❪

♦ ♥trt str r s♦♠ s♠♣s r s♥t t♦ rrt t♦ tP❯ t② ♦ ♦ ♥tr♥t♦♥ ② r♥ s♦r ♠♣♦② trs 60♦ ♦ tt② ♦ ♦t ♠ts ♣♦t♦♥s t ♥ ❱ s♦r s ♣ ♥ r♦♦♠ ♦ ×× ♠3 ♥ ts t② ♦s rts r♦♠ ②r t♦ ②r r ♣♥♥ ♦♥ t st♥ r♦♠ t s♦r ♠trs t♦ ♥t♠trs rs♣t② ❬♠❪

♦r ♦s rts r ♥st t t ♠♠ rrt♦r P P ♦ t ❯♥rst② ♦♥t♣r r♥ ♠♣♦② s♦r s 60♦♥s ♥s ♥ rrt♦r strtr tt ♦s rrt♦♥ ♦ s♠♣s ♥ ♥t♠trs ♦♠ ♥ ts t② ♦s rts r♦♠ t♦ ♠②r r ♠♦♥r♦♠ t♦ ♠ r♦♠ t s♦r rs♣t② ❬❱❪

rt ❳② ♥rt♦r

st♣ r♦♠ t r♦tr♦♥s r♦♣ ♦♥sst ♦ ♥ ❳r② rrt♦♥ s②st♠ P ♥ ❲ ❳r② t ss t♥st♥ trtt②♣ ♦r rt♦♥ts sts ♦♥ s♠♦♥t♦rs ❬P❪ ♣♥♥ ♦♥ t st♥ t ♦s rt t ts ♠♥ r♥s r♦♠ t♦ t♦ ②s

rrt♦♥ ♥t tt ♦sts t ❳r② t s s♦ q♣♣ t rssP s♠t♦♠t ♥ r ♣r♦ stt♦♥ r t ❳r② t ♥ ♠r ♥ ♠♦ ♦♠♣tr♦♥tr♦ ♠♦t♦r③ st♣♣r s s♦♥ ♥

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts

r s r♦♠ t ♦♥♣t ♥ t s tr♠② ♦♥tr♦ ♦r r♥ ♦ t♦

sr♠♥t q♣♠♥t

rtr③t♦♥ ♦ s♠♦♥t♦r ♦s♠trs

♥ ♥ s♥ tt ♦t ♥ ♣♥ ♦s ♥ ♠sr ♥ t s♠ ② ② r♥ t ♦t ♥rss t tr tr♠♥s ♣♦♥♦♥st♥t r♦t rr♥t ♥t♦♥ ♦♠♠♦♥ r♦t tr♦♥ ♥ ts s t♦♦♣rt ♥ rtr③ ts s ♥r rrt♦♥

s♠t② s♦s t s②st♠ s t♦ r♦t s ♥ ♣♥ ♦♦s♠trs r♥ rrt♦♥ tsts ♣rs♥t ♥ ts tss ♦r s②st♠ ♦♥ssts ♦ ♦♥ t② ♦r tr ♥ ♥ ♥t t ❯♥t q♣♣t st ♠♦ rs tt ♦ t♦ ♦♥♥t ♠①♠♠ ♦ ss♠t♥♦s② ♦t s r ♦♥♥t t♦ P P s ♥tr♥ r r♥ ❱❲ s♦tr ♦r ♠tr ♥ s♣♣② r♥♦ rr♥ts ♣ t♦ t r♥t t♠♥ strt♥ r♦♠ ♠s t♦ s ♦♥ rs t r♥t ♦s♠trs ♥r tst s♠ ♥str♠♥t ♦s t♦ ♠sr t♦ts ♥rt r♦ss t tr♠♥s ♥t ♠①♠♠ ♦t ♦ ❱ ❲tts s②st♠ t r♦t ♦ s ①♣♦s ♣ t♦ ♠trs r ② r♦♠ t r♦ttr♦♥s s ♥ ♣r♦r♠ ❬❪

❱❲ ♦♥tr♦ ♣♥ ♦s t♦ st ♣ t qst♦♥ ♣r♠trs ♥♠r ♦ ♥♥s t♠ ②s s rr♥t s r♣tt♦♥ t♠ t ♥ r♦r tqr t ♦♥ ♦r♠tt t①t ♦♥ ♦r s ♥♥ ♦s♠trs rr♦t sq♥t② ♦♥ tr t ♦tr r♦t t♠ ♦ t ♦ ♦s♠tr ts tr♦r r ♣♥♥ ♦ t ♥♠r ♦ s ♦♥♥t t♦ t s②st♠ ♥ ♥t t♠ rqr t♦ r s ♥② t ❯♥t ♥ ♥②♦st tr ♠♦ tt ♦s t♦ qr ♦♥tr tt ♠② s t♦ r♦rt ♦♥t♦♥ ♦ t rrt♦♥ ♠s r♥ t s♥s♦r tst

♠♦r t s♠ ♦ t ♦♥♥t♦♥ s ♦r t ♦s♠tr r♦t s ♥♥ s r ♦♥♥t s tt r♥ rt♦♥ ①♣♦sr t ♥t t ❯♥t ♣s t s tr♠♥s s♦rt t♦tr t♦ ♦ ♥② ss♥♣♥♦♠♥

t② ♥str♠♥ts ♥ s♦ s s ♦rt♦r② tst♥ st♥♦♥♠♦ t♦ rr② ♦t ❱ ♠sr♠♥ts ♦♥ ♣♥ ♦s tr ♥ ♦r rrt♦♥

♦r ♦s♠trs ♦♥② s♠♦♥t♦r ♣r♠tr ♥②③r P ss♦ ♥ s t♦ ♣r♦r♠ t stt tr♥sst♦r ♠sr♠♥ts ♣♣②♥ ♥ ♠sr♥rr♥ts ♥♦r ♦ts t②♣② t r♥ rr♥t d s ♥ ♠sr s ♥t♦♥ ♦ t t ❱gs ♥ r♥ Vds ♦ts

P ♥str♠♥t s ♣rt ♦ t q♣♠♥t ♦ t r♦tr♦♥sr♦♣ ♥ t ♥ s♦ ♥ s t♦ rtr③ tst strtrs ♥ ♦r♠ r♦rt♦ ♠sr ♦♠♣① tr♥sst♦r strtrs t② st♥ ♠tr① s ♦♥♥t

♦♠t♠s ts ♥str♠♥t s ♥ r♣ ② t t② ♦r tr s ♥str♠♥tss t s♠ rtrsts ♦ t ♠♦ t ♦ t♦ ♦♣rt ♣ t♦ ♠①♠♠ ♦t ♦ ❱

sr♠♥t q♣♠♥t

r t♣ ♦r ♥ ♣♥ ♦ ♦s♠trs rt♠ ♠sr♠♥ts

r ♠t r♣rs♥tt♦♥ ♦ t tr st♣ s ♦r t ♦t r♦t♦ s ♥ ♣♥ ♦s r♥ rrt♦♥ tsts ♦r ♥② ♥♥ t ♦s♠trs r♦♥♥t t♥ t ♦♠♠♦♥ ♥ t ♥♦r♠ ♦s tr♠♥s ♦ t st♠tr① ♥ ♦rr t♦ t ♦♥♥t♦♥s s♦rt r♥ rrt♦♥ ♥ t ♣trt s r♦t st ♦♥ ♥♦r♠ ♦♣♥ ♣♦st♦♥ t ♦tr t♦ r ♥①♣♦sr ♠♦

①♣r♠♥t q♣♠♥t ♦r rt♦♥ s♥s♦r sts

r t♣ s ♦r t rtr③t♦♥ ♦ t ♠trs ♥srt ♣tr ♦ tr s②st♠ t♦ ♦①s ♦t ♥r t ♦s♦s♦♣ r t ♥t t♥ s♥ t ♦t ♥t rt♥ s rs♣t② ♥ t ①tr♠ rt♥ s ♦ t♣tr t tt♥t♦r ♠♦ s s♦ s

t♦ t ♠sr♥ ♥♥s ♦ t P s♠♦♥t♦r ♣r♠tr ♥②③r ❬❪ s♦♥ ts s ♦t ♥str♠♥ts r ♦♥tr♦ ② P r♥♥♥ ❱❲ ♣r♦r♠

rtr③t♦♥ ♦ ♠trs

rtr③t♦♥ ♦ t ♠trs s ♥ ♦♥ t s♥ ♦rt♦r②tst♥ ♦♣ t t ❯♥rst② ♦♥t♣r rr s ♥ ts ♦rs ♥ ♥rr ♦s ♦♥ t rrt s♣♠♥ tt s ♣♦st♦♥ ♥ s♠♣s♦r tt ss ♥s ttt ♦① s s♦♥ ♥ ♠tt ♠♥s♥ts♥ s ♦t ② ♠♥s ♦ ♣♦t♦♠t♣r t♥ t s s♥ t♦ ♥t rt s t③ ♥ r♦r ② P r♥♥♥ ❱❲ ♣r♦r♠ ♦♥♥t t♦ t tst♥ t ♥tr

♥ ♦s♦s♦♣ s ♥ s♦ ♦♥♥t ♥ ♣r t♦ t ♥t ♥ ♦rr t♦ ♠♦♥t♦r ♥ r t♠ t ♦t♦♥ ♦ t ♠♥s♥t s♥ r♥ t r♦t ♣r♦r st♠t♦♥ t s ♣♣ t②♣② ♦r s♦♥ ♥ ♦rr t♦ t t ♦♠♥s♥t ♣ ♦r ♥t s♣♣s s♦ t tr ♣♦r ♥ ♦rt ♦♣rt♦♥ ♦ t r♦t ♦♠♣♦♥♥ts

s ①♣♥ ♥ t ♦s♠tr s♥ s ♥ ts ♦r s t ♠♣t♦t ♦ t ♠♥s♥t ♣ ♦ ♦ t ♥stt♦♥ ♦ r♦ ②♥♠ r♥♥ tt♥t♦r s ♥ s ♥ ♦rr t♦ ♦ t strt♦♥ ♦ t ♠♣t♦♥ ♥r♥ r♦t

♦r t r♦t ♦ t s rt♠ ♦s♠tr sr ♣r♦t♦t②♣s ♦ ♦♥♥r♦t s②st♠s ♥ t ♥ tst ♥ t r♠♦r ♦ ts tss ♦r r♦r t ts ♦ ts ①♣r♠♥t st♣s ♦r t s ♥ ♥ ♣tr

♣tr

♦s♠tr② ssss♠♥ts t t

P rrt♦♥ ts

♠♦♥ t rrt♦♥ ts sr ♥ ♣tr t ♦♥s ♦t ♥ t st①♣r♠♥t r ♦ t P rt♦r s ♣r r♦ ♦rts tss ♦r ts ♥ ♥ t r♥ ♣rt ♠s ♦ t②♣♥ ♥r② ♦s t♦ t r ♦♥s ①♣t t t

❱ ♣r♦t♦♥s ♦ t t② s ♥ s t♦ st②t rs♣♦♥s ♦ t s♥ s t♦ ♥r② r r♦♥s s t s♦♥ ♥t ♦♦♥ ♣tr ♥ ♣tr ♦r♦r t rt♦♥ ♥r♦♥♠♥t ♥rtr♦♥ t ♣♦♥t ♥ ts ♥rt ♠ s st♦♣♣ t② s♥ s♦ s t♦ t t ♦ ♦ t s st ♦r t ♥ tr♠s ♦tr rs♣♦♥s ♥ t♠♣♦r stt② s t s♦♥ ♥ ♣tr

♠① γ♥tr♦♥ ♦ t t② s s ♥st t♦♦ t♦ ♠sr t rs♣♦♥s ♦ t s ♥ ♦♠♣♦♥♥t rt♦♥ t rt ♦ rt♦♥ rt

♦tr t t rt♦♥ s♥s♦rs sts ♦r t ①♣r♠♥ts ♦r t st ②rs t ♥♠r ♦ rrt♦♥ ①♣r♠♥ts ♣r♦r♠ ♥♥② t ts tss s tr ♦♠♣①t② s ♦♥sr② ♥rs ①♣r♠♥t ss♠s tt♥ ♦♥♥ r♦t ♥ ①♣r♠♥ts ♣r♦r♠ t ♥♦♥ st♥r ♠ ♦♥t♦♥s ♥ ♦ ♥t♥st② r♥t ♠ s③ t r ♣r♦r♠ ♠♦r ♥ ♠♦r rq♥t② ♦♥ t ts ①♣r♠♥ts ♦♠s tr♦r t rqst ♦r ♠♦r ♣rsrtr③t♦♥ ♦ t ♠ ♣r♦ t ♠ ♥t♥st② ♥ t ♣rt ♦♠♣♦st♦♥ ♦t rt♦♥

♦ sts② ♦ ♠♥s t s ♦s♠tr② t♥qs r ♦♥t♥♦s② ♠♣r♦ ♥ ♦♣t♠③ r♦r s♦♠ ♦ ts ♦s♠tr② ♠t♦s ♥ st♥ t ♥ t r♠♦r ♦ ts tss ♦r ♥ t② sr ♥ t♦♦♥ st♦♥s ♦ ts ♣tr ♦r t t② srs ♦ ♠ ♣r♦t♥qs ② s♥ r♦♠ ❬❪ s♥st ♠s ♥ t♥ ♣t② t♠t♠♥s♥ ♠s ♣rs♥t ♦r t t② rt♦♥♠♣♥ s ♥ ♥rt♥ ♥ t ♦t♥ rsts sss t♦tr ttr ♦♠♣rs♦♥ t t ♣rt♦♥s r♦♠ ♦♥t r♦ s♠t♦♥

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts

Pr♦t♦♥ ♠ rtr③t♦♥ ♥ ♦s♠tr② ♥

tt♦♥ ♠sr♠♥ts

s ♠sr♠♥t ♣r♦r♠ ♦♥ t ❱ ♣r♦t♦♥ ♠ s t tr♠♥t♦♥♦ t ♣r♦t♦♥ ♥ ② t♥ t 24 ♥ 22 tt② ♦ ♠♥♠ ♦s sr♣t♦♥ ♦ ts ♠sr♠♥t t♥q s ♥ r② ♥ ♥ ♥t s ♦ ♥r② ♣r♦t♦♥s t s♦t♦♣s r ♣r♦ t ♥r rt♦♥s27♣♣♥24 ♥ 27♣♣♥22 rs♣t② ❬♦❪

r♦ssst♦♥s ♦ ts t♦ rt♦♥s ♥ rtr③ s ttt ts tt♦♥ t♥qs t s ♣♦ss t♦ ♦t♥ ♥ ♠sr♠♥ts t ♥r② ♦ ± s③ ♦ t ♠♥♠ ♦s t♦ s t t♥ss ♦ s♦♠♥r µ♠ s r②♥ r♦♠ t♦ ♠2 ♦r♥ t♦ t s③ ♦ t s♠♣s tt t♦ rrt s ♦ 24 ♥ 22 r ♦t ♦rs ♥ ②rsrs♣t② ♦r♥ t♦ t t♠ ♣s tr rrt♦♥ ♥ t rrt♦♥ t♠ts ♦♥ ♦ t t♦ s♦t♦♣s s ♦s♥ t♦ ♠sr ♦r t ♥ t♦♥

♥ ♥t♦ ♦♥t tt ♦♥③t♦♥ s t ♠♥ ♦♥trt♦♥ t♦ t ♥r② ♦ss ♦ r ♣rt ♥ tt ts ♠♥ t st♦♣♣♥ ♣♦r ① s ♥ ② tt♦ t s ♣♦ss t♦ s♠♣② ♦♥rt t ♥ ♥t♦ t ♦s ② ♣♦st♥ t♥ s♠♣s s♥ t ♦♦♥ ♦r♠

D = K × (dE/dx)m × Φ

r Φ s t ♣r♦t♦♥ ♥ ①♣rss ♥ ♣rts♠2 ①−10 s st♦r ♥ ①m ①♣rss ♥ MeV ·cm2/g s t ♠♥♠♠ ♦♥③♥ ♥r② ♦ss rt♦r ❱ ♣r♦t♦♥s t s s t♥ MeV ·cm2/g ♦r ♥r s♠♦♥t♦rs t②♣② rrt ♥ t ts ♦r ♥r② r ♣rts t ♦♥trt♦♥ ♦ ♥r ♥trt♦♥s ♥ t rst♥ s♦♥rs t♦ t ♦s ♥ t ♠s s② s♠ ♥ ♥ ts ♥t ♥r ♥♦r♠ r♠st♥s ❬❪

♠ ♣r♦♥ t ♦s♠tr ♠s

r♦♠ ♦s♠tr ♠s ❳ ②♣ ♥ r rr♥t② s ♦r♠ ♣r♦♥ ♥♠♥t ♥ ♦s ♠sr♠♥ts ♦r ♥ r♥ s♠♣ rrt♦♥♥ ♠♥ rtrst ♦ ts ♠ ♥ sr ♥

s♥stt② ♦ t r♦♠ ❳ ②♣ ♠ ♦s ♥ rt ♠sr♠♥t ♦ t ♣r♦t♦♥ ♠ ♣♦st♦♥ t ♦♥② s♣s ♦ ♣rts t♠♦♥s♠♣t♦♥ ♥ t ♥♠♥t ♦ t stt s ts ♦♥sr② r trs♣t t♦ t ♣r♦s ♣r♦r s t♥ ♣s ♦ ss tt r♥ ♦♥②tr ♥ r ♥♠r ♦ ♣r♦t♦♥ s♣s ∼

tr♥s♣r♥t ♠s r♦♠ ♥ tt ♦♣ rtrst ♦♦r tr ①♣♦sr r ♥st s t♦ ♠sr t s♦r ♣r♦t♦♥ ♦s r♥rrt♦♥ ♦r tr t③t♦♥ ♥ t rtr③t♦♥ ♦ t ♦s♠trs ♣rs♥t♥ t ♦♦♥ ♣trs sr s♠♣s ♦ ♠2 ♥ rrt ♥ t♦♦t♥ t rt♦♥ r s♦♥ ♥ tt ♦rrts t ♦♦r t ♥st②D t t s♦r ♦s

Pr♦t♦♥ ♠ rtr③t♦♥ ♥ ♦s♠tr② ♥

r rt♦♥ rs ♦r ♠s ♥ rt♦♥ rs ♦t♥ ♥ ♠♣t② ♠rrs ♦♠♣r t ♣r♦r t ♠rrs ♦t♥ t ♠♠r②s

♦r ts ①♣r♠♥t t ♠s r r♣♣ ♥ ♠♥♠ ♦s t♦ tt ♥♥♥ t② ♥ rrt t r②♥ ♥s t♦ ♣r♦ ♦ss r♦♠ ② t♦ ♠♦rt♥ ② s t ♦♣t ♥st② ♦ ♦t ♠ t②♣s ♥rss t t♠ r♥strt♦♥ ss t♥ rs tr rrt♦♥ ❬❪ t r♥s r ♣r♦r♠ trs t♠ ♦r t ♣rs♥t rt♦♥ ♥ ♥ ♦♣t ♥st② ♦ t ♠s s♠sr s♥ r ss♦ts tr♥s♠ss♦♥ ♥st♦♠tr ❯♥①♣♦ss♠♣s r s t♦ ♣r♦ s ♦♣t ♥st② s strt r♦♠ t♠sr ♦♥ ♥ ♦rr t♦ ♦t♥ ♥ ♣♦t t D s ♥t♦♥ ♦ t ♦s

♦r t ♠ t t ♦t♥ ♥ ♥ ♦♠♣r t t ♦♥r♦♠ t ♠♥trr ♦t♥ tr γ rrt♦♥ ♥ tt t♦ ♦t♥ rt♦♥r s♦ ♥s ♥ ①♣r♠♥t ♣♦♥ts r ♥ r♠♥t t♥ t rs♣t t♦ t t ♦ t ①♣r♠♥t t ♦r ♦ss < ② t r tr♠♥t ♥rss t♦ ttr t♥

♠ ♣r♦♥ t ♠s

♠trs ♥ s♣ ♦ t♥ ♠s s s ♦r ♦s ♠♣♣♥ ♣♣t♦♥s♥ sr ♥ ♥ s♦ tst t♦ ♠sr t ♣r♦ ♦ t ❱ ♣r♦t♦♥ ♠ ♥ t r♠♦r ♦ ts tss ♦r sr ♠s rtr♦r ①♣♦s t♦ t ♠ t t ♠ t♦ rtr③ t ♦r strt♥t ♦s♠tr sts tr rrt♦♥ t ♠s r s♥t t♦ t ❯♥rst② ♦♥t♣r ♦r tr r♦t t t tst♥

s♦s t♦ ♦s ♠♣s ♦t♥ t s ♥ t ♣r♦t♦♥ ♠ s r♥♥ ♥♦r♠ ♦♣rt ♦♥t♦♥s t♦t ♥ t t♦ ♣trs ♦ t ♠ s♣♦tsr ♦ t♦ r♥t s③s ♥ ♦t tsts t ♦ss ♦ ② ♥ ♣♦s ♥t ♠s ② sr ♣rt s♣s ♦ ♠s rt♦♥ s ♣r♦s ♦ ♦t

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts

r rs♦t♦♥ ♠ ♣r♦s ♠sr ② µ♠ ♠ ♠s♣♦t♦ ♦t ① ♠2 t ♥ s ♥ st♥r ♠ s♣♦t ♦ ♦t ① ♠2 rt ♥s

µ♠ rs♦t♦♥ ♥ r② s ♥ t tr♠♥t♦♥ ♦ t ♦s ♠♣ ♦rt rrt♦♥ sr s ♥ ❬s❪

♥ ♦ ts ♠s s ♥ ①♣♦s sr t♠s t♦ ♣r♦t♦♥ ♦ss ♦ ♠♦r t♥ ② ♣r♦t♦♥ Φ > 3×1012 p/cm2 tr t♦t ①♣♦sr t♦ ♣rt ♥s ♥ t ♦rr♦ 14 p/cm2 t ♠ ♦s♥t s♦ ♥② rt♦♥ ♦ ts ♣r♦r♠♥ ♣r♦♥t ♥s♥stt② ♦ ts ♠tr t♦ rt♦♥ ♠

r♦♠ t ♦tr s ♠s ♥ s s♦ t♦ tr♠♥ t ♠ ♣r♦ ♥♦♥t♦♥s ♦ ♦r ♠ ♥t♥sts ♥ ①♠♣ s ♥ r♣♦rt ♥ rt P ♣r♦t♦♥ ♠ t ♥ ♥t♥st② r ♦ ♦t tr ♦rrs ♦ ♠♥t s①trt ♥ rt t♦ ♥ t ♦s ♠♣ s ♥ ♠sr② tr ①♣♦sr ♦ ♠② ♣r♦r♠♥ ♦ t ♠tr s t♦ ♦♠♣r t t s♠ ♠sr♠♥t ♣r♦r♠ t tt♦♥ ♦ ♠♥♠ ♦s♣rs♥t ♥

♣rt t r r♥ ♥ t rs♦t♦♥ ♦ t ♦s ♠♣s ♦t♥ t t t♦t♥qs t ♠sr♠♥t t ♠♥♠ tt♦♥ t♦♦ s♦ r ♠♦♥t ♦ t♠♦rs t♠s t rs♣t t♦ t ♦♥ ♠♥ts t♠s s♥ ♥ t s♦ t tt♦♥ t♥q t s ♥ssr② t♦ r ♣r♦t♦♥ ♥ ♥♦ t♦tt t ♠tr t♦ ♠sr

♠ ♣r♦♥ s♥

♥ ♦r ♥ ♦♥♥ ♠t♦ t♦ tr♠♥ t ♣♦st♦♥ ♥ t ♣r♦ ♦ t ♣r♦t♦♥ ♠ ♠♦tt t st② st② ♦r ♥ ♥str♠♥t s ♦♥ t ♣r♦t♦♥♥ ♦♥r② tr♦♥ ♠ss♦♥ r♦♠ t♥ ♠t ♦s ❬P❪ ♦sr rqr t♦ ♠ ♦ ♦ ♦st ♥ rt② s♦rt tt② t♠ ♠tr♦r♦r t② t♦ ♦♥ t ♦♥ ♥ t♥ t♦ ♦ sttr♥ ♦ ♠ t ♦♥ t♦tr ♥ t ♥♦ t♦ ♦ s② ♥♥ ♠♥♠ ♦s r ♦s♥ s ♦♦♦♠♣r♦♠s t♦ sts② ♠♦st ♦ ts rqr♠♥ts tst st♣ s r③ t♦ r② st ♦ ♣r♠♥r② t♦♥s ♥ t♦ ♣r♦r♠ ♣r♦♦ ♦ ♣r♥♣ ♦r strt♥ ts♥ ♦ ♠ Pr♦ ♦♥t♦r P s②st♠

Pr♦t♦♥ ♠ rtr③t♦♥ ♥ ♦s♠tr② ♥

r ♦s ♠♣ rss tt♦♥ ♦ t♥q ♣r♦ t rs♦t♦♥♦ µ♠ ♦s ♠♣ ♦t♥ ② ♠♥s ♦ tt♦♥ ♦ ♠♥♠ ♦s ♠♥♠ ♦s♦ ♠♠2 r ss♠ ♥ ♠tr① t s♣♥ ♦ ♠♠

r t♣ s ♦r t t♦♥ ♦ t ♥ t ♠ sr♥♠♣♥ t ♣tr s rrr t♦ t s♥ qr t ♠♥♠ ♦ s ♣ ♦♥ t s♦ t ♠ s♣♦t

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts

r P ♠sr♠♥ts r ♠rs ♦♠♣r t t ♣r♦s ♦t♥ ② ♠♥s♦ tt♦♥ ♦s ♥ r♦♠ ♠s r♥t ♦♥t♥♦s ♥s

P tst st♣ s ♦♥sst ♦ ① ♠2 µ♠ t ♠♥♠ ♦♠♦♥t tr♥srs② ♦♥ t stt ♦♥ t ♠ t♦ ♣ss tr♦ t ♠ t ♦ t ♦ ♦ s tr② ♦♥♥t t♦ ♥ r♥s♠♣♥♠♣r ♦t ♥ t ♦♥t♥ r♦♦♠ ♠tr ♦♥ ♦① ♠♣s♥ s r ♦t t r♦② ③ s♦s♦♣ t ① rt♣♦st♦♥ t ♦ s s♣ t♦ r♥t ♦r③♦♥t ♣♦st♦♥s r♥♥ r♦♠ t♦ ♠♠♥ t r ♥trt ♦r ♦♥ ♣rt s♣ s ♠sr t st♣ ♥ ♦rr t♦t ♦r③♦♥t ♣r♦ s♦s t ♦t♥ rsts r ♠rs ♥♦r♠③t rs♣t t♦ t ♠①♠♠ ♥t♥st② ♦ t ♠ s♣♦t ♥ ♦♠♣r t t s♠♠sr♠♥t ♦t♥ ② t ♣r♦♥ t♥qs ♠♥t♦♥ ♦ r♦s ♥s ♦♦ r♠♥t ♦ t ♠sr♠♥ts ♥ t rr♥t ♦t r♦♠ t ♦ ♥ ♥ t ♥tr ♦ t ♠ s♣♦t ♠♦♥strt t st② ♦ ts ♠♣r♦♥s②st♠ ♥ ♦ t♦ strt t s♥ ♦ ♠t♣ P tt♦r

♦s♠tr② ♥ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦

r♥t ♦s♠tr② t♥qs r s t♦ ♠♦♥t♦r t ♥tr♦♥ ♥ ♥ t ♣♦st♦t ♦♥③♥ ♦s ♥ ts ♦♠♣① ♥r♦♥♠♥t ♦r rt♦♥ r♥ss tsts♥ s♦stt ♦s♠tr rtr③t♦♥s t ♥r♦♥♠♥t t ♠ st♥ r♦♠ t♠ ①s s t ♠♦st② s ♥ ts ♣♦st♦♥ t rt♦♥ s ♦♠♣♦s ♠♥②♦ ♥tr♦♥s t s♠ ♠♠ r② ♦♥t♠♥t♦♥ s♦s tts ♦ t ♣rt s♣tr ♥ ts ♦t♦♥ ❬❪

t♦♥s s ♦♥ s♠t♦♥s ♥ tt♦♥♦ t♥qs ❬❱♥❪ s s ♠sr♠♥ts t P♦②♠r♥♥ ♦s♠trs P ♦P♦t♦♠♥s♥tsss P ❬♦♥❪ r♦♠ ♠s ♥ ♦♥ tt♦rs ❬♦❪ r rr

♦s♠tr② ♥ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦

r Prt s♣tr ♥ t② t ♥t♠trs r♦♠ ♠ ①s ♥♦r♠③t♦ ♦♥ ♠♣♥♥ ❱ ♣r♦t♦♥

♦t ♦r t rt♦♥ ♦ t ♦t♦♥ t ♠ st♥ r♦♠ t ♠ ①s ♥ trt♦♥ ♠♣♥ ♣rs♥t r s♠♣s ♦ ♦s♠tr t②♣ r rrt t♦ ♥rs♥ ♥tr♦♥ ♥s

♦♥t r♦ s♠t♦♥s t t ❯ ❬s❪ ♦ ♥ rr ♦t t♦♣rt t r♦♥ ① ♥ t ♣r♦t♦♥ ♦ 24 ♥ t♥ ♦ ♣ t ♠r♦♠ t ♠ ①s ①♣t r ♦s ♥ t ♠♥♠ ♥♦r♠③ t♦ ♦♥♣r♦t♦♥ tt♥ t trt s s♦ ♥ ♦♠♣t sr♥ t 24 tt② tr♦r♦s t♦♥ ♦ t ♣rt ♥ ♥ tr♠s ♦ ❱ ♥tr♦♥ q♥t♥ Φeq ❬❪

s♦s t ♣r♦t♦♥ rt ♦ 24 ♣r ♥♥t ♣r♦t♦♥ ♣rt ② s♠t♦♥s ♥ ① ♠2 ♦s ♦♥t♥♦s ♥ ♦♠♣r t t ♠sr♠♥ts rr♦t t ♦s ♣ t r♥t st♥s r♦♠ t ♠ ①s r♥♥ r♦♠ ❩ ♠ t♦ ❩ ♠ ♠sr♠♥ts t ♦tt ♥s t♥ t st♣s ♦ ♠t ♦s ♦ ♦♥ sqr ♥t♠tr ♥ ♥♦r♠③ t♦ t ① ♠2 r r♦tt ♥ t♦ ♦ t ♦♠♣rs♦♥ t t s♠t♦♥ ♦t♣t t♦ sts ♦ 24♣r♦t♦♥ rts tr♥ ♦t t♦ ♥ r♠♥t t♥ ♦r t rrt♦♥ ♣♦st♦♥s st♥s r♦♠ t ♠ ①s ♥ t ss t ♠sr 24 ♣r♦t♦♥♦rst♠ts t ♦rrs♣♦♥♥ s♠t s ② ♦t

♦♥ tt♦rs r rt② ①♣♦s ♥ t ♥tr♦♥ t ♠♥tt♠♣rtr t♦t s♥ t♠ tr rrt♦♥ t s r ♥♥ ♦r ♠♥ t ♥ t ♥rs ♦ t rr♥t t ♣t♦♥ s ♠sr s①♣♥ ♥ rr♥t s t♥ ♦♥rt t♦ Φeq ♦♦♥t s♥ ♥ ♦♥ ❬♦❪ ♥ t rt♦♥ r ♦ s ♠t♦s ♦s♥ s♥ t s ♣♦ss t♦ ♦t♥ r♣r♦t② ♥ t ♥ ♠sr♠♥ts♥ r♥t ts ♦ tt♦rs r s

rsts ♦ ts t♥q r s♦♥ ♥ Φeq s ♦t♥

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts

r ❱t♦♥ ♦ t rt♦♥ t ♦♥t r♦ s♠t♦♥s 24Pr♦t♦♥ rt t r♥t st♥s r♦♠ t ♠ ①s ♣rt ♦♥ ① ♠2 ♦s r♦♠♦♥t r♦ s♠t♦♥ ♦♥t♥♦s ♥ ♥ ♦♠♣r t t ♦♥ rt② ♠sr tt tt♦♥♦s t♥q ♦tt ♥s Φeq r♦♠ ♦♥ tt♦rs ♣♦tt rss tΦeq t r♦♠ ♦♥t r♦ s♠t♦♥s

② t ♦♥ ♣rt tt♦rs s s ♣r♦♣♦rt♦♥ ♠ ♦♥trs r tr♣♦tt rss t s♠ q♥tt② t r♦♠ ♦♥t r♦ s♠t♦♥s

❲t rs♣t t♦ t ♦♥t r♦ s♠t♦♥s t Φeq s ♠sr ② t s♦♥tt♦rs s♦s ♦♦ ♥rt② t s s♦ ♦rst♠t ② rs♦♥s ♦r tsr♥ t♥ ♠sr♠♥t ♥ t s♠t♦♥ ♠t ♠♥♦ t s♥t ♣♦ss tr rrt♦♥ st♣ t♦ ♠sr t tt② ♦ t s♦rtt♠ 24 ♥♥ ♣♣② t t♦ ♥♦r♠③ t s♠t♦♥ ♦t♣t ♦r ts rs♦♥ t s♠t s ♥ s s♥ ♦♥② tt♦♥ ♠sr♠♥ts ♣r♦r♠ r♥ trst rrt♦♥ st♣s rtr♠♦r t♦ rt r s t♥ t♦ st ♠♦♥t♦♥s r♥ t ♦♥ r♥♥♥ ♦ t ①♣r♠♥t s♠ rt♦♥s ♥ ♥♦t ① ♥ ♥② t s♠t♦♥ ts ♥ t s♥ ♦ t ♦♥ tt♦rrs♣♦♥s ♠t s♦ t ② s♠ rr♦r rtss ♦♥ tt♦rs r♥t s ♦♦ t♦♦ ♦r ♠sr♥ Φeq ♥ r ts s t♦ ♣♦t t ①♣r♠♥tt s♦♥ ♥

s♦s t ♦♠♣rs♦♥ t♥ t ♦t ♦♥③♥ ♦s ♥ ♠♥♠st♠t ② s♠t♦♥s ♠♣t② r♦♥ ♠rrs ♥ t s ♠sr t r♦s♦s♠tr t②♣s ♦tr ♠rrs ♥ t ♣♦t ♣♦st ② t ♥tr♦♥♠♠♥r♦♥♠♥t ♥ t♥ ♠♥♠ ♦s s s♣♣♦s t♦ q t♦ t ♦♥ ①♣t ♥ t♥s♦stt s♠♦♥t♦rs s

s ♠sr t s♥st ♠s ♥ P ♦s♠trs r ♦♥ r rtr② t♦r ♦ ± t♥ t ♣rt r♦♠ s♠t♦♥s P t♥qs♦s ♥st t♦r ± rtr t♥ s♠t♦♥s s r♥ s ①♣t♥ s t♦ t r♥t ♥tr♦♥ ♥trt♦♥s ♥ t r♦s s♥st ♠trs ♦♥sttt♥ t ♠♣♦② ♦s♠trs ❬❱♥❪ ♥ t t② t ♥tr♦♥ s♣tr♠s ♦♠♥t ② st ♥ ♥r② ♥tr♦♥s ♦ t ♥tr♦♥s ♥rs r♦♠ ❱ t♦ ❱ ♥ ts r♥ ♥tr♦♥s ♣♦st s♥♥t rt♦♥ ♦ tr ♥r②

♦s♠tr② ♥ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦

r ♦♠♣rs♦♥ ♠♦♥ t r♥t ♠sr t ♠ r♦♠ t ♠ ①s♦t♥ ② r♥t ♦s♠tr ♠♥s ♦tt ♥s ♥ ♣♦tt s ♥st♥ r♥t t sts

♥ ♦♥♦♥③♥ ♥r② ♦sss ♥ ♥ ♥st ♥trt♦♥s tt ♣r♦ st ♥ t♣rts tt s♣ r♦♠ s♠♦♥t♦r ♠trs ♥tr♦♥ ♦♥trt♦♥ t♦ t ♥ s♠♦♥t♦rs t rs♣t t♦ t ♠♠ r②s s ts ♥ t ♦rr ♦ t♥♣r♥t ♥ rsts ♥ st♠t♦♥ s♠r t♥ t ♦♥ ♦t♥ ② ♦tr s②st♠ss t s ♥ s♦ ♣r♦ ♥ ♠sr♥ ♦ss ♥ ② ♠♥s ♦ s♦stt♦♥ ♦s♠trs ❬❪

♠♦st ♠♣♦rt♥t ♠♥s♠ rs♣♦♥s ♦r tr♥sr ♦ ♥r② r♦♠ ♥tr♦♥st♦ ♣♦②♠r sst♥s P ♥ r♦♠ ♠s s st sttr♥ r♦ ♣r♦t♦♥ ♥rt ♥ ts ② ♠♦ tr♦ t ♠tr ♣♦st♥ t ♥t♥tr♦♥ ♥r② ♦♥③t♦♥ ♥ t♦ t ♥rs rs♣♦♥s

♠s ♥ P ♠sr♠♥t r tr♦r ♥ ♦♦ r♠♥t ♥ ♥ ♥♥tr ♦ ± t s t♦ ♥♦t tt t ♠ ♣r♦s ♠♦st t s♠♠sr♠♥t ♦ t P t ♥ rr♦r ♦ ♦t ± P rs♣♦♥s s t♦r ♦r t rs♣t t♦ t P ♥ t ♥r♦♥♠♥t ♥ s ts t♥ t♥♥ ♠sr♠♥ts ♥ t s♠t♦♥ rsts s sr♣♥② r② ♦sr♥ ♣r♦s ♦r ❬♦♥❪ ♠② ①♣♥ t ♥ ♥tr♠t ♥tr♦♥ ♥trt♦♥ ♠♥s♠ ♥ t r♥t ♠tr ♦ t P srtt ♠♥♦♣♦s♣tss

♦r t P ♦s♠trs ♦♥② t ♦ ①♣r♠♥t t r ♦♠♣r t♦ tt♦rt t♦♥ ♦ t s♥ t♦rs ♦r t rs ♥ P ♥ ♦♥tt s t s ♠tr ♦r s♦stt ♦s♠trs

s♦s t ♥tr♦♥ ♥ ♣♦t♦♥ ♦♥③♥ s s♠t ♦r ♦♥ ♥ P t r♦♠ ❬ ❪ ♦♥ ts ♦♥ts t t♥tr♦♥ ♥ ♠♠ s♣tr s♠t ♦r t t② ♦ ♥s t♦♥ ♦ t s♦r ♦s ①♣rss ♥ ② ♥♦r♠③ t♦ ♦♥ ♥♥t ♣r♦t♦♥ rsts ♦ ts t♦♥s r r♣♦rt ♥ rt♦ t♥ t ♦s s

♦s♠tr② ssss♠♥ts t t P rrt♦♥ ts

r tr♦♥ ♥ ♥ ♣♦t♦♥s γ r♠ t♦rs ♥ ♥ P ♦r t ♥r② r♥❱÷ ❱

♦s ♥ ♦♥ ♦s ♥ P❬②♣r♦t♦♥❪ ❬②♣r♦t♦♥❪

♣♦t♦♥s ①−15 ①−15

♥tr♦♥s ①−15 ①−13

s♦r ♦s t♦rs ♥ t r♦♠ t ♣rt s♣tr

♠sr ♥ P ♥ t ♦s ♣♦s ♥ ♦♥ s t ② ♦♥t r♦ s ts♥ ② t ♦♦♥ qt♦♥

DPAD,measured

DSi,calculated

=DPAD,γ + k × DPAD,n

DSi,γ + DSi,n

r t ♦ss r t ♦♥s r♣♦rt ♥ ♥ t ♦♥t s t rts♥stt② ♦ ♥♥ ♦r ♥tr♦♥s ♦♠♣r t♦ ♠♠ r②s ❬t❪

rt rs♣♦♥s ♥ ♥♥ t♦ ♠♦♥♦♥rt ♥tr♦♥s r♥s r♦♠ t♦ ♦♠♣r t t rs♣♦♥s t♦ 60♦ ♣♦t♦♥s ♥ t ♥r② r♥ r♦♠ t♦ ❱ ❬❪ ♥ t ss ♦ t ♥tr♦♥ s♣tr♠ ♦ ♦♥t s ♥ ♦♥ ♦r t t② t t ♣♦st♦♥ ❩ ♠ ② ssttt♥ ♦ t ♥ q t ♦s rt♦ P s ♦♥ ♥ tr♥s ♦t t♦ q t♦ s s ♥ ♦♦ r♠♥t t t ①♣r♠♥t ♠sr♠♥t ♣rs♥t♥ t♦r ♦

♦♥s♦♥

♦♥s♦♥

rrt♦♥ ts ♥ t st ①♣r♠♥t r t tP rt♦r ♣② ♣r r♦ ♦r rt♦♥ r♥ss sts ♦r t ♦♠♣♦♥♥ts s s ♥ t rt♦♥ s♥s♦r sts st ♦ ts tss ♦r ♣rs ♣♦st♦♥♥ ♦ t ♣r♦t♦♥ ♠ ♥ ♥ rt rt♦♥ ♦ t ♠① γ♥tr♦♥ ♥r♦♥♠♥t r tr♦r ♣rrqst t♦ r♥t rrt♦♥ ♦ t s♥s♦rs ♥r st② ♦r ts rs♦♥ t ♠♣r♦♠♥t ♦ t ♠♣r♦♥ t♥qs ♥ t t♦♥ ♦ t ♦s ♠sr♠♥t ♥ ♠① ♥r♦♥♠♥t ♥ rss ♥ ts tss ♦r

♦r t t② sr ♠ ♣r♦ t♥qs ♥♥ r♦♠ s♥st ♠s ♠s tt♦♥ ♦s ♥ sr ❲t s ♠t♦st s ♣♦ss t♦ tr♠♥ t s♣ ♦ t ❱ ♣r♦t♦♥ ♠ ♥ µ♠s ♥t♦ ♠sr t ♥♠r ♦ ♣rts ♥ tr♦r t ♦s r t♦ t r♥t♠trs t ♥ r② ♦ ± ♦r t t② ♥ t ♦t♦♥ t ♠ st♥ r♦♠ t ♠ ①s t rt♦♥ ♠♣♥ rr ♦t ♦r ts tss ♦r s♦ ♥ r♠♥t ♦ ± ② ♦♠♣r♥ t ♣rt♦♥s r♦♠ ♦♥tr♦ s♠t♦♥ t ♠sr♠♥t ♣r♦r♠ ② t P♦②♠r♥♥ ♦s♠trs♦P♦t♦♠♥s♥t sss r♦♠ ♠s ♥ s♦♥ ♣rt tt♦rs

♣tr

rtr③t♦♥ ♦

♦s♠trs

♦s♠trs r ♣♥♥ tr♥sst♦rs s t♦ ♠sr t ♦♥③♥ ♥r②♣♦st♦♥ rt♦♥ ♦ tr♦♥♦ ♣rs ♥ s♠♦♥t♦r ♠trs ② t ♣ ♦ ♣♦st r ♥ t t ♦① 2 ②r ♦ t s t s ♥ sr♥ t ♥ ♣tr ♣♦st tr♣♣ r ♥ rt♥ ♦r ♦♥ ♣r♦s ♦t♠ t r♦♦♠ t♠♣rtr ♥ t♦ st ♦ t tr♥sst♦r t trs♦ ♦t❱th

s r ts ♥trt♥ s ♥ t ♦s♠tr ♥♦r♠t♦♥ s rt♥♥tr♥② tr r♦t ♥ t② r s ♥ rr ♦♥t♠ ♦s ♠sr♠♥ts♥ ♦ r ♣♦r ♦♥s♠♣t♦♥ r rqr s rtrsts t♦tr tt t tt ts s r② s♠ ♠♥s♦♥s r ♣s r♦ssst♦♥ ♦ ♠♠2 ♠ s st t♦ ♥st ♥ rt♦r ts t ①♣r♠♥ts ♦r t ♠sr♠♥t

rt♦♥ t♥ t t ♦t st ♥ t rt♦♥ ♦s str♦♥② ♣♥s♦♥ t tr ♥ t ♦① r♥ rrt♦♥ ♣♣ t s ❱G ♥ ♦♥ t♣r♦t♦♥ ♣r♦ss ♣r♠trs s♣② ♦♥ t t♥ss ♦ t t ♦① srt♦♥ s t♦ tr♠♥ ①♣r♠♥t② s♥ ♣r♦♣r rt rt♦♥ s♦r t t r♣♦rt ♥ ts ♣tr tr♦r rr t♦ s ①♣♦s t♦ rt♦♥ t❱G t♦ ♥t r♦♠ s♠♣ r♦t rt ♦♥rt♦♥

s rtr③t♦♥ ♣r♦r t

♥ t②♣s ♦ ♦s♠trs r♦♠ ♦r r♥t s♣♣rs ♥ ♥sttt♦ t tr ♣♣t② ♥ ♠① r♦♥ rt♦♥ ♥r♦♥♠♥ts s s ♥r③ ② st②♥ ♥ t tr rs♣♦♥ss t♦ t r♥t ♥ ♦ rt♦♥s tt♦♥sttt t ①♣r♠♥ts rt♦♥ s s t♥ t stt② ♦t ♦s♠tr ♥♦r♠t♦♥ ♦rt♠ ♥♥♥ ♦ t ♦①tr♣♣ r s♠♠r② ♦ t t s t♦tr t tr ♠♥ rtrsts r ♥ ♥

srt

r③t♦

♥♣r♦r

t

t♦♥ r♦tr♦♥s t♦♥ ①♣r♠♥t ♦♠s♦♥ s♥ ♦rt♦r② ♦ ♥②ss ♥

sr ♥tr ♥ ♦♥t♦rs tr♦♥s rttr ♦ ②st♠s

♦♥tr② ❯ ♥♠r ❯ rt♦♠ t♦♠s♦♥♦♠ sr

♠ P P

P

P

s♣ s♠ tox ♦ tox s♠ tox

②♣

①t♥ss ♠♣♥t t

♥♠ ②♣ ②♣

❲ rt♦

♦t rr♥t

µ

②♣ ♥t ± ± ±♦t ± ±❱

♥t γs♥stt②

Pr♦r t

♠❱②a

st r r ♦r ♥ Pst r

♣s ♦r ♣♦②♠r rrrs ♦r

♦s♠trs ♥stt ♦r ts tss ♦r r♦t rr♥t s ♥ s♣ ② t s♣♣rs t r♦♠ ❬ ♠❪ ♦t (a) t ♦r ♥s s

rtr③t♦♥ ♦ ♦s♠trs

♦s♠trs r s② s♣♣ ♥♣st ♥ r♥t ♣s ♦ r♦s♠trs ♥ ♠♥s♦♥s r♦r ♥ ♣♦ss t rt♦♥ rs♣♦♥s sts ♥ ♣r♦r♠ ♦♥ t r s♦♥ ♣ ♥ t ♦tr ss t ss ♦♥r♥♥ t♣s ♥ t♥ ♥t♦ ♦♥t s♦♠t♠s t t s♣♣♦rt ♦ ♦♥t r♦s♠t♦♥ t♦♦s ♥ t ♥②ss ♦ t ♦s♠trs rt♦♥ rs♣♦♥s

rt♦♥ rs♣♦♥s sts ♦r t t♦♥ ♦ ♦s♠trs r② ♦♥♥ ♥t♥s srs ♦ rrt♦♥ ♠♣♥s srs ♦ rrt♦♥ tsts ♣rs♥t ♥ ts♣tr ♥ rr ♦t ♥ t r♠♦r ♦ ts ♦r ♥ t ①♣r♠♥t tssr ♥ ♣tr ♦r ♦♠♣t♥ss t rsts ♦ ♦♠♣♠♥tr② rrt♦♥ tsts♣rs♥t ♥ ❬ ❪ ♦♠♣ ② t s♠ t♦r ♦t♥t ♥ ♥ ♥ t sss♦♥s

r t♦♥rtr③t♦♥ ♣r♦r ♣♣ t♦ ♦s♠trs

t♠r♦r② t♦♥ ♦ ♦t ot ♥ it tr♣♣ r ♥♥♥♦ ∆Vth ♦♦♥ r♦♥ ①♣♦sr ♦♠s r ♣r♠tr t♦ r♥t r♠sr♠♥ts t s ♦r t ②rs ♦ ❬❪ ♥ t s ♥♦t ♣♦sst♦ st② t ♥♥♥ ♦ ∆Vth ♦r t♠s ♦♠♣r t t ♦♣rt♦♥ t♦♠♣♦♥♥ts t♦♥ s s ♦♥ t ①♣r♠♥t s♦r♦♥ ♥♥♥ ♠t♦ ❬❪ s t♥q ♦♥ssts ♥ ♠♣t②♥ sq♥t② rt♦♥ ♦ t ts r♥ r ♥♥♥ ♣r♦ t ♥r♠♥t t♠♣rtrs tr ♥♥♥ st♣ tts ♦♥ ∆Vth r t♥ ♠sr t r♦♦♠ t♠♣rtr

s rtr③t♦♥ ♣r♦r t

♥ t st♦♥ ♣r♦r s ♦♠♣t ♥ t s st ♦r t ①♣r♠♥ts ♥t t rtr③t♦♥ ♣r♦r s ♥ strt ♦♥ tss ♥ ♦rr t♦ ♣r♦ t rqr rt♦♥ ♣r♠trs s♠♣s r♦♠ t t♣r♦r ♦r t ♥ ♠sr t♦ q♥t② t ②s ♣r♠trs♥② ♠sr♠♥ts ♥ t♦♥s ♠♥ t♦ t t r②♦♥ s♦tr♠♥♥♥ ♦r ♥ t ♣♦ss ♥♥ ♦ s♣♠♥t ♠ ts ♥ ts rs♣♦♥s tr rrt♦♥ ♥ r♦♥s ♥ rr ♦t

♦ t t ♦r ♣rs♥t ♥ ts ♣tr t ♦♣rt♥ss ♦ t sts s ♥ trrs ♣r♦♥ ♥r ♦♥t♦♥s ♥t♥st② ♦♠♣♦st♦♥ t♠♣rtr t s♠r t♦ t ♦♥s ①♣t t t ①♣r♠♥ts rsts♦ ts ♣rtr rrt♦♥ tst t♦tr t t ♦♥s ♦ t ♣♥ ♦ srtr③ ♥ t ♦♦♥ ♣tr ♣rs♥t tr ♥ ♣tr

♦♠♣r♥s ♦ t s st♦♥rtr③t♦♥ ♣r♦r ♣♣t ♥ t r♠♦r ♦ ts tss ♦r s ♥ ♥ t r♠ ♦

s r r♦♥s rs♣♦♥s ♥♥

rs♣♦♥s ♦ ♦s♠trs t♦ r ♣rts s ♥ ② st ♦rs♣ ♣♣t♦♥s ♥ ts t rs♣♦♥s ♦ t s t♦ r ♣rts ♠♥②tr♦♥s ♥ ♣r♦t♦♥s ♥ t ♥r② r♥ ❱ r ♦ ♥trst ❬❪ s sss♥ ♣tr ♥ t s ♦ t ①♣r♠♥ts t ♣rt s♣tr r ♦♠♥t② r ♣rts ♥ t ❱ r♥ ♥ t ♦tr ①♣r♠♥t r♦♥s ♦r♦r♠♦♥ t♦r t ♥trt♦♥ ♣♦♥t t r ♣rt s♣tr st t♦r r♥rs ♥ t ❱ r♥

r♥t r ♣rts ♥trt♥ t ♠ttr ♦s ♥r② t rt① tt s ♥ ② t t♦ qt♦♥ ❬r♦❪ t rt♥ ♥rs r♥t♦r ♣rt t②♣ ts rt r ts ♠♥♠♠ tt s r♦♥ ❱·♠2♦r t ♠♦rt② ♦ t ♠trs s ♦r ♣②ss ♥ tr♦♥ ♣r♣♦ss ♣rts♥ s ♥ ♥r② ♦♥t♦♥ r s② ♥♠ ♥♠♠ ♦♥③♥ Prts ♦r PsPr♦t♦♥s t ♠♦♠♥t r♥♥ r♦♠ t♦ ❱ ♣♦♥s r♦♠ t♦ ❱ ♥♠♦♥s r♦♠ t♦ ❱ r ♦r ①♠♣ ♥ ts ♦♥t♦♥ ♥ s♦ ① ∼ ❱·♠2 ♥ t② ♣ss tr♦ tt♦r ♠trs t r ♥t ♥rsts rt ♥ ♣rt② ♦♥sr ♦♥st♥t ♣ t♦ ♦t ❱ ♦r ①st② ♥rss s ♦ rtst ts t♦ s tt r ♦sr t♦ ❱·♠2

♣♥♥t② ♦♥ t ♥r② r ♣rts ♠② rrr s rt♦♥s ❳r②s γr②s ♥ st tr♦♥s r ♦ rt♦♥s Ps rs♦t ❱µ♠ t② ♣ss tr♦♦t s♠♦♥t♦r tr♦r t②♥ ♦♥sr s r② rt♦♥s ♦r♦r s♥ ♦♥② s♠ rt♦♥♦ ts ♥r② s tr♥srr t♦ s♦♥r② ♣rt ♣r ♥t ♥rr♦ ♦♥s tr s♥rt ♦♥ t ♣t ♦ t ♠♦♥ Ps ♦r♥ t♦ t s ①♣♥ ♥ ♥ tr♦♥♦ ♣rs r ♥rt ② ♦♥③t♦♥ ♥ ♥rr♦ r♦♥♥♥ r♦♠♥t♦♥ ts ♥ t s♥st ♦① ②r ♦ t s s ♥♣♣r s ts r ♠ ♠♦r ♠♣♦rt♥t ♥ s r ♦♣rt t ♦tr ③r♦ s ♠♦ s ♥ t s ♦ t ①♣r♠♥ts ♦r tsrs♦♥ t rs♣♦♥s ♦ s t♦ Ps tt rq♥t② ♣♦♣t t rt♦♥♥r♦♥♠♥t s ♣r r♦ ♥ ts tss ♦r

rtr③t♦♥ ♦ ♦s♠trs

r s s♥stt② t♦ Ps s♣♦♥s ♦ s t r♥t ♦①t♥ss ♥ t ♣♦t t γr② rs♣♦♥s ♦r t s tox µ♠ ♥ tox µ♠ ♥ µ♠ s♣♣ ② t ♣r♦r ♥ ♦♠♣r t♦ t♦♥s ♠sr ♦r Ps s♣♦♥s t♦ t ♥ t ♥r♦♥♠♥ts ①♣♦s t ❱G ❱

♥t ♦s♠trs ♦ r rrt ♥ t ❱ ♣r♦t♦♥♠ ♦ t t② ♥ ♥ t ♥r♦♥♠♥t ♦ t t② ♥ ♣♥ π ♦ ♥rs r♥♥ r♦♠ t♦ ♦t ❱ r s♠t♥♦s② ♣rs♥t stsr♦♠ ❬❪ ♦t♥ ♥ ❱ ❱ ♣♦st ♣♦♥s ♠ ♥ t♦ t ♣rs♥t rsts

s♦s t rs♣♦♥s ♦ tr ♦s♠trs t tr r♥t tox t♦Ps ♦♠♣r t♦ t s♣♣rs rr♥ γr② rs♣♦♥s rs ♠sr s ♥ ♣r♦ t ♥t ♣r♦ss ♦♥t♦♥s ♣rt ♦r t t♥ss♦ t s♥st t ②r ♦r t t♥♥st ♦① ♦r r ♥ t①♣r♠♥t ❱ ♣r♦t♦♥ t ♦♦ t rr♥ r t♥ t ①♣r♠♥trr♦r ♦r t ♥stt r♥ ♦r t ♥tr♠t ♦① tox µ♠ tr ♦ ② t t strt t♦ r r♦♠ t rr♥ r ♥②♦r t tr ♦① µ♠ t ♣♦♥ t s♦ r rs♣♦♥s r② r♦♠ ② ♥ t♦ ② r t ♣♦♥ s♥ rst s ♦r ② t♦r t rs♣t t♦t γr② ♦♥

s ①♣r♠♥t t ♣r♦ ♦ t ♥♥ r♦♠♥t♦♥ t♥ t SiO2

②r ♥ t t s rs♣♦♥s ♥ r② ♥r♥ t ♥♥ ♦ t t♦① t♥ss ♦r s♥s♦rs ♠ t t s♠ ♣r♦ss t r♦♠♥t♦♥ ts♣♣r t ♦ ♦r t ♦①s ♥ ts ♦♥t♦♥s ♥ t t tr t♥t t ♦① r② rt② ♦r rrt♦♥ ♦♠s q② t♦♦ t♦♣r♥t ♦♥③t♦♥ ♣rs r♦♠ r♦♠♥t♦♥

tr♣♣♥ ♣r♦t② Pt ♥ ♥ q s♦ ♣♥s ♦♥ t ♠♥tr♥♣r♦ss ♦ t s♦♥ ♦① ②r s s♦♥ ♥ r t rs♣♦♥s ♦ t tox µ♠ ♥ t ♥r♦♥♠♥t s ♥ ♣♦tt ♥ ♦♠♣rt t γr② ♦♥ ♥ t ♦s ♣♦st♦♥ ♥ t tr♥sst♦r ♦① s r♥ ②t P ♦♠♣♦♥♥t ♦ t rt♦♥ s ①t♥s② ①♣♥ tr ♦♥ ♥

s rtr③t♦♥ ♣r♦r t

♣tr ♥ t s♥ ♠sr ♥ strts t♦ tr♦♠ t rr♥ ♦♥ r② t ♦ ② ♦r t tr ♦① ♦ s tr♥r ♠rrs ♥ t r strt t r ①♥ ②

♥t s ♥② t s ♦ t tox µ♠ rrt ♥ ♥ ♣rs♥t ♥ ♦ P s s♦s rs♣♦♥s ♦r ❱♣r♦t♦♥s r② r ♦ t♦r t ♦s ♦ ②

♦ ♥♥ ♠♦♥strts tt r♦♠♥t♦♥ ts t♦ t♥ ♥t♦♦♥t ♥ t ♥tr♣rtt♦♥ ♦ t s♥ ♠sr t ♥s s s ♥ rt♦♥ s t♦ ts ♥ t♥ s② ♥t♦ ♦♥t ♥ trt♦♥ ♥r ♠sr♠♥t s ♦♠♣♦s ② s♥ ♣rt t②♣ ♥ t s ♦t ①♣r♠♥ts t r rs♣♦♥s t♦ ♥♥ r♦♠♥t♦♥ ♠ ♠t♥ t♦r r s♦t♦♥s ♥ ♣r♦♣♦s t♦ ♦♥t ♦r ts t ♥♠②

♣r♠tr③ t s rs♣♦♥s rs t♦ Ps ♥ ♦rr t♦ ♦rrt t ♠srs♥

♣♣② s ❱G 6= ❱ r♥ rt♦♥ ①♣♦sr

s s t t♥ ♦① ②rs ♥ ♦rr t♦ r t r♦♠♥t♦♥ ts

rst s♦t♦♥ ♠♣s ♥t♥s rrt♦♥ ♠♣♥s s ♦♥ ♣rt♦♥s r♦♠ t♦♥t r♦ s♠t♦♥s ♦ t ♥♥♦♥ rt♦♥ ♥r♦♥♠♥t tt s t♦ ♠sr s♦♥ s♦t♦♥ s s ♦♥② ② ♠♥ t r♦t rtr② ♠♦r ♦♠♣t♦r♦r t srs ♦ rrt♦♥ tsts t s s rqr t♦♣r♦ t t♥ss ♦ ts s♦t♦♥ ♥ t rt♦♥ s trs♦t♦♥ ♣♣rs tr♦r t ♠♦r ♣♣r♦♣rt ♦r t ♠sr♠♥t ♦ ♥ ♥♥♦♥♠① rt♦♥

t s t♦ ♥♦t r tt t t③t♦♥ ♦ t♥♦① s ♦♥t ♦ t♦ ttrt♦♥ ♦ss t r② s♥stt② ♦r ♥ t ♦♥t♦♥s ①♣t t t ①♣r♠♥ts ts ♦s♥t r♣rs♥t sr♦s ♦♥str♥t s ①♣♥ tr♥

s rs♣♦♥s t♦ ♥r② ♥tr♦♥s

s ♠♥t♦♥ ♥ ♣tr ♥r② ♥tr♦♥s ♣rs♥t r②r ♥ trt♦♥ ♦ t ①♣r♠♥ts ♦s t♦ t ♥trt♦♥ r♦♥ ♥ ♥t♥s♥tr♦♥ r♦♥ ∼ 1013 − 1014 cm−2/y s ①♣t t♦ ♦♥ t ① ♦ rr♦♥ ♦♠♥ rt② r♦♠ t ♥trt♦♥ ♣♦♥t ♥ t ♦tr ♣rt ♦ t ①♣r♠♥ts♥tr♦♥ s ♦ ∼ 1010 − 1012 cm−2/y r ♥st ①♣t t♦ t ♠♥ ♦♠♣♦♥♥t♦ t rt♦♥ ♥r♦♥♠♥t

♥ rst ①♣r♠♥t ♣rs♥t ♥ ❬ ❪ s♥♥t r♥s ♥ trs♣♦♥s ♦ ♥♣ r ♥ ♣ s r ♦sr ♥ t♠① γ♥tr♦♥ ♥r♦♥♠♥t ♦ t t② ♥ ♣rtr t s r♦♠ ♦♥② ♥♣st ♥ ♣st ♣♥ s♦ r② ♥tr♦♥s♥stt② tt s ttrt t♦ t ♥tr♦♥ ♥trt♦♥s t t ♣♥ ♦ t

rtr③t♦♥ ♦ ♦s♠trs

ts ♦tr ①♣♦s s r♦♠ ♥ s♦♥st r ♥tr♦♥ s♥stts t t ♦♠♣t r♥t rs♣♦♥s ♦rs

♦r t ♦ ♠♥t♦♥ rs♦♥s t st② ♦ t s ♥tr♦♥ rs♣♦♥s ♦r Φeq r♥ s ♥ ①t♥ ♥ t ♥ ts st♦♥ ♥♥ ♦ t♣♥ ♥ st ♥tr♦♥ ♠ tr♦r r ss ♠♥②♥♥ t ♥trt♦♥ ♦ t s♥s♦rs t t ①♣r♠♥ts

①♣r♠♥t st② ♣rs♥t r s ♥ rr ♦t ♥ t ♣r ♥tr♦♥s♦r ♦ t t♦ ❯♥rst② ♦ ♦♥ ❯ sr ♥ tt♣r♦s ♣r ♥ ♠♦♥♦♥rt ♥tr♦♥ ♠ ♦ ♥ ♥r② ♦ ❱ ♥ t r② ♦ γr② ♦♥t♠♥t♦♥ ♥tr♦♥ rs♣♦♥s ♦ ♣s ♥ r ♦r♠ tox µ♠ ♥ tox µ♠ s ts ♥stts s t ♦♥ ♦ t s♠ ♣s ♦r t P♦②t②♥ P ss ♦ r♥tt♥sss s s♦♥ tst s ♥ ♦♥ ♥ ♦rr t♦ s♠t t ♣s ♣st♣♥ rsts ♦ ts ①♣r♠♥t s ♥ ♦♠♣r r t♦ t ♣rt♦♥s ♦ ♦♥t r♦ s♠t♦♥ s♥ t ♣ ❬♦❪

①♣r♠♥t st♣ ♦r t ♥tr♦♥ rrt♦♥

s♠♣s r ♠♦♥t t t s♥s♥ sr ♣r♣♥r t♦ t ♠ ♥①♣♦s t♦ ① ♦ ×1013 cm−2 · h−1 ♦rrs♣♦♥♥ t♦ t♦t ♥tr♦♥ ♥ Φ♦ ×1014 cm−2 ♠t ♥ ♦rs ♦ rrt♦♥ r t rrt♦♥ s♣♦t ♦ ♠ rs s ♦r t sr ①♣r♠♥t t ♠ ♥t♥st② r s♠♦♦t② ②♦t

♦r t♥ Pr♥t rt ♦rs Ps ♦ ♠2 r ♦♥t♥♥ s① r s r ♣r♦ ♥ ss♠ s s♦♥ ♥ s① str ♥ tr r ♠♦♥t ♥ ♥ r ♦ sqr ♠♠trs ♥♦♥ ♦r♥r ♦ ♠ts sqr s ♥t ② ♥ r s t♥ t♦♣♦st♦♥ t ♦r Ps t t s♠ st♥ r♦♠ t ♥tr ♦ t ♠ t♦ rs♣♦♥s ♦r t ♦s♠tr srs r ♦♥② ② ♣r♥t ♣r♦♥ ♦♦ r♣r♦t② ♦ t ♠sr rsts

♥ ♦r s ①♣♦s rt② t♦ t ♥tr♦♥ ♠ t ♦tr tr r♦r t ♣♦②t②♥ P ss ♦ r♥t t♥sss ♠♠ ♠♠ ♥ ♠♠♥ ♦rr t♦ s♠t r♥t ♣st ♣♥ t♥ r♥ t ss♠②s♦s t♦ P ss r② ♣♦st♦♥ ♦♥ t♦♣ ♦ t♦ Ps rt ♥ s ♥ t♥♦r P ss♠② ♦ ♦r ♦rs s ♥srt ♥t♦ t② ♦r ♥t♦ ♦ ♦ t♠♦♣ ♣♦②t②♥ P ♠♥s♦♥s ♦ t P ♦ ♥t t② r ♠ × ♠ × ♠ ♥ ♠ × ♠ × ♠ rs♣t② s

P ♠tr ♦♣ s ♥tr♦♥ s♥ ♦r t tt♦r t ❬P♦s❪ s s t♦ s sttr ♥tr♦♥s ♥rt ② ♥trt♦♥ ♦t ♣r♠r② ♥tr♦♥ ♠ t srr♦♥♥ ♠trs ♥ t rrt♦♥ r ②r♦♥ ♦♥t♥ ♥ P s s♦♥ ♦♥ ♥tr♦♥s t t♠ s ♣tr♥ t♠ t rt♦♥ 6♥α3 tt s ♥♦t ♦♠♣♥ ② ♠♠ r② ♠ss♦♥ ❬P♦s❪t♦ t ♠♠ r♦♥ ♣rs♥t ♥ t t② s r② ♦ ♦r t ♣rs♥t①♣r♠♥t ♥ ♥♣♥♥t tr♠♥t♦♥ ♦ t ♠♠ r② ♦♥t♠♥t♦♥ ♦ t ♠s ♥ rr ♦t s ♠sr♠♥ts ♦r ts s ❬❪ r tt

s rtr③t♦♥ ♣r♦r t

r ①♣r♠♥t st♣ s ♥st ♥ t ♠♥ t ♦ t ♦s♠tr ss♠② P st♥s ♦r t♠ ♦♣ ♣♦②t②♥ s s s♥ ♥st sttr♥tr♦♥s ♥ t ♠♥ ① s ♥ s♥ ♥ t ♦r rt♥ ♦r♥r ♦ ♠ts sqr ♥t ②

♥ t rrt♦♥ ♣♦st♦♥ t s♥s♦r r ♦s ♦ ② t♦ γr②s rt♦♥ ♦♥ ts ♠sr♠♥t s r♥s r t♥ ♥ ③r♦ s ♠♦r♥ rrt♦♥ t t ①♣r♠♥t q♣♠♥t sr ♥

s♣♦♥s ♦ r s t♦ t ♣r ♥tr♦♥ ♠

♦ ♦ t t♦♥ ♦ t ♥tr♦♥ rs♣♦♥ss rt♦♥ sr♥ t rs♣♦♥s t♦ ♠♠ rt♦♥ s ♥ s rs♣♦♥s t♦ 60♦ ♠♠r②ss t ♠♦st rq♥t② s rt♦♥ t♦ ♦♥rt t s♥ ♥t♦ s♦r♦s ♦r t ♣rs♥t t♦♥ t ∆Vth rss ♦s rs ♦r ♠♠ r②s r♦t♥ ♦♠♥♥ t t ♦ ♥ rrt♦♥ rr ♦t t t t② ♥60♦ t ♣r♦ ② t ♠♥trrs

♥ ♥t♦ ♦♥t t ♠sr♠♥ts ♦ t ♠♠r② ♦♥t♠♥t♦♥ sr♥ t ♣r♥t st♦♥ t ♥ rs♣♦♥ss t♦ t ❱♥tr♦♥s r t s ♦♦s ♥tr♦♥ s♣tr♠ ♦ t ♠ ❬r❪ s♦ t t s♦r ♦♥③♥♦s t♦rs df (E) s♠t ♦r t♥ s♠♦♥t♦rs ♥ s♠r ♥r② ♥tr♦♥ ❬❪ rst♥ ♥ ♥ r df (E) ♦×10−12 Gy ·cm2 ♥ ts ② t ♠t t♦t ♥tr♦♥ ♥ ♦ ×1014 cm−2

s ♦♥rt ♥t♦ ♦s ♥ ♦♥ ♦ ♦t ②❯s♥ t ♣r♠tr③t♦♥ ♦ t ♠♠r② rs♣♦♥s ♥ t ♠sr ♠♠

r② r♦♥ t ①♣t st ♦ t trs♦ ♦t t♦ ♠♠ r②s ♦rt ♥ t s r t ♦r r♥ ② strt♥ts s r♦♠ t ♠sr trs♦ ♦t st ♠sr ♥ t ♠ t s♣♦ss t♦ ♦t♥ t rs♣♦♥s t♦ ♥tr♦♥s

♥ t ♠rrs r t ♥tr♦♥ rs♣♦♥ss ♦t♥ t t ♦ ♣r♦r♦r t r s ♦r ♦♠♣rs♦♥ s♦ t ♠♠ r② rs♣♦♥ss ♦ t s♠s ♥ ♣♦tt s ♥s ♦tt ♥ ♦r s♦ ♥ ♦r rs ♦ r ♣♦tt s ♥t♦♥ ♦ ♦t s♦r ♦s ♥ ♦♥ ♦r ①①s ♥ t♦t ♥tr♦♥ ♥ ♣♣r ①①s s♠♠r③s t♥ t ♠sr

rtr③t♦♥ ♦ ♦s♠trs

r s♣♦♥ss ♦ r s ①♣♦s t♦ t ❱ ❯ ♥tr♦♥♠ ♠rrs ♦♠♣r t♦ t ♠♠ rs♣♦♥s ♥s ♦♣♥ t ♣♦♥ts rrt♦ s t ♦♥s r rrr t♦ s♠♣s t ♣♦tt s♥t♦♥ ♦ ♦t s♦r ♦s ♥ ♦♥ ♦r ①①s ♥ t♦t ♥tr♦♥ ♥ ♣♣r①①s s ①♣♦s ♥ ③r♦s ♠♦

s rtr③t♦♥ ♣r♦r t

♦ ♦sr♥ ♦sr♥ ② ②

♠❱② ♠❱②

♥tr♦♥

♠♠

♦ ♦sr♥ ♦sr♥ ② ②

♠❱② ♠❱②

♥tr♦♥

♠♠

tr♦♥ s♥stts ♦ r s s ①♣♦s ♥ ③r♦s ♠♦

s♥stts ♠❱② ♦r ♦ t♦ ② ♥ t♦ ② ♦ss ♦r ♠♠r②s ♥ ♥tr♦♥s

s ①♣r♠♥ts ♦♥r♠ t ♦trs ♣rt ❬❪ ♥ ♠♦♥strt ❬r♦❪ ♥♠② tt t ♥t ♥② ♦♥③t♦♥ s rst♥ t ♦① ②r tr t ♥tr ♦ t ♣rt rss t ♦r ts ♥ s♦♥ ♥ t ♣r♦s st♦♥ tt s rs♣♦♥ ss t♦ ♣rts ♥ ♥r ♥r② r♥sr s s ♥♦♦♥ ♣r♦t♦♥s ❬❪ ♥stt② t♦t ♥tr♦♥ ♠ ♥ ♠❱ ♣r ♥t ♦s s t st t♠s ♦r t♥ s♥stt② t♦♠♠ r②s ♥ t ♦ ♦s r♥ ♣ t♦ ♦t ② t rt♦♥ s ♥ ♠r rt♦♥ t♦rs ♥ t ♦rr ♦ ♦t t♦ ♥ r♣♦rt ♦rs♠r ♦s r♥s ♥ ♦tr ♦rs ❬r♦ P❪ ♣r♦ts ♦ ♥♣ ♥ ♥α rt♦♥s s ♦ t rqr t♦ ♥♥ r♦♠♥t♦♥s rst t ♥♠r ♦ ♦s tr♣♣ ♣r ② ♥ ♥ t s♥ ♥ ♠❱♣r ② s r

♦ stt♠♥ts ♥ r t♥ ♥t♦ ♦♥t tt ♥ t t ♦① ♦t s ①♣♦s ♥ ③r♦s ♠♦ t tr r♦ss t ♦①②r t♦ t ♦r ♥t♦♥ ♣♦t♥t ❬❪ s ♦t t♦r ♦r t rs♣t t♦t s t s ♥ ♠♦♥strt ❬r❪ tt ♥ t ♦① t ss♥stt② s ♣r♦♣♦rt♦♥ t♦ E0.7 ♦ ♥ ♦r stt♦♥ t rt♦♥ t♦r rt♦ ♦s♥stts t♦ ♠♠ r②s rss ♥tr♦♥s ♦r t s s ①♣t t♦ t♦r 20.7 ∼ r t rs♣t t♦ t s♠♣s s s ♥ ♦♦ r♠♥t tt ♠sr♠♥ts ♣r♦r♠ r ♦♥ t♦ t s t r♥t ♦① t♥sss s t s s♦♥ ♥ q

Ratio γ

n(NMRC)

Ratio γ

n(REM)

∼ 1.6

♥♦t r♥ t♥ ♥tr♦♥ ♥ ♠♠ rs♣♦♥ss s ♣♦tt ♥ st r♥ ♥ r s♣ ♥r t r♥t t②♣s ♦ rt♦♥ ♦r t st♥♥r ♦① t s♦t trs♦ ♦t sts ♦r ♥tr♦♥ ♥ ♠♠ r②s r♦♥② st② r♥t ♦r ♦r t s t ♦① t rs♣♦♥s r

rtr③t♦♥ ♦ ♦s♠trs

r s♣♦♥s ♦ s t♦ rrt♦♥ ♥ t ts ♦ t ❲t ♠♦♥ ♥ tr♥ ♠rrs t rs♣♦♥s ♥ t ♥ ts ♥ ♣♦tt rr ♠rrs r ♥st t rt♦♥ r s♣♣ ② t♠♥trr

♦r t ♥tr♦♥s strts t♦ strt rr t♥ ♦r ♠♠ r②s ♥ t rs♣♦♥s ♦ ② s ♥r strt♦♥ ♥ ♣r♦♣r ♦♥rs♦♥ ♦ ♥ t♦ ♦s ♦ ①♣trs r♦♠ t t♦ t②♣s ♦ rt♦♥ t♦ ♦♥ qt ♦s② s♦ tr s ♥♦ ♦♦s♠♥s♠ ♦r t ♠s♠t

♣♦ss ①♣♥t♦♥ ♦r r♥s ♥ r s♣ s ♥ t ♣r♦s ♦ ♦①tr♣♣ r ♥ t ♦r ss s ♣r♦ ♥ ♠♦ ♦r ①♠♣ ② t♥tr♦t♦♥ ♦ ♥ rt♦♥ ts ♥ 2 ② ♥tr♦♥ ♥s r♥s ♥r ♣r♦ t♦ r♥s ♥ t ♣r♦ ♦ t ♥tr♥ ♥ tr♥ ts ♣♣②r♥t rstr♥♥ ♦rs ♦♥ tr♦♥s tt♠♣t♥ t♦ t ♦① ♥ t t♥♥r♦① ♦ t s ts t ♦sr tr s ts ♥t tr s× r r② t s ♦ s ♦r ♥tr♦♥ ♦s♠tr② t ♦s rqrsr rt♦♥

♦r t s tr ♥tr♦♥ s♥stt② s ♥ t ♥ t ♠①γ♥tr♦♥ ♦ r s ♥ ①♣♦s t♦ Φeq ♦×1012 cm−2 ♥ t♦ ♦ ♦t ② t♦ tr r② t t♦① ②rts s ♣r♦ r② s♥stt② ♦♦ ♣♦t ♦ tr ∆❱th ♥t♦♥♦ t ♦r s♦s tt ∆❱th rs ♥r② ♣ t♦ ♦t ② t♦ t s st♣♦ss t♦ ♠sr ♥rss ♦r r ♦ss ∆❱th ♦♠s str♦♥② s♥r♠♦♥ q② t♦r strt♦♥ ♦ ② rsts ♦ ts rrt♦♥ tst ♥ ♣♦tt ♥ r t ♠sr ♥ ♠♦♥ ♠rrss ♥ ♦♠♣r t♦ t γr② rt♦♥ rs s♣♣ ② t ♠♥trr rr ♠rrs

s rtr③t♦♥ ♣r♦r t

r s♣♦♥ss ♦ t ♥ s ♦r t r♥t P ss s ♦r t ♦♠♣rs♦♥ ♦ ts ①♣r♠♥t rsts t t s♠t♦♥s♥ t ♣trs t s♥s r ♣♦tt s ♥t♦♥ ♦ t t♦t ♥tr♦♥ ♥ ♦♠♣rs♦♥ t♥ r ♥ P ♦r s ♦♠♣rs♦♥ t♥ r ♥ P ♦r s s ①♣♦s t ❱G ❱

♥ t r♥ ♠sr ♥ t rrt♦♥ tst t rs♣♦♥s ts ①t②t rt♦♥ r ♥t♥ tt t s ss♥t② s♥st ♦♥② t♦ t ♣♦t♦♥♦♠♣♦♥♥t ♦ t rt♦♥ ♥ ts ♥tr♦♥♥s♥st s s ♥ r♠♥tt t t t t r ①♣♦sr t ♥tr♦♥ ♦♥trt♦♥ t♦ t ♦♥③♥ ♥ st♠t r♦♠ ❬❪ t♦ t♥ t♥ t ①♣r♠♥t rr♦r tt ts t ♠sr♠♥ts ♥ t♦♥ t♦ tt s ♦ ♦♥tr♦♥ rrt♦♥ s ♥ ♣r♦♥ t♦ ♥♦t ♥ ♥② ♠sr ♥s ♥ t ds❱gs

rtrsts tt ♦ t ts s♥ ♦r r♦♠ t ♣r γr② rs♣♦♥ss ♦♥ ♥ ❬♦❪ ♥ rts t tr♥

P♥ ♥♥ ♦♥ rs♣♦♥s

t ♦r t P ♦r s♠♣s r trt s ♦r t r s♠♣s ♣rs♥t♥ ♥ ♥ t rs♣♦♥ss ♦ t ♥ s ♦r t r♥t P ss ♦ ♥rs♥ t♥sss r♦♠ ♠♠ t♦ ♠♠r ♣♦tt ♥ ♥r s s ♥t♦♥ ♦ t t♦t ♥tr♦♥ ♥

qr ♠♦♥ ♥ tr♥r ♠♣t② ♠rrs r♣rs♥t ♥ ♦t ♣trs t Pss ♦ ♠♠ ♠♠ ♥ ♠♠ t♥ss rs♣t② ♦ ♦♠♣r t ♥♥ ♦ tss ♦♥ t s rs♣♦♥s t t ♦ t ♥♦r r s r s♦ ♣♦tt♥ t rs ♠rrs ♥② ♥ t s♥stt② ♥♥♠♥ts ♠sr♦r t s ♦r ② P ss t rs♣t t♦ t r s♠♣s r s♠♠r③ ♥ ♥♦② t t rt s♥stts ♦r ♦ ×1013 cm−2 ♥ ×1014 cm−2 t♦t ♥tr♦♥ ♥s r ♥

rtr③t♦♥ ♦ ♦s♠trs

♦ Φr♥ Φr♥

×1013 cm−2 ×1014 cm−2

♠♠ P ♠♠ P ♠♠ P

♦ Φr♥ Φr♥

×1013 cm−2 ×1014 cm−2

♠♠ P ♠♠ P ♠♠ P

tr♦♥ s♥stts ♦ r s s ①♣♦s ♥ ③r♦s ♠♦

Prt P t♥ss ♠♠ ♠♠ ♠♠

e− ×10−4 ×10−3 ×10−3

e+ ×10−5 ×10−4 ×10−4

p+ γ

♥♥s ♦ t ♣rt ①♣t ♥tr♦♥s ♥ ♦rr rt♦♥ r♦♠

s♠t♦♥s ♦r ♣s sts

♦ ♠♦ t ♥♥ ♦ t P s♦rrs t ♣rt ♣r♦t♦♥ r♦♠ ♣♦②t②♥ss s t s♥ t s♠t♦♥ t♦♦ ❬♦❪ ♥ t ♠♦ ♥tr♦♥♠ ♦ ♥♥ts♠ rs ts ♣r♣♥r② ♣♦②t②♥ ♦s ♦ ① ♠2 sr ♥ t sr t♥sss ♥ ♠ rt♦♥ ♥tr♦♥ ♥r② s r②♥♦r♥ t♦ ss♥ strt♦♥ ♦ t ♦ ❱ r♦♥ t ♠♥ ♦ ❱

s♦s t t rt ♥♥s ♦ ♣rts ①♣t ♥tr♦♥st r♦♠ t ♣♦②t②♥ ♥ ♦rr rt♦♥ s ♥t♦♥ ♦ s t♥ss st r ♦t♥ t sttsts s ♦♥ 8 ♥tr♦♥s ♥ ♦♥ t tr r♥tss

♥ ♥ t ♥♥♠♥t ♦ ♦s t♦ P ♦r s♠t♥ ♣♦②♠r ♣♥ s ② ♠♦♥strt P ss t s ♥tr♦♥ ♦♥rtr ♣r♦♥ r♦ ♣r♦t♦♥s t ♥rs ♣ t♦ ❱ ♦♥r♠♥ t♦r ♦ r♦♥♥r ♥ rr ♦r r♥t ♦① t♥sss ♥tr♦♥ ♥rs ♥♥s ❬r♦❪ s♠t♦♥ ♠♦♥strts tt t γ ♥ s ♦t t♠s ♦r t♥ t ♣r♦t♦♥ ♥ t tr♦♥♣♦str♦♥ ♣r♦t♦♥ s ♥♥ ts ①♣r♠♥ts t t♦♥ ♦ t P ss ♥ t r♥ t♦ ♠♠ ♥rss t♥tr♦♥ s♥stt② ♦♥ r ② t♦r ♦ ♦r t s ♥ ② t♦r ♦

s rtr③t♦♥ ♣r♦r t

♦r t s ♦r ♥s ♦r t♥ ×1013 cm−2 t r ♥st ♦sr r♥s ♥ t s♥stts ♦ t t♦ t②♣s r ♣♦ss② r♥ ②t r♥t r ♦ strt♦♥ ♦r t ♥♥♠♥t ♦ s♥stt② ②s r♦♥ t♦r ♦r ♦t s ♣♥♥ ♦♥ t t♥ss ♦ t P sss ♥♦t ①♣t ❲ ♣rts ♦r rt♦♥ r♦♠ t♦ ♠♠ trt♦♥s ♦sr r ♥st ♦r t s ♥ ♦r s♥①♣t ♦r ssts r♣t ①♣r♠♥t

s rsts ♥② ♦♥r♠ t ♣st ♣♥ s rs♣♦♥s ♦ t ♥♥♥tr♦♥ s♥stt② t s ♦♥ ♥ t s ♦ t s ♥ t ♠① γ♥tr♦♥ ♦ ♦r rtr ♥②ss s♥ ♠♦r rtr♣rs♥tt♦♥s ♦ strtrs ♠② r② ts ♣♣r♥t t ♦ s♥s♦r②rt♥ss ♦♥ r ② s♠t♦♥s s♦ s♦ s ♦♥ t r ♥tr♦♥s♣tr t ttr r② ♥ t s♣tr♠ ♦ ❱ ♣r♦ ② t ♥rt♦♥ st♠♥ts ttr r ♦r t t♥ss ♦ t P♦♥rtrs ❬♦r❪

tt② ♦ t ♦s♠tr ♥♦r♠t♦♥ s♦r♦♥ ♥♥♥ sts

stt② ♦ t ♦s♠tr ♥♦r♠t♦♥ ♥♥♥ ♦ t otit tr♣♣ r♦r t♠ s t ♠♦st ♠♣♦rt♥t ♣r♠tr tt s t♦ t t♦ r♥t r ♠sr♠♥ts t s ♦r t ②rs ♦ t ①♣r♠♥ts s♣♦♥t♥♦s r♦r② ♦ t tr♣♣ r ❬❪ ♦rs ♥ ♦♠♣tt♦♥ t t♣ ♦ r ♥ ② rt♦♥ ♥♥♥ ts ♦♥ t ♠♣♦② ♦s♠trs♥ tr♦r ♠♣♦rt♥t r♥ ♦t st♦♥ ♥ ♦♣rt♦♥ ♣r♦s ♦ t ①♣r♠♥ts

♥ t rst s st♦♥ t ♦ss ♦ s♥ ♥ s② tt ♥ ♦rrt♦r t ♦rt♦♠♥ ♣rt r♥ r♥ ♦♣rt♦♥ ♣r♦s ♥st s♣② ♥t s r ①♣♦s t♦ ♦ ♦srts t ♥♥♥ ♦ t tr♣♣ r ♦♥♦t t t rt♦♥ ♣ ♥ ♥ str♦♥② t t ♦s♠tr r② ♥ tsstt♦♥ t rs♣♦♥s r strts t♦ r r♦♠ t ♦♥ tr♠♥ ♥ t rt♦♥♣s s② rsts ♦ st rrt♦♥ r♥s ♦♠♥ s♦r ♦ rr♦r ♥ t ♠sr♠♥t ♥ ①tr♠ ss t ①ss ♦ ♥♥♥ ♥ ♥ r♥ t s s♥t♦ rs ♥ t s r ①♣♦s t♦ r② ♦ ♦srts ❬❪

tst♥ ♦ t s stt② ♦r t ♥♥♦t ♦♦s② ♦♥ ♦♥ tt♠s ♦ t ♠♥ ♦♣rt♦♥ ♦r ts rs♦♥ ♥ rt tst♥ ♣r♦rs rqr t♦ t t s ♦r ♥ ♦rr t♦ tr♠♥ t stt② ♦r t ♣♣t♦♥ ♣rt♦♥ ♠t♦ s ♥ ts ♣tr s s ♦♥ t ♠sr♠♥t ♦ ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ❬s❪ s t♥q ♦♥sr♥♦♥② t ♦①tr♣♣ r ♥ t tr♠ ♥♥♥ ♦ t ♦♥ssts ♥ ♠♣t②♥sq♥t② rt♦♥ ♦ t ts r♥ r ♥♥♥ ♣r♦ t ♥r♠♥t t♠♣rtrs ♥ t s ♥ ♠♦♥strt ♥r rt♥ ♦♥t♦♥s t♦ ♦ ♣rt♦♥♥ ♦rs ♦ t ②r t♠s ♥♥♥ ♦ rrt s ❬❪

s♦r♦♥ ♥♥♥ sts rr ♦t ♦r ♥ ts ♦r r ♣r♦r♠ s♥ t♠♣rtr st♣ strs ♥t♦♥ ♥ s t♠ ❬❪ ♦ s

rtr③t♦♥ ♦ ♦s♠trs

s ♣♣ r♥ rrt♦♥ ♥ ♦♦♥ s♦r♦♥ ♥♥♥ ❲♥ ♣♦ss t♥♥ ♦♠♣♦♥♥ts r ♠♦♥t ♦♥ ♠t ♣♥s t t ♠ t♦ ♠①♠③ ttr♠ ①♥ r♥ t t♥ ♥ ♦♦♦♥ st♣s tr ♥♥♥ st♣t s♥ r♦♠ t s Vth s ♥ ♠sr ♥ ts ♥♥♥ rt♦♥

UF =Vth − Vth(♦r rrt♦♥)

Vth(tr rrt♦♥) − Vth(♦r rrt♦♥)

s s t♦ q♥t② t ♥♥♥ ♣r♦ss r♦♠ t s♦r♦♥ ♥♥♥ r rtrsts t♠♣rtrs ∗ ♥ t♥ ①trt s s t ♣r♦♣♦rt♦♥ ♦ ts♥♥♥ t ♥ t♠♣rtr ❬❪ ∗ ♦rrs♣♦♥s t♦ tr♥st♦♥ t♠♣rtrsss♦t t♦ r♥t tt♦♥ ♥r② s ❯s♥ t tt♦♥ ♥r② s t r♦♠ ∗ t s t♥ ♣♦ss t♦ t t ♥♥♥ ♦ ts t ♥② t♠♣rtr♦r ♥② t♠ t♦t ♣r♦r♠♥ s♦tr♠ ♥♥♥ ①♣r♠♥ts

♥ t ♣rs♥t st♦♥ t s♦r♦♥ ♥♥♥ ♦rs ♠sr ♥ t r♥trt♦♥ s ♦r t ♥ s r sss ♥ ss ♥t♦♥ t♦ ♥t② t ♦♠♣♦♥♥ts tt t stt② rqr♠♥ts ♦r t ①♣r♠♥ts

rrt♦♥s ♦ t ♦♠♣♦♥♥ts ♥②③ ♥ ts st♦♥ r ♣r♦r♠ tγr②s ♥ t ❱ ♣r♦t♦♥s ♦ ♥ ♥ t s♦♥r② rt♦♥ ♥r♦♥♠♥t♦ tt ♦♥ssts ♦ ♥r② ♣♦t♦♥s r♦s♣tr♠ ♥tr♦♥s ♥ r♣rts ♥ t ❱ ♥r② r♥ s ①♣♥ ♥ t t rrt♦♥ ♣♦st♦♥s ♦r t ♣rs♥t ①♣r♠♥ts ❩ ♠ ♥ r ♠ t ♦♥trt♦♥ ♦r ♣rts s ②s t♦ ♦rrs ♦ ♠♥t ♦r t rs♣t t♦ t ♥tr♦♥s♦♠♣♦♥♥t ts sss♥ t t r♦r ♥ ♦♥② ♥tr♦♥ ♥s q♦t ♥ t ♦♦♥

s♦s tr ①♣r♠♥t ♥♥♥ rs ♥ t ♥r ② r♥ ♦r t ②♣ tox µ♠ s ①♣r♠♥t t ♦♦♥rrt♦♥s t r♥t ♥ ♦ ♣rts s♦ t s♠ ♦r t r st②sst② tr♣♣ ♣ t♦ ♥ t♥ strts s♠♦♦t② t♦ r♦r t t♠♣rtrs♦s t♦ t rt♦♥♥ r ♣ s ♥ ♦♠♣t② ♥♥♦r♥ t♦ ❬ s ❪ ts ♦r ♦rrs♣♦♥s t♦ ♦♥st♥t r♦r② t♦ t tr♠ tr♣♣♥ ♦ t Qot s ♥t ♣♦st s♦r♦♥ ♥♥♥rs ♦r t ♦tr strtrs ♣rs♥t ♦♥ t s♠ ②♣ t tox µ♠ s♦ s♠r ♦rs

♠r rsts r s ♦r t P s♦♥ ♥ tr♣♣r ♦s♥t strt t♦ r♦r ♦r t♠♣rtrs ♦r t♥ ♥ t t ♠①♠♠t♠♣rtr r ♦♥ t ♣rs♥t ①♣r♠♥ts ♦ t r sst② tr♣♣ ♥ t ♣r♦♥ tr tr♣♣♥ ♣t② q ♦rs ♥ ♠sr ♦r t s P ♥ P r t r strts t♦r♦r ②s t♥ ♥ ♦r ts s s♣♣ ♥ ♣st ♣rrrs t rrt♦♥ ♥ ♥tr♦♥ s ♥♦t ♥ ♣r♦r♠ ♥tr♦♥t♦♣r♦t♦♥ ♦♥rs♦♥ ♥ ♣st t♦ ♥ ♥♥ ♦ t ♣♦s ♦s t t♦ q♥t②♥ tr♠ ♦ ♦s s s♦♥ ♥ ♦r ts rs♦♥ ♦♥② t ♦r γr②s ♥ ❱ ♣r♦t♦♥s ♥ ♠sr

s♦s t rsts ♦ t tst ♣r♦r♠ ♦♥ t s r ts♦r♦♥ ♥♥♥ rs ♦r γr②s ♥ ♥ ♠① s t ♦ ♦ss s♦ ♥s

s rtr③t♦♥ ♣r♦r t

r ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r ②♣ stox µ♠ ①♠♣s ♦ ♠sr s♦r♦♥ ♥♥♥ rs ♦♦♥ rrt♦♥ tγr②s sqr ♠rrs ♥ t ♠① r♦♥ ♦ rr ♠rrs ♥ ♥ t ❱ ♣r♦t♦♥ ♠ ♦ tr♥r ♠rrs

r ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r P s ①♠♣s ♦♠sr s♦r♦♥ ♥♥♥ rs ♦♦♥ rrt♦♥ t γr②s sqr ♠rrs ♥♥ t ❱ ♣r♦t♦♥ ♠ ♦ tr♥r ♥ rr ♠rrs

rtr③t♦♥ ♦ ♦s♠trs

r ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r s ①♠♣s ♦ ♠sr s♦r♦♥ ♥♥♥ rs ♦♦♥ rrt♦♥ t γr②s r♥t sqr ♠rrs♥ t ♠① r♦♥ ♦ rr ♠rrs ♥ ♥ t ❱ ♣r♦t♦♥ ♠ ♦ tr♥r ♠rrs

♦rs γr② r ♠sr tr ①♣♦sr t♦ ② s♦s ♥ t♦♥rt♦♥ t♥ ♥ ♦r♦r tr ♣r♦ ♦ r♦r② ♣ t♦ ♥ t ♥ ♣rt ♦ t s♦r♦♥ ①♣r♠♥t t rs strt ♥ t♦ r♥ t s ♦ t r♦♥ rrt♦♥ ♦r ♦ ② ♦♥ ♣rt ♦♥t♥♦s②rs ♦r t ♥stt t♠♣rtr r♥ t♦t s♦♥ ♥② r♦r② s♥s ♥t s r rt♦♥ ♥s ♦r r♥ ♥♥♥ ♠♦r ♦♠♣①♣♥♦♠♥ t♥ t tr♣♣ r r♦r② s tr♦r t♦ ss♠ ♦rt s♦ ♣♦♥t ♦t tt ♥ t s ♦ t ♦♠♣♦♥♥t rrt ♥ tΦeq ss♦t t♦ t s♦r s t♦♦ ♦ t♦ ♠ ts ♣♦ss ♥♥ ♥♥♥② ♦tr rt♦♥ t ♠♥s♠ t♥ rtr♣♣♥ ♣♥♦♠♥ ❬❪

♥ t s ♦ t s t s♦r♦♥ ♥♥♥ ♥♥♦t s t♦ ①trt♣r♠trs tt ♦ t♦ ♣rt t ♦♥tr♠ ♦r t r♦♦♠ t♠♣rtr r♥ t t s♦r♦♥ ♥♥♥ ♠t♦ s s s sr♥♥ ♣r♦r t♦ ♥t② ts t tr♠ ♦rs t t♦ t s r ♦♥ ♦ts s ♥ t ♠sr ♦r ♥ ♥tr♣rt s r♥♥ ♦ ♦♠♣①♣♥♦♠♥ tt ♥ ♣② ♥ ♠♣♦rt♥t r♦ ♥ t ♦t♦♥ ♦ t tr♣♣ r ♦rt♠ s ♦♥sq♥ ♦ ts ts s ♥ ♥t t♦ ♣♦ss s♦r♦ ♣r♦♠s ♥ s ♦r ♦♥t♠ ♥ r s♦tr♠ ♣♣t♦♥s

♦r ♣r♠♥r② t♦♥ ♦ t s♥s♦rs t r tr♠♥ t♦ ∼ ② ♥ ♣r γr② ♥ ♥ ♣♦tt ♥ ♥ ♦♥srs ♥ t s ♦ t s ♦ ts s s♦ r② stt②♦ t tr♣♣ r t ♠sr ❯F ∼ ♣ t♦ ♥ t s♠

t♦♥ ♦ t ♦s♠trs ♦r t

r ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r s rrt ♥♠①r♦♥ ♠♣t② ♠rrs ♥ t ❱ ♣r♦t♦♥s ♠rrs r♦♥♠rrs♦♥t♥♦s ♥ r s♦s t s♦r♦♥ ♥♥♥ ♦r ♦ tt srrt t ♠♠r②s

s♦r♦♥ ♥♥♥ rs t r r s♦ s♦♥ t sss♦♥t♥ ♥t♦ ♦♥t ts s♦♥ t st ♥ tr ♥

♥② s♦r♦♥ ♥♥♥ rs r ♠sr s♦ ♦r t ♥ts s s♦♠ ♥s ♦rs r s♦ ♦♥ ♦r s ♦ t ♥♠r♦ s tst t t ♠♦♠♥t t s ♥♦t ♣♦ss t♦ r t♦♥ ♦ tss s ♦♥ t s♦r♦♥ ♥♥♥ t♥q

s♠♠r③s t rsts ♦ t ♣rs♥t s♦r♦♥ ♥♥♥ tsts ♦r♥ t♦ ❬s❪ ♥ t s s♦ rr s♦r♦♥ ♥♥♥ ♦rt s r tt t s♠ ♥t r s tr♣♣ t♥ t 2 tr♥sst♦r ②r trt s♦rt ♥♥♥ t♠ t t♠♣rtr ♦r t ♦♥ ♥♥♥ t♠ t ♦t♠♣rtr r♦r s r ♦ ♠rt t ①♣r♠♥t s♦r♦♥ t♠♣rtrt t s♥ ♦ss s tr♠♥ ♥ st♠t♦♥ ♦ t s♦tr♠ ♥♥♥ ♥ ♦♥ ② s♥ t t♦r ♦ tr♠ rt♦♥ r♦r ss♠♥ ×107 s−1 ❬❪ t s ♣♦ss t♦ t t t♠ t ♥t r♥t ♥stt s r ①♣t t♦ ♦s ♦ tr s♥ rst♦ ts t♦♥ s ♥ r♣♦rt ♥ t st ♦♠♥ ♦

t♦♥ ♦ t ♦s♠trs ♦r t

rsts ♦ t ♣r♦s st♦♥s ♥ s♠♠r③ s ♦♦s

• ♣rs♥ ♦ ♣rts t t ①♣r♠♥ts sst t t③t♦♥

rtr③t♦♥ ♦ ♦s♠trs

tox sr r♥ ♥ q♥ ↔ tt②♣ µ♠ ♦r |UF | ∼ t

♥s ♣rt♦♥ ♥♦t ♣♦ss rr / ②r

P rr ≥ ②rsP rr > ②rsP rr > ②rs s ♠sr t♦♥ ♥♦t ♣♦ss rr → ∞

♠♠r② ♦ t s♦r♦♥ ♥♥♥ tst ♦♥ t ♥t s

♦ ♥s t♥ ♦① s µ♠ ♥ ♦rr t♦ ♦ ♥♥ r♦♠♥t♦♥ ts ♦r t r♥ ♦ ♥trst tt ①t♥s ♣ t♦ s♦♠ t♥s ♦ ②♥rs♥ t tox r rs♣♦♥s ♦rs ♠② ♣♣r tr rt♥ stt ♣♥ ♦♥ t ♦① ♣r♦t♦♥ ♣r♦sss

• rs♣♦♥ss ♦ r♥t ♦s♠trs ♦r t r♥ ♦ st♥tr♦♥ ♥s ♦ ♥trst ♦r t s♦ r s♥stt② ② t♦r ♦ trs♣t t♦ γr② rs♣♦♥s ♦r ♦ss ♣ t♦ ② t r t s s♦ ♦♥tt str♦♥ strt♦♥ ts ♥ ♣♣r ♥ t s t r♥tt ♦①s

• ♥ t ♥tr♦♥ rrt♦♥ tst t s s♦♥ tt t ♣rs♥ ♦ ♣st ♣s♠t ② ss ♦ ♣♦②t②♥ ♦♥ t ♠ ♥tr② s ♥ s♥♥t② ♥rs t rs♣♦♥s t♦ ♥tr♦♥s t♦r ♦ ♣ t♦ s ♦♥ ♥ ts ♦r ❲s r t♦t ♦ s ♥tr♦♥♥s♥st ♥tr♦♥ ②r♦♥♦s ♠tr ♥tr♦♥ s♥stt② s r r t♥ t s♥stt② ♦r♠♠ r②s ❯s♥ ♣♦②t②♥ ss ♦ ♥ ♠♠ t s ♦♥ tt ♥t t♥♥st ②r s s♥t t♦ ♥rs t s♥stt② t rs♣t t♦ t ♦♥♠sr ♦r γr②s

• ♦♥r♥♥ t stt② sts ♣rt ♦r t s ♥ t s ♦r ♦♠♣t st ♦ ♠sr♠♥ts s ♥♦t t♦tr s s♦ rr rt♦♥ ♦r ♦ t ♦s♠tr s♥ ♥ stst♦r② stt② ♦r ②rs t♠ s

r♦ss ♥ ts rsts t ♣♣r t♦ t st ♦r ♠♦♥t♦r♥ t ♠♦st ♦st ♥r♦♥♠♥ts ♦ t ①♣r♠♥ts ♥ t♦tr ♥ s t s ♥ ①♣♥ ♥ ♣tr t t♥♦① s t ♠♥♠♠ s♥stt② s ♠t s♦ tt ♥q ♥♥♦t s♥t ♦r ♣♣t♦♥s

♦r t ♦t♦♥s t t ①♣r♠♥ts r s♥stt② ♠sr♠♥t♠② r rqr r ♥r② r ② r♦♠ t ♥trt♦♥ r♦♥s rt♦♥ ①♣t ♥ ts ♦t♦♥s ♦♠♣♦s ♠♥② ♦ ♥tr♦♥s ♥ γr②s Ps ♦♥sttt s♠ r♦♥ r♦r t ♠t tr rr② ①

rtr③t♦♥ ♦ t

t t♥s ♦ ② ♦r ②rs ♦ ♦♣rt♦♥ ♠♦♥t♦r♥ ♦ ts ♥r♦♥♠♥t♥ s♦ ♣r♦r♠ t t ♦① r♦♠ t ♦ ♠sr♠♥ts t s tr♦r t st s t ♦♠♥s ♥ s♥stt② t♦tr t♥ stt② ♦r t♠

♥ t ♥①t t♦ st♦♥s ♦ ts ♣tr t ♥②ss ♦ ts t♦ s ♣rs♥t

rtr③t♦♥ ♦ t

rt♦♥ rs ♥ ♦♣rt♦♥ ♣r♠trs

s s♣♣ ② t ♦rt♦r② ♦ ♥②ss ♥ rttr ♦ ②st♠s ♥ r♥ ♥ rrt ♥ r♥t ♣rt s t t ♦ t♦ tr♠♥rt♦♥ rs ♥ t ♦♣rt ♣r♠trs t♦ s t t ①♣r♠♥ts ♦♥t♥s ♦♥② ♦♥ s strtr t ♥ ♦① t t♥ss ♦ µ♠

s s ♥ ♦♣rt t r♦t rr♥t ♦ µ s ♥t ② t♠♥trr ♦♦♥ ♠sr♠♥ts ♦ t ♣♦♥t s ♥t ♥ ❬♠❪❯s♥ t t s rr♥t t s♥stt② t♦ t♠♣rtrss♦t t♦ ∆Vth s ♥ t ♦rr ♦ ♠❱ s♦ tt s♥stt② ♥ t ♠② r♥♥ ♣r♦ s st② ♥rss t rrt♦♥ t♦ ♠❱ t ♦ ② t♠♣rtr ♥ rt♦♥s t♦ t ♦s ♠sr♠♥t r tr♦r ♣t♥ t ♦rr ♦ t t ♠①♠♠ ♦s ♦ ② ❬❪

♦ tr♠♥ t r♦t ♣r♦t♦♦ ♦r t rt♦♥ r♥s ♠sr♠♥ts ♦ trt♠ ♥stt② ♦r rt♣ s♦ ♥ ♣r♦r♠ ❬❪ ♦r ♥ ♥rrt t ∆Vth s ♥ ♦♥ t♦ ♥rs ♥ t r♥ ♦ ♠❱ r♦♠ t♦ s♦♥s tr t ♥t♦♥ ♦ t r♦t rr♥t tr ♦ ② ts ♥rss t♦ ♦t ♠❱ ♦rrs♣♦♥♥ t♦ ss t♥ t rs♣t t∆Vth r t ② s ♠sr s t♦tr t ♦tr ♥♣♥♥t rsts♦♥ ♥ trtr ❬♠❪ sst t♦ ♣r♦r♠ t r♦t ♦ t ∆Vth tr s♦♥ r♦♠ t strt ♦ t rr♥t ♥t♦♥

s♦s t rsts ♦ t r♥t rrt♦♥ tsts ♣r♦r♠ ♦♥ t ①♣♦s ♥ ③r♦ s ♠♦ t t ♦ sr r♦t ♣r♦t♦♦①♣r♠♥t t r♦♠ γr②s ❱ ♣r♦t♦♥s s s ♦r t♦ r♥t ♥tr♦♥♥r♦♥♠♥ts r ♣rs♥t ♦♦ ♣♦t ♦ ∆Vth s ♥t♦♥ ♦ t s♦s tt∆Vth rs ♠♦st ♥r② ♣ t♦ ♦t ② t♦ t s st ♣♦ss t♦ ♠sr ♥rss t r ♦ss ∆Vth ♦♠s str♦♥② s♥r ♠♦♥ q② t♦rsstrt♦♥ tr ② ts st ♦♥② st② s ♥

♦r ♦ss ①♥ ② s♦s tt t rt♦♥ rs♣♦♥s rs ♥♥ s♦♣ ♥ t r ♦ strt♦♥ ♣♣rs t♦ r♥t ♥r ①♣♦sr t♦ r♥trt♦♥ s t♦ ts ♥♥ ssts t♦ ♠t t ♦♣rt♦♥ r♥ ♦ ts t♦ ♠①♠♠ ♦ ② t r ♦ss ts tr s ♥ ♦♥ t♦ ♦ ♥trst ♥ t s ♦ t s t ①♣♥ tr ♦♥ ♥

t ①♣r♠♥t t ♥ t r♥ ② ♥ ♦♥♥♥t② tt tq t♦ ♦t♥ t ♦♦♥ ♣r♠tr③t♦♥

rtr③t♦♥ ♦ ♦s♠trs

r t♦♥ rs♣♦♥s ♦ s trs♦ ♦tst t µ s ♣♦tt rss t r♦t t♠ s ♦♠♣rs t♥ ♥ s ①♣r♠♥t 60♦ t ♣♦tt r ♦♠ r♦♠ t ♣r♦r ♥ r♦♠ ♦♥ rrt♦♥t t ♦♥t♣r ❯♥rst② ♥tr♦♥ t r r♦♠ t rt♦r t ♥r♦♠ t t② t ♥② t ❱ ♠ ♦ t t② s♥ s t♦ tr♠♥ ♣r♦t♦♥ t s ①♣♦s ♥ ③r♦s ♠♦

rtr③t♦♥ ♦ t

∆Vth = a × Db ta = 0.432 V/Gy

b = 0.9404for 10−2 Gy < D < 10 Gy

r② ♦ t ♣rs♥t t s ♦ ± ♣ t♦ ♦ss ♦ ② ♥ ♥ tr♥ r♦♠ t♦ ② ♠♦r rt t ♥ tr♠♥ q ♥ st s r rr♦r ♥ t ♠sr s ♦

♥♥♥ ♦r ♥ s♣♠♥t ♠ ♥ r♦♥

s♦r♦♥ ♥♥♥ sts rr ♦t ♦♥ t s ♥ r②♣rs♥t ♥ ♥ ts st♦♥ ts t rsss t ♣rtr♠♣ss t♦ t ♣♣t♦♥ ♦ t t t ①♣r♠♥ts s♦r♦♥♥♥♥ rsts s♦ ♦♠♣r r t st ♦ ①♣r♠♥t s♦tr♠ ♥♥♥ t r♦r ♦r ♠♦♥ts tr rrt♦♥ ♥ t s♦♥r② rt♦♥ ♥r♦♥♠♥t ♦ t t② t s

♦tt rs ♥ ♣♦tt t sqr ♥ tr♥r ♠rrs r♣rs♥ts♦r♦♥ ♥♥♥ ♦rs ♦r t♦ s rrt ♥ t ♠①r♦♥ t♦s s ♦ ② ♥ ② rs♣t② sss ♥ t s r st♦ r♠♠r tt ♥ t ♥♥♥ rs ♣rs♥t ♥ ts st♦♥ ∆Vth s ♥♥♦r♠③ t♦ ♥t② ♥ ts ♥♥♥ rt♦♥ s ♥ s t♦ q♥t② t ♥♥♥♣r♦sss ❬❪ s r② ♣♦♥t ♦t t t♦ s s♦ r♠r stt②♦ ∆Vth tt ♦s ♥♦t strt t♦ r♦r ♥t t♠♣rtrs ①♥ s♠r♦r s ♥ ♠sr r♦♠ tr ①♣♦s t♦ ② ♦ ♣r ♦♥③♥ ♠♠r②s r♦♠ ♦t s♦r r♦♥ ♠rrs ♥

t s ♣♦ss t♥ t♦ ♦♥sr tt ts rst tr ♠sr ♦rs r ♠♥② t♦ t ot ♥ it ♥♥♥ ♣♣②♥ t s♦r♦♥ ♠t♦ ♦♥ ts t stst s ♣♦ss t♦ st♠t r♦♦♠ t♠♣rtr r♦r② ♦ ∆Vth ss t♥ ♦r 4

♦rs t♥ ②s ×107 sec−1 s t♦r ♦ tr♠ rt♦♥ s ♣rt♦♥s ♥ ①♥t r♠♥t t ①♣r♠♥t t ♣rs♥t ♥ ❬♠ s❪ ♦rt s♠ s ①♣♦s t♦ t♥s ♦ ② ♥ ♣r ♦♥③♥ rt♦♥ ♥r♦♥♠♥t ♥tr♦♥ ♥ tt s t t ①♣♦s t♦ ② ♦s ♥♦t ① ×1011 cm−2♥ r♠♥t t ♣r♦s ♦r ❬♦❪ ts ♦ ♥tr♦♥ rrt♦♥ s ♥♦t①♣t t♦ ♥ ♥② ♠sr ♥s ♥ t ds❱gs tr♥sst♦r rtrsts

r ♣♦tt t ♠♦♥ ♠rrs ♥ s♦s ♥st t s♦r♦♥♥♥♥ ♦r ♦ ♦rt rrt ♣ t♦ ♦ ② ♥ ts st s ♥ ①♣♦s ♥ ♣r t♦ ♥tr♦♥ ♥ ♦ ♦t ×1013 cm−2♦r ts s♠♣ t ∆Vth r♦rs ♦t t t♠♣rtr ♦ r② tts rrt♦♥ ♥ ♦r♣♣♥ ♣♥♦♠♥♦♥ tt r♦rs ♥ t ♣rs♥t t♠st t♥ ♥t♦ ♦♥t t s t♥ ♣♦ss t♦ ♦♥sr tt ♦r s ♥tr♦♥ ♥t ♥♠r ♦ s♣♠♥t ♠s ♥rt ② t ♣r ♣rt ①♣♦sr s ♥♦ t♦ ♥ ♥ ds❱gs ♠♦t♦♥ t ♦sr ♥♥♥ ♥ t♥ ss♠t♦ ♦rrs♣♦♥ t♦ s♣♠♥t ♠s r♦r②

rtr③t♦♥ ♦ ♦s♠trs

r ①♣r♠♥t s♦tr♠ ♥♥♥ rs r♥t ♠rrs ♦r s♠sr ♦♦♥ rrt♦♥ ♥ t ♠①r♦♥ t t s♦ ♥s r♣rs♥t t t♠♣rtr r♦r r♥ t s♦tr♠ ♠sr♠♥ts t ② ♥ s♦t rsts ♦ t s♦tr♠ ♥♥♥ t♦♥ s ♦♥ t r♦r ♦ s♦♥ rt♦♥♥ ts t♥ ♥t♦ ♦♥t t r t♠♣rtr ♣r♦ r♥ t ♦rt♥ ♠♦♥ts①♣r♠♥t

♦r♥ t t ♦s♠tr s♥ Vth r♦t r♦♠ ss ♥ rt② ♦t Vgs ♦t♥ ♦r r tr♥sst♦r r♦♠ t qt♦♥

Id = β · (Vgs − VT )2 · (1 + λVds)

♥ ♦♥st♥t rr♥t d s ♦r t♥ t tr♥sst♦r s♦rr♥ ♦♥♥t♦♥s ♦♥st♥t λ ♦♥② ♣♥s ♦♥ t ♥♥ ♦♠tr② ♥ ♦♥ t ♥♥ rrr♠♦t② µ

t♦♠ s♣♠♥ts ❬♥❪ ♥ t s♠♦♥t♦r ②r ♥ rs♣♦♥s ♦rt rt♦♥ ♦ t tr♥sst♦r ♥♥ ♠♦t② ❬❪ tt ♥ tr♥ ♠② ♥rst ♥♥ rsst♥ ❬❪ ❱ t ♣r♠tr λ t ♠ ♥ tsr t ♦s♠tr s♥ ♠sr tr♦ q r♦r ♥ ♦rr t♦ sssstr t t♦♥ rt♦♥ ♥ t ∆Vgs r♦r② ♥ rt t♦ t ♦rr♥♦ s♣♠♥t ♠ s♦♥ srs ♦ s s ①♣♦s t♦ t ♣r ❱♣r♦t♦♥ ♠ ♦ t t② ♥♥♥ ♠sr♠♥ts rt t♦ ts s♦♥rrt♦♥ tst r ♣♦tt t ♠rrs ♥

r♦♠ ts st t sts t s ♣♦ss t♦ ♥t② ♦♠♠♦♥ srs ♦ tr♥st♦♥t♠♣rtrs ❬s❪ ♥t♦♥ ♣♦♥t ♦ t ①♣r♠♥t s♦r♦♥ ♥♥♥ r∗

1 ∗

2 ♥ ∗

3 tt ♠② ♦rrs♣♦♥ t♦ t t♠♣rtrs t t r♥t t②♣s ♦ rt♦♥♥ ts s♣♦♥t♥♦s② ss♦t♥ s♦♥ ❬♦❪ ♦r♥ t♦ ❬♦r❪ ts ∗ ♠② ♥t t r♦r② ♦

rtr③t♦♥ ♦ t

t ②♣ ♦r② ∗ i A,i i

s−1 ❱

❱P ×108 ❱ ×1010 ❱❱ ×109

Pr♠trs ♦ t rt♦♥♥ ts ♥ ①trt r♦♠ t s♦r♦♥ ♥♥♥ tst

rt♦♥♥ ♥trs ♦r♠ ② ♥② ts ❱ ♥ t s♦♥ tt t ♠♣rts t♦♠s ♦r t ♦tr ♥s ♦ r② t ♦ ②♣♦tss t ♠rtrsts ①trt r♦♠ t ♣r♦t♦♥ s♦r♦♥ ♥♥♥ rs ♥ s ♥♦t♦ ♣rt t s♦tr♠ ♥♥♥ ♦r ♦ ∆Vgs ♦r t ② rrt s∆Vgst ♥♦r♠③ t♦ ts ♥t ∆Vgs s s♦ ♦♠♣t t♥ ♥t♦ ♦♥ttt t t♠♣♥♥ ♦ t ts ss♦t♦♥ s sr ② rst ♦rr ♣r♦ss ❬♦❪

∆Vgs(t)

∆Vgs(0)=

3∑

i=1

Bi · exp(−σi · t)

σi = Ai · exp

(

−EA,i

kBT

)

r t s t ♥♥♥ t♠ σi s t ♣r♦t② ♣r ♥t t♠ ♦r t t t♦ ss♦t s−1 ♥ i s t rt♦♥ ♦ ∆Vgs tt r♦rs t t ss♦t♦♥♦ t ①♣r♠♥t ♣r♠tr r♦♠ t rs ♦ t♠♣rtr♣♥♥ ♦ σi s ♥ ② ♥ rr♥s rt♦♥ r i s t t♦r ♦ tr♠rt♦♥ ♦ t s−1 A,i s t tt♦♥ ♥r② ♦r ss♦t♦♥ ♦ t ❱ B s t ♦t③♠♥♥s ♦♥st♥t ♥ s t ♥♥♥ t♠♣rtr

♦r♥ t♦ ❬♦r ♦ ❪ t rtrst t♠♣rtrs ∗

1 ∗

2 ♥∗

3 ♦ ♦rrs♣♦♥ ts t♦ t r♦r② ♦ t ❱P ❱ ♥ ❱❱ ♥trs rs♣t② ts t ♠r♦s♦♣ ♣r♠trs ♦ t ♥t t ♦♥ ♥ t ♦♠♥t♦♥ rr♥s s ♣r♠trs r t ♦♥s tt ♣♣r ♥ q

s♦s ♥② t ♦♠♣rs♦♥ t♥ t r r♦♠ q ♥ t ①♣r♠♥t ♥♥♥ r♦r ♦r ♠♦♥ts ♦r tr tr♥sst♦rs ♥♣♥♥t②rrt ♥ t s♠ s♦♥r② rt♦♥ tr s r ①♣♦s t♦ r♥t s ♥ t♦ ♥tr♦♥ ♥s r♥♥ r♦♠ ×1012 cm−2 t♦×1013 cm−2 t s t♦ ♥♦t tt t t♦♥ t q ts ♥t♦ ♦♥t tr t♠♣rtr ♣r♦ r♦r r♥ t ♠sr♠♥t ♦ t t t s t♥ ♣♦ss t♦ ♦♦ t tr♠ ♥♥♥ ♦ t ts t ♥② t♠ ♦ t ①♣r♠♥t ♣rt♦♥ t ♦♥ t r t♠♣rtr ♣r♦ s s♦♥r② ②①s ♦ ts t ①♣r♠♥t t ttr t♥ ♣ t♦ ♦t ×103 ♦rs r② ♦t t♦♥ s st r② ♦♦ tr ♦rt♥ ♠♦♥ts

t♦♥ ♥ t ②♣♦tss ♣rs♥t ♥ ts st♦♥ s s♦ ♦♥r♠ ② t♠sr♠♥t ♣r♦r♠ ♦♥ t r♥ ♦ r s ♠sr♠♥t s ♥ rr♦t ② ♠sr♥ t Ids − Vd rtrst r ♦ t t♥ t r♥

rtr③t♦♥ ♦ ♦s♠trs

r r♥ rr♥t♦t rtrsts ♦ s ❱ ♦r ♥rrt tr♥sst♦r ♠♣t② r♦♥ ♠rrs ♥ ♦♦♥ rrt♦♥ t♦ Φeq ♦ ♦t×1013 cm−2 r♦♥ ♠rrs

tr♠♥ ♥ s♦r ♦② ♥ t tr♠♥s s♦rt t♦tr rsts ♦ ts tst ♥ ♣♦tt ♥ r t ❱ r♥ rtrst ♦r rrt♦♥♠♣t② ♠rrs s ♥ ♦♠♣r t♦ t s♠ r ♠sr tr ② ♥tr♦♥rrt♦♥ ♥ t r rt♦r ♠rrs ♥ t ♦rr ♣rt ♦t rs ♦r ♥ ♦t s ♦r ①♠♣ ❱d ❱ t r♥ rr♥t rstsr ♦ ♠♦r t♥ t♦ ♦rrs ♦ ♠♥t ♦r Φeq ♦ ♦t ×1013 cm−2

s ♠♥t♦♥ ♦r ♥ t ♣r♥♣ t ♥ t r♠♥s tr tr♣♣♥ ♥ t ♦① ♥ t t 2 ♥tr t ♣r ①♣♦sr t♦ ♥tr♦♥s ♥ st r♦♥s ♥ ♥r ♥s rrr r♠♦ ♥ t s♦♥ sstrt tss♥ t sstrt rsstt② t♦ ♥rs ❬❪ t t s♠ s♦♥ s t ♣♥s♦♥ s sr rr ♥

♦r♠② t ♥rs ♥ t sstrt rsstt② s ♦♥② s♠ t ♦♥ t r♥rr♥t s♥ rrs rr♥t ♥ ♥ ♥rs♦♥ ②r t t sr ♥t ♥rs♦♥ ②r ♦♥t♦♥ s rtr ♥s♥st t♦ t sstrt ♦♣♥ ♦r t ♥rs ♥ sstrt rsstt② ♦ ①♣t t♦ ♥rs t t ♦ tr♥ s♣r r♦♥ ♥t② ♦♥ t t♦ rt② ♦♥tt t s♦r P♥tr♦ t♥ r♥ ♥ s♦r ♦ t♥ ♦r r♦♠ t t ♦ ❬❪♥ rr♥s tr♥ ts ♥ ♦♠ sr♦s t ♥ Φeq ≫ sstrt ♦♣♥♦♥♥trt♦♥

rtr③t♦♥ ♦ t

♦♠♥ t♦ t ∆Vgs ♠sr♠♥t t ♥ st ♣♦♥t ♦t tt t ♠sr♠♥t ♦ t r ∆❱T ♦ t tr♥sst♦r ♣r♦② ♠♠♥ t♦ ts t t♦ts ♥♣♥♥ ♥ t tr♥sst♦rs ♥♥ ♠♦t② rt♦♥

s♦r♦♥ ♥♥♥ ♣r♦r s ♥ s ♥ t s ♦ t s s♦ t♦ t t s♣♠♥t ♠ ♥♥♥ ♥ t♥ tr ♦♥ t♠♦r ♦♠♣rs♦♥ t♥ t ♥♥♥ ♣rt♦♥ ♥ st ♦ ①♣r♠♥tt r♦r ♦r ♠♦♥ts s ♦♥ t♦ r② rt t s t♥ s♦♥ tt ♥ ts♥ ♦ ts ♥ ② rs rt♦♥ ♥r♦♥♠♥t rtrst ♦ ①♣r♠♥ts ♥ t s♥ t s♦r♦♥ ♥♥♥ ♠t♦ ♠ts ♥ tr♦r ♥ t♦♥ rr♦rs ♥ t ∆Vgs ♠sr♠♥t s s ♥♦♥ r t♦ s ♦ s ♦r ♠♦♥ts ♦ tr♠ ♥♥♥ ♦r s♦r ♦ss♣ t♦ t ② r♥ ♣r♦♥ tt t tst s ② ♦♠♣② t t stt② rqr♠♥ts ♥ ♥r ①tr♠② rt♦♥ s

rtr③t♦♥ ♦ t

rt♦♥ rs ♥ ♦♣rt♦♥ ♣r♠trs

s s♣♣ ② t ①♦r t t♦♥ ①♣r♠♥t ♥ ♦♥t♦rs ♥ ❯♥t ♥♦♠ r rrt ♥ ♣rt s t t♦ t♦ tr♠♥ rt♦♥ r ♥ t ♦♣rt♦♥ ♣r♠trs t♦ s t t ①♣r♠♥ts t♦ t s ♣ ♦♥t♥s ♦r strtrs tr♥t t♦① t♥ss ♦♥② t strtrs ♥ t♥ t ♦① t♥ss②♣ r ♦♥sr ♦r t ①♣r♠♥ts ♦r ts rs♦♥ st♦♥ ♣r♦r s s t♦ st t st ②♣ s♠♣s s ♣♣♥① ♥ ♦♥② tst tox µ♠ r ♥stt ♥ t

s s r ♦♣rt ♦♦♥ t ♠♥trr ♥t♦♥s t r♦t rr♥t ♦ µ ♦r ts s ♥♦t r ② t ♣r♦r t♦ ♦rrs♣♦♥♥ t♦ t ♣♦♥t ♦ t ♦r ts rs♦♥ ♥ t♦♥ ♦ ttr♥sst♦r s ♥ rr ♦t ② ♠sr♥ t tr♥sst♦r r♥ rr♥t s ♥t♦♥ ♦ Vgs ♦r t♠♣rtrs r♥♥ r♦♠ t♦ s♦s trr♥t♦t rtrsts ♦ t t t t♠♣rtr s ♣r♠tr ♦r♥ ♣♦♥t r♦♥ ♥ t s♥stt② t♦ t♠♣rtr s r rt② t♦ ③r♦♦r t µ♠ s s ♥ ♦♥ r t♦ t♥ ♥ µt♦ t r♦t rr♥t s s t s ♠sr s ♦r ♦r♥ t♣r♦s ♠sr t ❬ ❪ ♥ t t t r♦♠ t ♣r♦r µs ♥ ♣t s st♥r r♦t rr♥t ♦r♦r s ♦♥r♠ ② ts♥stt② t♦ t♠♣rtr ss♦t t♦ t ∆Vth t µ s st ♥ sst♥ ♠❱ s♦ tt ♦s♠tr② ♥ t ② r♥ s ♥♦t ♠♣r ② ♣♥ t♦ ♠♥t♦♥ r♦t rr♥t

♠♥t ♦ t t♠♣rtr ♣♥♥ ♥rss t rrt♦♥ r♥♦t ♠❱ t ♦ ② s s♦♥ ♥ r t t♠♣rtr♣♥♥ s ♥ t r♦♠ t r♦r r♥ ❳r② ♥ ♠① r♦♥ rrt♦♥s rr♦r ♦♥ t ♣rs♥t t s ♥ t t♦ ± ♥ ♦t Tc ♥ ♠sr♠♥ts t♠♣rtr♥ rt♦♥s

rtr③t♦♥ ♦ ♦s♠trs

r ♠♣rtr s♥stt② ♦ t ②♣ tr♠♥t♦♥ ♦ t ♣♦♥t ♠♣rtr ♦♥t c ♥ ♠❱ ♠sr t ♥rs♥ ♦r µ ①♣r♠♥t ♣♦♥ts r♦♠ ❳r② ♥ ♠① r♦♥ rrt♦♥ stt ♦ t ①♣r♠♥t t s♦ |Tc| ×10−3 mV · Gy−1s ①♣♦s t ❱G ❱

♦ t ♦s ♠sr♠♥t r tr♦r ♥ t ♦rr ♦ t t ♠①♠♠ ♦s ♦ ② ② tt♥ t t ♦ t ♦♦♥ t♠♣rtr ♣♥♥ s♥t♦♥ ♦ t ♥ ♦♥

|Tc| = 2.8 × 10−3 mV/ · Gy−1

♦r ♠r ♥ ♦r② ♦s♠tr② ts r ♦ t♠♣rtr s♥stt② ♥s ♣r♦♠ ♠♥s t♠♣rtr ♦♠♣♥st♦♥ ♦ s♦♠ s♦rt s ♥t r②♥ ts ♦r ♥

sr♠♥ts ♦ t rt♠ ♥stt② ♦r rt♣ s♦ ♣r♦r♠♦r t µ♠ s ❬❪ ♦r ♥ ♥rrt t ∆Vth s♥ ♦♥ t♦ ♥rs ♥ r ♦ ♠❱ r♦♠ t♦ s♦♥s tr t ♥t♦♥ ♦t r♦t rr♥t tr ♦ s♦♠ t♥s ♦ ② ts ♥rss t♦ ♦t ♠❱ r♣rs♥t♥ ts ♦ t ∆Vth ♠sr t s ♦ss tt s ♥ t ♦rr♦ ❱ s ♠sr s sst t♦ ♣♣② ♦r t s r♦t rr♥tt st ♦r s♦♥ ♦r t ∆Vth s ♠sr ♥ ts ♦♥t♦♥ t rt♣♥ ♣t s ♦ s t ①♣r♠♥t rr♦r ♥ t ♦r r♥ ♦ ♥trst ♦r t ♦ s♦♠ t♥s ♦ ②

s♦s t rsts ♦ t r♥t rrt♦♥ tsts ♣r♦r♠ ♦♥ s t t ♦ r♦t ♣r♦t♦♦ ♥ t t s♠♣s ①♣♦s ♥ ③r♦s ♠♦ ♦♠ ♦ t ♣♦tt t ♦♠s r♦♠ ❬ ❪ ①♣r♠♥tt r♦♠ ♥♥ r♥t tst♠s ♥ ♣♦tt tr s ts ♦♥ ♣t♦♥ ♦♦ ♣♦t ♦ ∆Vth s ♥t♦♥ ♦ t s♦s tt ∆Vth rs ♠♦st♥r② ♣ t♦ ♦t t♦ ② t♦ t s st ♣♦ss t♦ ♠sr ♥rss tr ♦ss ∆Vth s♠♦♦t② rs t♦r strt♦♥ tt ♣♣r tr ♦ ②

♦r ♦r t♥ ② t ①♣r♠♥t t r♦♠ ♣♦t♦♥s Ps ♥ ♠① r ♥ r② ♦♦ r♠♥t ♦♦♥ t s♠ rs♣♦♥s ♦r s s♦♥ ♥

rtr③t♦♥ ♦ t

r t♦♥ rs♣♦♥s ♦ ②♣ s tox µ♠ trs♦ ♦t st t µ s ♣♦tt rss t r♦t t♠ s stt♦ t♥ ♥ s ①♣r♠♥t 60♦ t ♣♦tt r ♦♠ r♦♠ t ♣r♦r♥ r♦♠ ♦♥ rrt♦♥ t t t② ♥tr♦♥ t r r♦♠ t t② t ♥ t t② t ❯ ❱ ♠ ♦ t t② ♥t ❱ ♦ t P t② t P r s ♦r ♣r♦t♦♥ rrt♦♥s t ♦r ♣♦st♣♦♥s r♦♠ ♦r rrt♦♥s s t①t s ♥ s♦ ♣♦tt tr ♥② t s♥stt② t♦❳r②s t♥st♥ trt tr t ♠♠ ♦ t t♦ r♥t r♦t rr♥ts s♦♥ ♣♦tt s ①♣♦s ♥ ③r♦s ♠♦

rtr③t♦♥ ♦ ♦s♠trs

t ♥ t ♣r♦s t rs♣♦♥s ♦ t s t♦ ♣r ♥tr♦♥♠ r♦ss ♠rrs ♥ s r② r ② t♦r ♦ ♦t t♦ s ①♣t s ♦♥r♠s t str♦♥② r rs♣♦♥s ♦ ts s t♦ ♥tr♦♥s ♣rt♦r t ♦♥trt♦♥ tt ts ♣rts t♦ t ♦♥③♥ ♥ t rrt♦♥tst t ❳r②s t Vth ♥rss s ♥t♦♥ ♦ t s ♥ ♠sr ♦r t♦♣rt♦♥ rr♥t ♦ µ ♠♣t② sqr ♠rrs s s ♦r t rr♥t♦ µ ♠rrs rsts ♦ ts t♦ rrt♦♥ tsts s♦ tt t rtrt♦♥ rs♣♦♥s s t s♠ ♦r t t♦ ♦♣rt♥ rr♥ts s rst sst s♥ s r ♠♣♦rt♥t t♠♣rtr rt♦♥s r ①♣t tt t② ♥ ♦♣rt t t rr♥t µ ② ♣♥ t st ♦ rt♦♥rs ♣rs♥t ♥ ♦r♦r ♣rt r♦♠ t rt♦♥ ♦ t s t♠♣rtr ♣♥♥ ② ♦♣rt♥ t t ♦r rr♥t t ♥t ♦t ♦ t s s r ② s♦♠ ♥rs ♦ ♠❱ s ♦♥sq♥ ♦ ts t ♠sr♠♥tr♥ ♦ t s♥s♦r ♥ st② ①t♥

①♣r♠♥t t ♥ t r♥ ② t ①s♦♥ ♦ t ♥tr♦♥ ×st ♥ tr♦r tt t q t♦ ♦t♥ t ♦♦♥ ♣r♠tr③t♦♥ ♦r t s

∆Vth = a × Db t

a = 0.01854 V/Gyb = 0.91072

for 10−1 Gy < D < 40 Gy

(0 < ∆Vth < 0.5343)

a = 0.02921 V/Gyb = 0.78778

for 40 Gy < D < 2 × 103 Gy

r② ♦ t ♣rs♥t t s ♦ ± ♥ t r♥ r♦♠ ② t♦ ② ♠♦r rt t ♥ tr♠♥ ♦r q ♥ st s r rrr♦r ± s t♦rt ♥ t ♠sr

♥♥♥ ♦r ♥ s♣♠♥t ♠ ts ♥r♦♥

s♦r♦♥ ♥♥♥ sts rr ♦t ♦♥ t s ♥r② ♣rs♥t ♥ ♥ ts st♦♥ ts t ♦♠♣r t st♦ ①♣r♠♥t s♦tr♠ ♥♥♥ t r♦r ♦r ♠♦♥ts tr rrt♦♥ ♥t s♦♥r② rt♦♥ ♥r♦♥♠♥t ♦ t t② t s

s♦s t rst ♦ ts ♦♥tr♠ ♥♥♥ ♣r♦ ♥♥♥rt♦♥ s ♥ t ② ♥ t st ♦ t trs♦ ♦t ♦ t tr♥sst♦rr♦r t ♥② t♠ st♣ Vth(t) ② t ♦♥ ♠sr ♠♠t② tr t rrt♦♥t t Vth(0) s ①♣♦s t♦ ♣r② ♦♥③♥ rt♦♥ ♥ t ♦rr ♦s♦♠ ♥r ♦ ② s♦ r♠r stt② ② ♦♦s♥ ss t♥ ♦ t ♥ttrs♦ ♦t ①♣♦s t♦ r ♦s ♦ ♣r② ♦♥③♥ rt♦♥♦s t ♠♦r s♥ ♥ t ♦rr ♦ ♦r ♠♦♥ts ♦♦♥ t ♥t♦♥s ♦

rtr③t♦♥ ♦ t

r ①♣r♠♥t s♦tr♠ ♥♥♥ rs r♥t ♠rrs ♦r ②♣ s ♠sr ♦♦♥ rrt♦♥ ♥ t ♠①r♦♥ t t s♦ ♥s r♣rs♥t t t♠♣rtr r♦r r♥ t s♦tr♠ ♠sr♠♥ts ♥s rrr t♦ t s♦♥r② ②①s s ①♣♦s ♥ ③r♦s ♠♦

♥ t t ♠sr ♥ t ♣rt♦♥ ♦ t s♦tr♠ ♥♥♥♦r ♦ t s t ♦ ♥ ♦ss ♦ ♦t tr ②r ♥♥♥t♠ r rsts ♣♣r t♦ ♦r ② t♦r ♦ t♦ trs♣t t s♦r♦♥ ♥♥♥ st♠t♦♥

♣rt♦♥ s ♦♥ s♦r♦♥ ♥♥♥ s♠s ts t♦ ♦rst♠t t♦♥srt ♥ t r♠♦r ♦ st♦♥ ♣r♦r s t s ♥ s ♥ ts rst♣rt ♦ t ♣tr ♣♦ss ①♣♥t♦♥ ♦t ts t♦ s♦r♥t sts ♦ ♥♥♥t ♦r t s ♥ ♠♥♦ ♥ ♠② ttrt t♦ ② ♣♦ ♥trtr♣♣♥ stts s ①♣♥ ♥ ♣tr t sts r ♣♦st rs♥ tr♣♣ r s② tr② t♥t ♦r rrt♦♥ ♥ t② r trr ②rt♦♥ ①♣♦sr ♦r♦r t② ♦♣ r♦♠ s♦♥s t♦ t♦s♥s ♦ s♦♥str rrt♦♥ ♥ t s ♦ ♣ tr♥sst♦rs t② tr♦r ♦♥trt♦♥tt s t♦ t ♦♥ ♦ t tr♣♣ r ♥ t s♦♥ ♦①

♥tr stt ♥st② r♦t ♥ ♠♣♦rt♥t ♥ t tr♥sst♦rs r ①♣♦s♥ ♥s ♦♥t♦♥s s s ♥ r ♦♥ ♦♥ tr ③r♦s ♠♦ ①♣♦sr t♦ ♥rs♥ ♦ss ♦ ❳r②s ♣ t♦ ② ② ♣♣②♥ t❲♥♦r ♠t♦ ❬❲❪ ♦♥ t st ♦ Ids −Vgs rs ♠sr tr ♥② rrt♦♥st♣ t s ♥ ♦♥ tt t ♦♥trt♦♥ ♦ t it ♦♥ t r♦r Vth r♦♠ t

rtr③t♦♥ t♥q ♦s trs♦ ♦t st ♥ ♥ tr♥sst♦r t♦ s♣rt ♥t♦ sts t♦ ♥tr tr♣s ♥ tr♣♣ ♦① r s ♠t♦ s s ♦♥ ttr♠♥t♦♥ ♦ t ♦ Ids − Vgs rtrst ♦ t ♦r ♥ Vds tr rrt♦♥ ♦rrtr ts s ❬❲❪

rtr③t♦♥ ♦ ♦s♠trs

r r♥ rr♥t♦t rtrsts ♦ ②♣ tox µ♠ s s ①♣♦s ♥ ③r♦s ♠♦ t♦ ♥rs♥ ♦ss ♦ ❳r②s t♦ st② tts ♦ t ♦♥ t r♥ ♦t

rrt tr♥sst♦r s ♦t ♦r ♦ss ♦ ② ♥ q② ♥rs t♦ ♠♦rt♥ ♦r ♦ss ①♥ t ②

♥ ts ② t ♦ ♥tr stts r② ♦♣ ♥ t rrt tr♥sst♦rsit ♥ s♦② ♦♥t♥ t♦ r♦ ♥rs♥ t Vth ♦r t♠ s s♥ ♥rs ♥ts ♣rt② ♦♠♣♥st t ♦ss ♦ t ot ♠sr ♥ ♣rt t t s♦r♦♥♥♥♥ t♥q ♥ t s♦r♦♥ ♥♥♥ ♣r♦r ♥♦t t♦ ♦♥t t♦r ♦ t it ts ♥ ①♣♥ t r♥s ♦sr t♥ t t♦ ♥♥♥♣r♦rs

s t t ♦t t♦ t ♠sr♠♥t ♦♦s s ♥ t ♦t♦♥ ♦ t ①♣r♠♥ts r t rt♦♥ ♥r♦♥♠♥ts t ♠♦st ♦st ♥ ♥♦② t♦ t s ♥ ♦♥ ♦r t s ♥ t ♠sr♠♥t ♦ t Ids − Vd rtrsts r s ♥ rr ♦t② r♥♥♥ ❱ ♠sr♠♥ts ♦ t rrt s t♥ t r♥ tr♠♥♥ s♦r ♦② ♥ t tr♠♥s s♦rt t♦tr s s ♦♥ t t ♦ t♦♥stt ♣♦ss ♠♦t♦♥s ♥ t s♦♥ sstrt

s♦s t rsts ♦ srs ♦ rrt♦♥s rr ♦♥ ♥ ♣r♦♥③♥ rt♦♥ ♥r♦♥♠♥t t ♥rs♥ ♦s ♦ ❳r②s ♣rs♥t t ♥ ♠sr ♦♥ t s♠ ♣ tr ♥② rrt♦♥ st♣ ♦♠♣t Ids − Vd

rtrsts s ♥ ♠sr r♥t ♥s ♥ ♦♠♣r t t rtrst♠sr ♦r t ♥rrt ♠♣t② r♦♥ ♠rrs ♥ s r ♦ ♠rt

rtr③t♦♥ ♦ t

r r♥ rr♥t♦t rtrsts ♦ ②♣ tox µ♠ s s ①♣♦s ♥ ③r♦s ♠♦ t♦ ♥rs♥ r♦♥ ♥s t♦ st② tts ♦ t s♣♠♥t ♠ ♦♥ t r♥ ♦t ①♣r♠♥t t ♦♠s ♦r♠ ❱ ♣r♦t♦♥ rrt♦♥ P ♥ r♦♠ ♥tr♦♥ ①♣♦sr t t r rt♦r

♥ Id ♦ µ t r♥ ♦t s ♥ ♦♥ t♦ ♥ ss t♥ ♥ t r♥ ♦ ♠♦r t♥ ② ♥ t ♠sr rt♦♥ t♥ t ①♣r♠♥trr♦rs ♥ ♦♥sr♥ t r② ♦ ♠♥ ♣♦r t ♣♦t♦♥s t t♦ t ♦♥ t sstrt ♥ ♥t

♥② s♦s t ♠sr♠♥t ♦ t rsts Ids − Vd rtrsts ♦r srs ♦ s rrt t st r♦♥s t ♣rs♥t ♥ ts ♣♦t ♦♠sr♦♠ r♥t s ♠sr tr ①♣♦sr t♦ t ❱ ♣r♦t♦♥s ♥ tP t② ♥ tr ♥tr♦♥ ①♣♦sr t t r rt♦r ♥♥ s r ♦ ♠rt ♥ Id ♦ µ t r♥ ♦t s ♥ ♦♥ t♦ ♥ ♦r♦t ♥ t Φeq r♥ ①♥ ×1013 cm−2

s s♦♥ rst s♦s r rt♦♥ ♥ t r♥ ♦rr ♦t t♥ t ♣r♦s ♦♥ ♥ ♥rs ♦ t tr♥sst♦r rr♥t ♦ ♦t ♦♥ ♦rr ♦ ♠♥ts ♥ s♦ ♦sr ♥ t ♥stt Φeq r♥ ♦r t t ♦♥ t rr♥t s ♥♦ ♥♥ ♦♥ t ♥t♦♥ s ♦r t ♦s♠tr r♦t ♦♥t♥ t t♦ r♥s ♦♥ t ♥t Ids − Vd rs t s♥♦t t♦t tt t rr ♦♣rt♦♥ ♦ ts s t t ①♣r♠♥ts s ♦♥t♦ ♦♠♣r♦♠s ♥ ♥② ② ② t s♠ ♥ ♣rtrt♦♥s ♥ t rr♥t ♦sr ♦r ①♣♦sr t♦ s ♦ rt♦r ♥tr♦♥s ♥ ♣r♦t♦♥s

rtr③t♦♥ ♦ ♦s♠trs

♣♥ sss ♦r t ①♣r

♠♥ts

s♣② ♦r ♦s♠trs t s ♦ ♥♣♣r♦♣rt ♠trs ♦t ♦s t♦♦r r♦♥ t♠ ♥ ♠♦② t rt♦♥ rs♣♦♥s ♥♥ rr♦rs ♥ t ♠sr♠♥ts ♦r ①♠♣ s t s ♥ s♦♥ ♦r ♥ ♦r ♥tr♦♥s ts♣rts ♥ ♥trt t t s♥s♦rs ♣♥ ♥ s♥♥t② ♥♥ t ♠sr ♦s ♠r ts ♥ s♦ ♦♥ ♦r ♦ ♥r② ♣♦t♦♥s s ♦♠♥t ♦r①♠♣ ♥ ❬♦s❪ ♦♥trr② r r♦♥s ♥ ♦♦s rt♦♥ ♦ tr♥r② ♥s t ♣ ♠trs ♥ t♦ ♥ ♥rst♠t♦♥ ♦ t rt♦♥ ♦ss ♦♥srt♦♥s r② ♣♣② t♦ t s ♦ t t♦ s rtr③r ♦r ①♣r♠♥ts

r♦r t ♦♠♠r② tr♥sst♦r ♣♥ ♦ ♥♦t sts② t rqr♠♥ts ♥ tr♠s ♦ ♠♥s♦♥s ♥ ♠♣♦② ♠trs s st♦♠♠ ♣♥ s ♥ s♣② ♣r♦ ♦r t ♣♣t♦♥s ♥ t rst ♣rt ♦ tsst♦♥ t sts rr ♦t ♦r t ♦♣♠♥t ♦ ts st♦♠ ♣ sr

♦ t♦♥s ♦ t ts ♦ ♣♥ ♠trs r strt ♦rr ♦r ♥ ♦rr t♦ t r♦r♦s② ♥t♦ ♦♥t r♥t ts ♦ t ♠trs ♥st ♦♠♣① ♥ ♥ ♦rr t♦ ♦♣t♠③ t s♥s♦r ♣♥ t s ♦ s♠t♦♥ t♦♦s s ♥s♣♥s

♦♥t r♦ ♠♦ s ♦♥ t ❬♦ ❪ ♠t♦♥ ♦♦t str♦r ♥ ♦♣ t♦ st② t ts ♦ t ♣♥ ♦♥ t s rs♣♦♥s s♠t♦♥ ♠♦ ①♣♦ts ♥ ♣ts t♦ sr t s♥s♦rs♥ t ♥ r st ♦ ♣②ss ♣r♦sss t♦ st② t ts ♥ ② ♦♠♣①rt♦♥ ♥r♦♥♠♥t s s ①♣t t

♦r t ♦♥t r♦ ♠♦s ♥ rt② ♣♣ t♦ t ♦♠♣① s♠t♦♥♦ t ♠① ♥r♦♥♠♥t t② ♥ t♦ t s♥ st ♦ ①♣r♠♥tt r♦♠ s♠♣ ♥ tr♠s ♦ ♣rt s♣tr ♦♥r② ♦♥t♦♥s t rrt♦♥①♣r♠♥ts t♦ ts rst ①♣r♠♥ts ♥ s♠t♦♥s ♥♦t ♠t t ♦♠♣①t② ♦ t ♥r♦♥♠♥t t② ♠t r② s t♦ ♣r♦ ♥♦r t ♦ ♦ st s♥s♦r ♣♥ ♠trs ♦r t ♠♦sr ♥ ts ♣tr s ♥ ♥tr② ♦♣ ② t ♦ ♥♦ t②♥ t r♠♦r ♦ ts tss ♦r t rst ①♣r♠♥t ♠♣♥s ♦t t♦ tst♦♥ ♣rs♥t ♥ t ♠sr♠♥ts ♦♠♣r t t rst s♠t♦♥r♥s

s rrt♦♥ tsts r ♣r♦r♠ ② ♠sr♥ t rs♣♦♥s ♦ ♦s♠trs ♠♦♥t ♥s t ♣ rrr ♥ ♦r t s ♦ r♥t t♥sss♥ r♦s ♠trs

P♥ s♥ sts

r ♠trs ♥ t ♥♥ ♠♥ 23 ♠♥♠ tr r♣t ♣♦①②ss ♦♥ 24 ♥ r②♠ ①

st♥ ♦r sttt♦ ③♦♥ s r

♣♥ sss ♦r t ①♣r♠♥ts

r ♣ rrr r♦♠♠♥ ♦r t s t♦ s t t ①♣r♠♥ts ♥ t ♣tr ♦r s × ♥ × r ♠♦♥t ♥r♦♥ ♥ t

♥ ♦rr t♦ ♥ t ♦♥ st ♦r t ♣♥ ♦ t ♥ s t♦ s t t ①♣r♠♥ts

❲t♦t ♥tr♥ ♥ ts ts ♥t ♠trs ♥ t ♦♦♥ r♥t rtr s ♦r ①♠♣

t rsts ♦ ♥②t t♦♥s ♥♦♥ t tr♥s♣♦rt ♥s ♠ttr ♦ ♥tr♦♥s ❬①❪ ♣♦t♦♥s ❬❪ tr♦♥s ♥ ♣r♦t♦♥s ❬❪

t t♦♥ ♦ ♠♥ ♣r♦♣rts t ♠trs tr♠ ♦♥tt②tr♠ ①♣♥s♦♥ rsstt② t

t t② ♦ t st ♠tr ♥ t ♣♦sst② t♦ ♣ ♣♦t ♦ t

t ♦sts ♦ t ♠tr ♥ t ♣ ♠♥tr♥

♠♥ 23 ♦r ♠♦st ♦♠♠♦♥② r♠ tr♥ ♦t t♦ t ♠tr tt ♣r♦s t st ♦♠♣r♦♠s ♠♦♥ t ♦ rqr♠♥ts ♦r♦r srs ♦ r♦♥t r♠ rrrs s ♦♥ t♦ r② ♥ t♦s♥ ♣rts ♥♦s t ♦ ♥t t♥ t♦ ts ♣♥ ♠♦ st ♣♥ s s♦♥ ♥ r② ② q♣♣ t s♥s♦rs ts ♠♥s♦♥s r♦t ♠2 sr ♥ ♠♠ t♥ss

s♣ ♥s t ♦s ♠①♠♠ ♦ tr♥sst♦r s ♥ s t♦ ♠♦♥t tr ♦♥♥t♦♥s r ♠ ♥ ❲ ♠t③t♦♥ ♣♥ ♥ r♦♥♥ ♣s ♦ ♦t µ♠ t s t ♣ ♠♦♥t♥♥s t ♣ s st♦♠♠ t ♥♠r ♦ s tt q♣ t ♣ ♥r② r♦♠ t♦ ♣♦♥ sr rqsts ♦r t ♥tr♥ ♦♥♥t♦♥s ♦ t ♦r s ♥ st♥r③ ♥ ♦rr t♦ ♥ ♦♥ ♦r t ♣♥♦t ♦ t ♦s♠tr♣ ts ♦♥ t ♦♥♥t♦♥s ♥ ♦♥ ♦♥ t r♥ s♠ ♦ t♥ ♦ ♦♥ t t♦♣ ♦ t rrr ♥ ♦rr t♦ ♣r♦tt t s r♦♠st ♥ ♠♥ ♠ r♥ ♥♥ r♥t ♥s ♦ ♠trs r sts s ♦r s rrr ♦r t ♦ ♦ t s ♦♥sttts ♦♥ ♦ t ♣r♠trs

rtr③t♦♥ ♦ ♦s♠trs

r t ♦♥♥t♦♥ ②♦t ♦r t ♣ rrr r♦♠♠♥ ♦r t s t♦ s t t ①♣r♠♥ts

♣♥ sss ♦r t ①♣r♠♥ts

♥t

rt♦♥ ♥t ♠♠ tr♦♥s t♦ ❱ ♣r♦t♦♥s t♦ ❱

♣♦t♦♥ tr♥s♠ss♦♥ ❱ ♥tr♦♥s tt♥t♦♥

♥②t t♦♥s ♦ t rt♦♥ tr♥s♣♦rt rtrsts ♦r t ♣♥ s t♦♥ ♥ rr ♦t ss♠♥ s♠♣② rrr♦♠tr② ♠② ♠♠ s ♦ ♠♥

♦r t ♦♣t♠③t♦♥ ♦ t s♥s♦r rrr s♥ ♦r ts rs♦♥ t ♠tr ♦ sss ♥ t tr ♥ ts st♦♥

♥ t ♣♥ s ♥ ♥ srs ♦ ♥②t t♦♥s♥♦♥ t rt♦♥ tr♥s♣♦rt tr♦♦t t ♣♥ ♠tr r ♦♥ st♦♥s r ♠ ♦♥ s♠♣ ♦♠tr② r♠ s ♠♠ t ♥ trrsts r s♠♠r③ ♥ ts ♦ t ❲ ♠t③t♦♥ s ♥s♦ ♦♥sr ♥ t♦ t ♦ t♦♥s t♦ s♣♣♠♥tr② ②rs ♦ µ♠ ♦♦ ♥ ♥st♥ rs♣t② ts ♦ ts ② ♠t ②rs ♦♥ t ♦t♦♥s ♥ ♦♥ t♦ ♥ t ♦rr ♦ ♦t♥ rsts rr② stst♦r② ♦r ♥tr♦♥ ♥ ♣♦t♦♥s ♣ s tr♥s♣r♥t t♦ ♥tr♦♥s ♥♦♠♣t② trs ♦ ♥r② ♣♦t♦♥s tt r ♦t♥ rs♣♦♥s ♦ ♥♥♠♥t ♦sts s ♦♠♥t ♥ ❬♦s❪ r r ♥st t ♥r② t♦s tr♠♥♦r tr♦♥ ♥ ♣r♦t♦♥s ♦ r ts s ♣r♦♣r ♦ ♦r t s♦ tr♦r t♥

♠♦ ♦ t ①♣r♠♥ts ♣♥

s s♠t♦♥ ♣♣t♦♥ s ♥ ♦♣ t♦ st② t ts ♦♥ ts♥s♦rs ♥ ①♣♦s t♦ r♥t rt♦♥ ♥r♦♥♠♥ts t sr♣t♦♥ ♦ t♦♠tr② ♦ t s♥s♦rs s ♥ ♠♣♠♥t ♥ t s♠t♦♥ s ♥ s♥ r♦♠t tr♠♥s♦♥ ♠♦ ♦ ♥ ♥ t t ♦

❱r♦s ♣♥ ♦♣t♦♥s ♥ st ♦r t st② ♦ s♣ ♦♥rt♦♥s♦r ①♠♣ s ss ♦ r♥t t♥sss ♥ ♦ r♥t ♠trs♥ ♣ s rrr ♥ ♦rr t♦ t tr t♥ss ♥t♦ ♦♥t ♥ t♦♥t r♦ s♠t♦♥

s♠t♦♥ ss st♦♥ ♦ ♣②ss ♣r♦sss ♦t ♦ t♦s ♥ t ♦♦t ♦r ♣rt t②♣ ♠♦s ♦ t ♦ ♥r② tr♦♠♥t♣ ♦r ♣♦t♦♥s ♥ r ♣rts ♥ st ♦ r♦♥ ♠♦s ♦r♥ r♥tr♥s r♦♠ t r② ♥rs t②♣ ♦r ♦♥ t♦ ♥tr♥r tr♥s♣♦rt ♣rqr♠ ♥ ♥r ①tt♦♥ ♦r♦r r♦s ♦♣t♦♥s ♦ tr♥t ♣②ss♠♦s r ♥ t s♠t♦♥ t♦ t ♣♦ss s②st♠t ts

rtr③t♦♥ ♦ ♦s♠trs

r ♠♥s♦♥ ♦ t ♠♦ ♦ t ♣ rrr ♦st♥ t s

r r♦♥t ♦ t ♠♦ ♦ t ♣ rrr ♦st♥ t s rrr ♦st♥ ♦r s♠♦♥t♦r s ♣♥ ♦♥rt♦♥ ♦rt s♠t

♣♥ sss ♦r t ①♣r♠♥ts

r ①♣r♠♥t t♦♥ ♦ t ♦♥t r♦ ♠♦ ② ♠♥s ♦ ♣r♦t♦♥♥ ♥tr♦♥ ①♣r♠♥t t ①♣r♠♥t rsts ♦t♥ t P t② ❱♣r♦t♦♥s ①♣r♠♥t rsts ♦t♥ t t t② t rt♦r ♥tr♦♥s♣tr♠

P♥ ①♣r♠♥t t♦♥ ♥ ♦♠♣rs♦♥ t s♠t♦♥s

t♦ rt♦♥ s st ♦r t rst t♦♥ sts r t ♥r②Pr♦t♦♥ rrt♦♥ t② P t P s ♥ t ♥tr♦♥s r♦♠ t r rt♦r s

s♥s♦r rrr r rrt t P t ❱ ♣r♦t♦♥s t ♥r ① ♦ ♦t ×108 protons/s/cm2 s♠♣s r ♠♦♥t ♥ r♠♥ ①♣♦s ♣r♣♥r② t♦ t ♠①s t t rrr rrt♦♥s r♣r♦r♠ ♣♥ t♠ ♥t♦ t rt♦r ♦r tr♦ ♥ rrt♦♥ t tt ♦♣s r♦ ♣♦st♦♥ ♥ ♥trs t rt♦r r♦♠ ♦ ♦r t ♣rs♥t ①♣r♠♥tt rt♦r ♣♦r s st t♦ ❲ r♥ t ①♣♦sr ♥ t ♥r rt♦r ts♠♣s r s♦ ①♣♦s t♦ ♥ ♠♣♦rt♥t ♠♠r② ♦♠♣♦♥♥t t♦ t ❱ q♥t ♥tr♦♥ ① ♥ t r ♣r♦s② rt ♥ t ♥♥t♦♥ ♠sr♠♥ts ♥ ♣r♦r♠ ♥ ♣r r♥ ts rrt♦♥ tst ♥♦rr t♦ ♥rs t ♣rs♦♥ ♦ t ♦♠♣rt ♦s♠tr②

♠♦ s t♦ rr② ♦♥ t t♦♥ ①♣r♠♥ts s t ♥ t t♦ ss t rrt♦♥s r ①t st♣②st♣ ①♣♦s♥ t s♠♣st♦ ♥rs♥ ♣rt ♥ tr ♥② ①♣♦sr r♦t ② s strt t♦ r♦rt s♥s♦rs ♦t ♥rss r♥ t rrt♦♥ st♣s t ♣ rrr s ♦rt r♥t t♥sss ♦ r♦s ♠trs ♥ ♦rr t♦ s♠t r♥t ♦♣t♦♥s ♦r♥ ♠trs st r ♠♥ ♣♦①②ss t ♦♠♠♦♥♣r♥trt ♦r ♠tr ♥ ♣t♦♥ r♦♠ t♠ t♦ t♠ t rrr s ①♣♦sr ♥ ♦rr t♦ r② t ♠sr s♥ t♦ ♦♥sst♥t t t t♦rt rt♦♥ r

♥ s♦ t ①♣r♠♥t rsts ♦t♥ t ❱♣r♦t♦♥s ♥ ♥ t ♠① γ♥tr♦♥ ♦ t ♥r rt♦r rs♣t② ♥ t s♦ t ❱ ♣r♦t♦♥s t t ♦ t r♥t ♠trs ♦♥ t rs♣♦♥s

rtr③t♦♥ ♦ ♦s♠trs

r ♥r② ♣♦st ♥ t s♥s♦rs s ♥t♦♥ ♦ t ♠♥ t♥ss rst♥r♦♠ s♠t rrt♦♥ t ♣r♦t♦♥s t r♦s ♥rs ♥ ❱

r s ♥ ♦r ♠tr ♠♣♦② ♦ ♥② t♥ss t ♦ s♦ ♥ t tt ♣♦♥ts ♦♥ t t rt♦♥ rs♣♦♥s ♦ t ♥♦r t♥ t ①♣r♠♥t rr♦r ♦ ± ♥ t ♠sr♠♥t ♦ t ♣r♦t♦♥ ♥ ♣r♦t♦♥ ♦s t s t♦ ♥♦t tt ♥ ♣♥ t ♣ tt s ♥ t rt♦♥ ♦ t ♥♦♠♥ ♣r♦t♦♥s s tr♥r ♠rr ♦ ♥♦ ts ♥ tt ♦♥r♠♥ ts t ♥ ♦♥trt♦♥♦ t ♠t③t♦♥ ②rs ♣♦s ♦♥ t ♣ rrr

♠♦st t s♠ stt♦♥ s ♥ ♦♥ ♦r t ♥tr♦♥ t ♦ ♠♥♠ ♥ ♣t♦♥ s s♦ t♦ tr♥s♣r♥t t♦ t rt♦r ♥ r♥ ♦t♥sss ♦♥ r♦♠ t♦ ♦t ♠♠ r♥t s t stt♦♥ ♦r t r♠ s♦r r♠ ss ①♥ ♠♠ t♥ss t rs♣♦♥s rsts ♥♥ ♦♦t

s rst st♣ t s♠t♦♥ ♠♦ sr ♥ s ♥ r♥ ♦r ♣r♣r♦t♦♥ ♠s ♦ r♥t ♥rs tt t ♣r♣♥r② t rrr s♠t ②♥rs♥ t♥sss ♦ r♥t ♠trs ♥r② ♣♦st ♥ t s♥s♦rs rst♥ r♦♠ ♣r♠r② ♥ s♦♥r② ♣rt ♥trt♦♥s s t ② t s♠t♦♥ ts t ♥r② ♣♦s ♥ t trt ♦♠ s♦♥ s s♠t♥ t ♣s ♥ ♣r♦t♦♥s ♦ ❱ ♥ ❱ r ♥ t♦r t ♣♣♥ s ♥t♦♥ ♦ t r♠ t♥ss s♦s st♦♥ ♦ tst ♦t♥ t Al2O3 s r♥ t ❱ ♦♥r♠s t ①♣r♠♥t rstss♦♥ tt ♣r♦t♦♥s ♦ s ♥ ♥r② ♥ ♣♥trt ♣ t♦ ♠♠ ♦ r♠ t♦tt♦ ♥trr t t ♦s ♠sr ② t s t♥ t rr♦r ② r♥t ♥r② ♦ t ♣r♦t♦♥s r♦♠ ❱ t♦ ❱ t s♠ rst s ♦t♥ ♦r ❱ ♣r♦t♦♥s str♦♥ ♦s ♥♥♠♥t s ♣rt ② t s♠t♦♥ r♥

♦♥s♦♥

r ♥r② s♣tr ♦t♥ t ♠♦♥♦♥rt ♣r♦t♦♥s ❱ ♥ ❱t r♥t ♣♥ s ♦♥rt♦♥s

♥rs ♦r ♠♠ t r♠ s rsts s♦ tt ② ♥♥ ♠trs t♥sss ♥ ♥rs t s♠

t♦♥ t ♣r♦t♦♥s ♥ s s ♣rt t♦♦ ♥ r ①♣r♠♥t rsts r♥♦t t♦ ♦♣t♠③ t t♦ ♠♦♥t ♦♥ t s♥s♦r rrr ♥st t t ①♣r♠♥ts s♠t♦♥s ♦r t ♠① rt♦r r rr♥t② ♦♥♦♥♥ ts s♦♥ t♦♥ st② r s t♥ ♥ t s♠t♦♥ ♦ t rt♦r γr②sr♦♥ tt t♦tr t t s♦♥rs r♦♠ ♥tr♦♥ ♥trt♦♥ s rs♣♦♥s♦ rt♦♥ ♦ t ♣♦st♦♥ ♥ t t②r ♦ t s

♦♥s♦♥

♥ t rst ♣rt ♦ ts ♣tr t st♦♥ ♦ t ♦s♠trs st ♦r t♦♣rt♦♥ ♥ t rt♦♥ ♥r♦♥♠♥t ♦ t ①♣r♠♥ts s ♥ rss

r♦♠ t st♦♥ ♣r♦r sss ♥ ts ♣tr t ♥ stt ♥ ♥rtt t ♦ ♦ t♥ ♦① tox ∼ µ♠ r♥ ♦s ♠sr♠♥ts ♦rsr s ♦ ♦s ♣ t♦ t♥s ♦ ② t ♦s ♥♦t ♦r t s♥stt② t♦ ♠srr② s♠ ♦ss < ② ❯♥s t♥♦① s s♦ t♥ t tr str♦♥ ♥♦ t♦ ♠♥♠③ t r♦♠♥t♦♥ ts tt ♠② rs♣♦♥s ♦rs r rs♣♦♥ss ♥ rt♦♥ s t r♥t s t ♦♥s ①♣tt t ①♣r♠♥ts ♦r♦r ② s♥ t♥ ♦① s t s♥stt② t♦♥r② ♥tr♦♥s s ♣t ♦ ♣♦ss strt♦♥ ts t♦ ♥tr♦♥ ♥s r ♦

♦♣♣♦st stt♦♥ ♥ ♦sr t t ♦① s tox ∼ µ♠tt ♣r♦ ♠ r s♥stts ♠② ♥ ts s t t ♦t st ♣r♥t ♦s s ♠ r ts ♠t♥ t ♠sr ♦s r♥ ♣ t♦ t♥s ♦ ② tr ♦ss ♥ t s st ♣♦ss t♦ ♠sr ♥rs t rs♣♦♥ss♥ ♠① s♦ t♦ r♥ ② r♥t rs ♦ strt♦♥ ♦r t r♥t

rtr③t♦♥ ♦ ♦s♠trs

♣rt t②♣s s s r tr♦r st ♦r ♠sr♠♥ts ♥ ♦♥t♥st②γ♥ s r t ♦♥trt♦♥ ♦ Ps s ♥ s t s t s ♥ t rt♦♥♥r♦♥♠♥t ①♣t ♥ t ①tr♥ tt♦r ②rs ♦ t ①♣r♠♥ts

♥♥♥ ts ♥ ♥tr♦ ♠♦r rr♦rs ♥ t ♠sr♠♥ts ♣r♦r♠ ②s ♦r ♦♥tr♠ ♣r♦s ②rs t ♥♦ ♦ t s♥♥♥ ♦r s ts ♥ ss♥t ♠♥t ♦r t st♦♥ s ♦ t♠♣♦sst② t♦ st② ♥♥♥ ts ♦♥ t s♠ t♠s s t ①♣r♠♥ts♦♣rt♦♥ ♥ rt ♠t♦ t♦ rtr③ t s ♥♥♥ ♦rs s♥ s ♥ ts ♦r s♦r♦♥ ♥♥♥ ①♣r♠♥ts r ts rr ♦t ♥tr rsts t③ t♦ ♥t② s t ♥♦♠♦s ♥♥♥ ♦rs

r♦♠ t st♦♥ ♣r♦r t rst tt t♦ s r ♥ t♦ t rt♦♥ ♠♦♥t♦r♥ rqr♠♥t ♦ t ①♣r♠♥ts s t♦ s tt♦ ♦♠♣t② r♥t ♦① t♥sss r t tox µ♠ ♦r t♠sr♠♥t ♦ ♦ ♦ ♥t♥st② ♠① γ♥tr♦♥ ♥ t ②♣ t tox µ♠ ♦r t ♠sr♠♥t ♥ ♥t♥st②r♦♥ s

♦r t st s t ♥♥♥ sts ♥ t ② ♦♠♣r♥ ts♦r♦♥ ♥♥♥ rsts t srs ♦ s♦tr♠ ♥♥♥ t r♦r ♦r ♠♦rt♥ ♦♥ ②r ♦♦♥ t ①♣♦sr ♦ t s t♦ t ♠① r♦♥ ♥r♦♥♠♥t♦ t t②

♦r t s t s ♥ ♦♥ tt tr ♥♥♥ ♦r ♥ rs rt♦♥ ♠② s♦ ♦♠♣♦♥♥t t♦ t r♦r ♦ rt♦♥♥s♣♠♥t ♠s ♥ t ♥t②♣ s♦♥ ♦ t tr♥sst♦r s ♣♣rs ♥t r♦♥ ♦♠♣♦♥♥t ♦ t ♠① rt♦♥ ①s s♦♠ 12 cm−2 ♥ t s ♠♦st② t♦ t ♠♣♦② s r♦t ♣r♦r ♠sr♠♥t ♦ t tr♥sst♦r∆Vgs ♥r rrt♦♥ ♦r ① r♥ rr♥t s ♥♥s r s♦ ♦♥r♠ r② t tr♠♥t♦♥ ♦ t tr♥sst♦r r♥ rtrst tt s♦ r ♥rs♦ t sstrt rsstt② tr ♥tr♦♥ rrt♦♥ ♦r tr ♦t ♦♥ ①♣♦sr ♥ r♦♥ t s s♦♥ stst♦r②♥♥♥ ♣r♦♣rts tt r♥t tr stt② ♦r t ♣♣t♦♥s

♦r t t s♦r♦♥ ♥♥♥ ♣rt♦♥ rsts r ♦rst♠t ② t♦r ♦ t♦ t rs♣t t♦ t ♠sr s♦tr♠ t ♦r ②r ♠sr s♦tr♠ ♥♥♥ s♦s rt♦♥ ♦ t ♦s♠tr s♥ ♦ ss t♥ ♦r ♥ t r♥ ♦ ② r♥ ♥ t t♦ ♥♥♥ ♣r♦rs s♥ ♠♥♦ ♥ t s ♥ ttrt t♦ t ♦♥trt♦♥ ♦ t ♥trstts ttr ♥♦t ♦♥t ♥ t ♣rt♦♥ s ♦♥ t s♦r♦♥ ♥♥♥ ♣r♦r ♦rts s t sstrt rsstt② s ♥ ♦♥ t♦ ♥tr t♥ tr ①♣♦sr t♦ ①♥ ② ♥ ♣r ♦♥③♥ ♥r♦♥♠♥t t s♦tr r♦♥ rrt♦♥ ①♥ t Φeq ♦ ×1013 cm−2

♦s♠tr② ♠sr♠♥t t s r② ♦♥ t ♦♠♦♥t② ♦ t ♣r♦r ts ♦ s ♥ t t rs♣♦♥s ♦ s s s t♦ tr♠♥ trt♦♥ rs♣♦♥s r rt♦♥ ♥ t♥ t s ss♠ t♦ q t♦ t♦♥ ♦ t ♦tr s s ♥ t ♥♥♦♥ rt♦♥ ♦r ts rs♦♥ t♦♥tr♦ ♦ t ♣rrrt♦♥ ♣r♠trs ♦ t s s ♦ ♥♠♥t ♠♣♦rt♥ s r s♣♣ ♥ ♦♠♦♥♦s ts ♣rrtr③ r♦♠

♦♥s♦♥

t ♠♥trr ♦r t s t r♠♥♥t st♦ ♦ t r r ♦t r♦♠ t ♣r♦r tst♥ ♣r♦r ♥ st ♦ st♦♥ ♣r♠trs tr♦r ♥ r♥ ♥ ♦rr t♦ st t s t rtrsts sts② ♣♣t♦♥s s st♦♥ ♥ tst♥ ♣r♦r s r♣♦rt ♥♣♣♥①

①♣r♠♥ts ♣rs♥t ♥ ts ♣tr s♦ tt ♥ t ♦♥t①t ♦ t t ♠♦♥t♥ ♦ ♦s♠trsrr♦♥♥ ♠trs s♥♥t ♥♥ ♦♥ trrs♣♦♥s t♦ ♥tr♦♥s ♥♦ rst r s♦ ♦♥ ♥ trtr ♥ t s ♦ ♦♥r②♣♦t♦♥s ♦r t ♦♣♠♥t ♦ rt♦♥ s♥s♦r ts ♠♥s tt ♣r♠♥r②rt♦♥s ♦ s♥ ♦s♠trs ♥ ♥ r♦♥ ♠s ♥ s t♦ st♦♣rt♦♥ ♦s♠trs ♥ ♦s rt♦♥ ♦ t rt♦♥ s♥s♦r t♦ r②♥ ♦♥② ♣r♦r♠ t ts ♥ s♥ ♥ s♥ t ♠tr ♥r♦♥♠♥t ♥ trr② ♣♦st♦♥ ♦ t ①♣r♠♥t

♥♦tr ♣♣r♦ s t♦ ♦♣ s♥s♦r ♣♥ tt ♠♥♠③s t ♣rt ♥trt♦♥ t t s s♦t♦♥ s sss ♥ ts ♣tr r t rsts ♦ trrt♦♥ ①♣r♠♥ts r s ♥ t st② ♦ st♦♠♠ ♣♥

♦ st② ♥ t t ♦♠♣tt② ♦ ts ♣♥ t t rt♦♥ ♥r♦♥♠♥t t ♦♥t r♦ ♦ s ♥ ♣r♣r ♥ ts ♣tr ts ♠♦s ♥ sr t rrt♦♥ ①♣r♠♥ts ♦t t♦ ts t♦♥ r ♣rs♥t♥ tr rsts ♥② sss

♣tr

rtr③t♦♥ ♦ ♣♥ ♦s

♥ ♣tr t s ♥ s♦♥ tt t ♣rt ♥s ①♣t ♦r ②rs ♥t ♦r ①♣r♠♥ts ♦ t rt♦r ♠♦st② r♦♥s ♥ ♣ π± t ♦r r♦ ②♥♠ r♥ ♦ ♠♦r t♥ ♦rrs ♦ ♠♥t r♦♠ 910 t♦1415 ♣rts♠2 t s♠♦♥t♦r ♦s♠tr t②♣s s ♦r ♣rt ♥♠sr♠♥t r t rsstt② ♦rr s ♣♥ ♦s sr ♥ ♦ ♦r s r♦ ②♥♠ r♥ t♦tr t s♥stt② ♥ ♦ ♥r♥ ♦♥ s♥ s r② ♥♦t ♥♦

♣♥ ♦s s♦ r♦♥♣♥♥t ♥rs ♦ t ♦t t♥ trtr♠♥s ♥ t② r s♣♣ t ♦♥st♥t ♦rr rr♥t ♥ s♦♠ ♦ts s ♥ ①t♥s② rtr③ ♦r ♥tr♦♥ tt♦♥ t rs♣♦♥s ♦♣♥ ♦ s ♥ r♦♥ ♥r♦♥♠♥t s♠r t♦ t ♦♥ ①♣t t t ①♣r♠♥ts s t♦ st st ♥ t s ♣rrqst ♦r tr t③t♦♥ ♥ tst②♣ ♦ ♣♣t♦♥

s♥stt② ♣♥ ♦s ♥ ♦♣ ♠♥② ♦r ♠ ♥ ♠tr②♣r♣♦ss ♥ t ♦ ♥tr♦♥ ♠sr♠♥t ❬♦♣ Pr♦ ♦s❪ ♦r t ♣r♣♦ss♦ ts ♦r t♦ t②♣s ♦ ♣♥ ♦s ♥ st ♥ ♥stt ♦r t ♥s rst s ♠♥tr ② t ♥tr ♦r t♦♥ P②ssP ♦ t ❯♥rst② ♦ ❲♦♦♥♦♥ str t s♦♥ ♦♥ r t♦ ♦sstrt ② t ③ tr♦♦② ♥sttt ♦ Pr ③ ♣ ② r ♥♦♥♥r t ♦♠♠r ♥♠ ♦ ♦♥ s ♦♥ ♦ ♥

s t sss ♥ t tr t ♦s♠tr rs♣♦♥s r♦♠ ts s♥stt② s ♥ ♦r ♠①♠♠ Φeq r♥ ♦ t ♦rr ♦ 12 cm−2 ♦rstrt♦♥ ♣♥♦♠♥ ♣♣r ♦ ①t♥ t ♠sr♠♥t r♥ t♦ t ♦ t sr 14 cm−2 ♥♦tr s tr♦r ♥ r♦♠ ♣r♠♥r② stsrr ♦t t ♥ t ♥♥ts ♦♦ ♥t ♦r s ♣r♣♦s s♠s t♦ t♦♠♠r ♣♥ ♦ ♠♦ P❲ ❬❪

♠ ♦ ts ♣tr s ts t♦ ♣rs♥t ♥ t t rtr③t♦♥ ♦ ts♦♠♠r ♦ P❲ ♥ t♦ ♣r♦ ts ♣♣t② s str♦♥ ♦s♠tr ♥t ♥ r♥ ♦ ♥trst ♦r t ♦r♦r t ♠sr♠♥t ♦ t ②♣r♠trs ♦ t s♥stt② P ♥ ♦s s♦ ♣rs♥t r

s s t rs♦♥ ② s♦♠t♠s ts s r ♥t t t ♥♠ ♦ ♥tr♦♥ ♦s

♦♠♠r P❲ ♣♥ ♦s

r ♣♥ ♦s P❲ s ♦♠♠r② s♣♣ ♥ rt♥ s t♦♣♦r♥r ♥ t♥ s ♦tt♦♠ ♦r♥r ♣s

♦♠♠r P❲ ♣♥ ♦s

P❲ ♦s r ♣r♦ ② sr s♠♦♥t♦r ♦♠♣♥s ❯ t ♣♣t♦♥s ♦ ts ♦s r ♠♥② ♥ t ♦ ♣♦t♦♥trr♣trs ♥ r♠♦t ♦♥tr♦s st ♦ t②♣ tr ♥ ♦♣trtrsts ♦r ts ♥ ♦♥ ♥ ❬♣❪ ♦r♥ t♦ t tr♦♥♥♦♠♥tr t ♣rt ♥♠r P❲ ♠♥s t ♦♦♥ s t ♠tr s♦r t t r♦♥ ♦ t s♦♥ P ♥ts t rt ♥t♦♥ P rt♦♥ s♥st ♦ ♥ ❲ s t sr ♥♠r ❬❪ t tt tss r ♦♠♠r② ♥ r ♥♠rs t rt② ♦ ♦st e♠s t ♣♦sst② ♦ s♥ t♠ s ♥tr♦♥ ♦s♠tr ♥ ttrt ♣r♦s♣t

s ♦ ♦♥ssts ♦ s♠ ① ♠♠2 s♦♥ t t ♣rt ♦ t ♦♠♣♦♥♥t♥s ♥ ♣st ♣♥ ♦s ♥ s② ♥♥ s s♦♥ ♥ s♦♠♣♦♥♥t s ♥ tr r♥t ♣♥s s ♦♦♥

• P❲ tr♥s♣r♥t ♣st ♣♥ tt ♦s t t♦ s♥stt♦ t r♦♠ ♥♠ t♦ ♥♠

• P❲ ♣st ♣♥ t ②t tr tt ♠ts t t s♥stt② ♦ t t♦ ♦t ♥♠ t♦ ♥♠ s rt♥ s ♦

• P❲ t ♣r♦s ♦♥ t ♥ ♣st ♣♥ s t♥ s♦

s ♦ tr ♦r s♥stt② t♦ t ♥ tr ♠♥s♦♥s tt ♦s ♥ s②♥♥ ♥ss ♥t t s♠♣s s ♦r s st② r ♣ ♦s ♦t t②♣ P❲

rtr③t♦♥ ♦ ♣♥ ♦s

♦♥s♦♥s r♦♠ ♣r♦s sts

st② ♦ t P❲ ♦ ♣r♦ ② s ♥tr♦♥ s♥s♦r s rss t s♥ rsts ♦ rrt♦♥ tsts ♥ t ♥tr♦♥ ♦t P t② t ❬❪ r s♠♠r③ ♥ ♣♦rt r♦♠ ♥t ❬❪ ♥ r t ♦♦♥

• t s r ♣rs♥t ♥ s t♥ss ❲ µ♠ ♥ rsstt② ρ Ω·♠

• t ♦s r ♠sr ♥ ♦♥t♦♥ ♦ ♥tr♠t ♥t♦♥ ♠ ♣♣②♥ ♦♥st♥t ♦rr rr♥t tr t rt♦♥ ①♣♦sr

• t rs♣♦♥s ♦ t ♦s t♦ ♥tr♦♥s r s♦♠t♠s r r♦♠ t ♥rt②

• t ♠sr s♥stt② t♦ ♥tr♦♥s > ❱ r ♦ ♦t ♠❱12 cm−2 ♦r ♣rt ♥s ♠sr ♥ t ♥t st② r♦♥ s♦♠ 12 cm−2 ♥♦t ♥ ♥② r ♥♦r♠t♦♥ ♦t t ♦s ♦rt ♦r ♥tr♦♥ ♥s

• rrt♦♥ t γr②s r ♣r♦r♠ ♦♥ ts ♦s ♥ tr rs♣♦♥s s♦♥ t♦ r② ♦ ♦♠♣r t♦ tr ♥tr♦♥ s♥stt② ♦r ② ♦ ♦♥③♥♦s ❱F st ♦ ♦t ♠❱ s ♠sr s ♦rrs♣♦♥s t♦ ♥tr♦♥s♥stt② ♦ ♦t ①12 cm−2

• ♦♦♥ ♥tr♦♥ rrt♦♥ ♦ Φ(>140keV ) ①13 cm−2 r♦♦♠ t♠♣rtr♥♥♥ ♦ ❱F ♦ ♦t s ♠sr tr ②s

s♣♦♥s ♦ P❲ t♦ ♥tr♦♥ ♥ ♣r♦t♦♥ rrt♦♥

r♦♠ sr rrt♦♥ ♠♣♥s r rr ♦t ①♣♦s♥ t P❲ ♦st♦ t rt ❱ ♣r♦t♦♥ ♠ ♦ t t② ♥ t♦ t ♥tr♦♥ ♥r♦♥♠♥t ♦ t t② t

st♦♥ ♦ ts ♣r♠♥r② rsts s ♥ s♠♠r③ ♥ ❬❪r t ♠sr♠♥ts ♣r♦r♠ r♥ rt♦♥ ①♣♦sr ♦♥♥ ♥ ♣♦tt s ♥t♦♥ ♦ Φeq ♦r t t♦ ts ♦ ♦ ♦♠♣rs♦♥ ♦ t tt t rsts ♦t♥ ♥ t t② ♣r♦t♦♥ ♥s r ♦♥rt ♥t♦Φeq ② ♠♥s ♦ t r♥ss t♦r κ ❬♦❪

♦♥♥ ♣r♦t♦♥ t r ♦t♥ r♦♠ r♥t rrt♦♥ tsts ♣r♦r♠t r♦s ①s r♥♥ r♦♠ ①8 t♦ ①10 ♣r♦t♦♥s♠2 × s) ♥ t ♦♥st ♥tr♦♥s r ♦t♥ t ♥ q♥t ① ♦ ①7 ♥tr♦♥s♠2 × s) ♣♦tt t ♥ ♠sr t ♥ ♥tr♠t ♥t♦♥ ♠ t ♦rr rr♥t ♣s r♥♥ r♦♠ ♠s t♦ ♠s rt♦♥ ♥ ts ♦♥t♦♥ ♥♦s♥♥t r♥s rr♥ t rs♣♦♥s ♦ t s t♦ t t♦ r♥t ♣rtsr ♦sr ♦t t st ♦♦ t s♠ tr♥ r♣rs♥t ② t ♦tt ♥ ♥ t♥ ♥ rr♦r ♦ ±

♦r ♥ t tr ♥ ♥t t r♦♥ ♣ t♦ Φeq ∼ ①12 cm−2 ♥ ts r ♥♦t s♥st t♦ st r♦♥s t rs♣♦♥s s ♥r ♥ ♥ r♠♥t t t

♦♠♠r P❲ ♣♥ ♦s

r P❲ ♦♥♥ s ♦♥ ♠sr♠♥ts t t ♥ tst

s♣♠♥t ♠ s♥ ♥ s♦♥ ②♣♦tss s ♣ t♦ sr14 cm−2 ♣r♦♥ tt ts s st t♦ ♠sr ♣rt ♥s ♦rr ♦t st ∆❱F ♦ ❱ s ♠sr ♦r ♥tr♦♥ q♥t ♥ ♦①13 cm−2 ♥ ♥t♦ ♦♥t t r♥ ♥ t r♦t ♠t♦s ♥ ♥ t♣rt s♣tr ts ♣rt s♥stt② s ♥ r♠♥t t t r② s ♠sr② ♥t ❬❪

♥ t ♦♥♥ ♠sr♠♥ts r s♦ ♦♠♣r t srs ♦ t t♥♠♠t② tr rrt♦♥ ♦♥ t♦t ♣r♦r♠♥ ♥② ♥♥♥ ♣r♦r ♦r tr r♦t ❬❪ ❲ t ♦♥♥ t r♣rs♥t t ❱F ♥rs r♦♠ ts♠ t ♦♥ ♠sr♠♥ts ♦♠ r♦♠ r♥t s♠♣s ♦ t♠ ①♣♦s t♦ r♥t ♣rt ♥ ♦r t ♦♥ t ♣rs♥t ♥ t ♥tstrt♦♥ ❱F s ♥♥♦♥ rtss t r♠♥t ♦ t ♥♥♥ t sr♦♥ ±

♥ ♣r t t tsts ♣rs♥t ♥ srs ♦ r♦♦♠ t♠♣rtr ♥♥♥ ♠sr♠♥ts r ♣r♦r♠ ② s♦ ♦♦♥ ♣r♦t♦♥s rrt♦♥ ♦①14 cm−2 rs ♥ ❱F ♦ ♠♦r t♥ tr ♦rs s rst rstts r tt ♦r ts ♦♥tr♠ ♥♥♥ ♣♥♦♠♥ ♥ ♥ ss ♦rt ♣rs♦♥ ♥ t ♣rt ♥ ♠sr♠♥ts

♥ ♦ t ♣r♦t♦♥ rs♣♦♥s rs ♣rs♥t ♥ s ♥ ③♦♦♠ ♥ t ♦♥ r♥ ♥ s♦♥ ♥ ♥ ♥r s ♥②ss ♦ t ♦r ♦ tsr ♦♥r♠s t s t♦rt② ♣rt ② rt③ ♥ rst♦♥ ❬❪ ♦r ♦rsstt② s♠ ❲ rt♦ ♣♥ ♦ ♦♣rt♥ t ♥tr♠t ♥t♦♥ ssr ♥

♦rr ♦t r♦ss t ♦ strts t♦ rs ♥r rrt♦♥ t♦ t

rtr③t♦♥ ♦ ♣♥ ♦s

r P❲ rt♦♥ rs♣♦♥s ♦r t ♦ Φeq

♣r♦♠♥♥t rss ♦ ❱Fj s ② t rs ♦ t ♠♥♦rt② rrr t♠♥rs♥ t rrt♦♥ t ♦t s♥stt② t♦ ♣rts ♦♠s ♣♦st t♦ t s♦♥ ♥t rss ❱Fj ♥rss ♥ t s rsst♥ ❱Fb

tt strts s♦ t♦ ♥rs t ♥rs♥ Φeq s t♦ tst t r ♣r♦r r♦♠ r♥t s♥s♦r ts ♣r♦

② r♦s ♠♥trrs ♥ r♥t ♣r♦t♦♥ sts ♥ ♥ r♥t t♠ ♣r♦s ♦r strt♥ s②st♠t st② ♦ t P❲ s♥s♦r t ♦ ♦s s♥ ♣r♦r ♥ ♠sr ❬ ♠❪ t t ♠ t♦ ♥sr t ♦♠♦♥t②♦ t s ♥r st② ♦s ♠sr ♥ t ♦♦♥ ♦ ts ♣tr t❱ ♥ ❱ t♥qs ♥ ♦t ♦rr ♥ rrs s ♠♦ r tr♦r str♦♠ ts t ❬♦❪

s♠♠r③s t ♠sr ♦ s t♦ t ♦♠♦♥♦s s♥s♦rt s r ♦ ♠rt t ♥t ♦t ♥r ♠ ♦♥st♥t rr♥t ♥t♦♥s ♥ ♠sr t♠♣rtr r♦r r♥ t ♠sr♠♥t s ± r♦♠ ts ♣r♠♥r② sr♥♥ t s ♣♦ss t♦ ♥t② tt t ♦st srs ♦s ♣r♦ ② ♣rs♥t ♥ ♥t ♦t ❱F,0 ♦r ♦ ♦t trs♣t t♦ t ♦♥s ♥♣♥♥t② ♦♥ t ♣♥ t②♣ t ♦tr ♦srst t♦ ♦♠♦♥♦s t♥ ± t ♥ r ❱F,0 ♦ ❱ s trrt♥ t ♦♠♣♦♥♥ts t ♦tr s r ♣t t♦ s ♥t ♦♦♥ ♥stt♦♥s

rs s ♠sr♠♥ts

tr sr st♣s ♦ ♣r♦t♦♥ rrt♦♥ ♥ t t② t tr♠♥t♦♥ ♦t ♦ rr♥t s ♥ ♦♥ ② ♠♥s ♦ ❱ ♥ ❱ ♠sr♠♥ts rt♦♥♥ ♥rs ♦ t rr♥t ∆ s ♥ ② t r♥ t♥

♦♠♠r P❲ ♣♥ ♦s

♦♠♣♥② P Pr♦t♦♥ ❨r ♦ ♠r ♦ r ❱F,0

t②♣ st ♣r♦r♠♥t ♣s t ♠ ❱

P❲ ❯ ± P❲ ②s ± P❲ ②s ± P❲ ②s ±

P❲ ±

P❲ ♦s ♦r t sts rr ♦t t

t rr♥t ♠sr tr ♥ ♦r rrt♦♥ ❬♦❪ ♥ t rr♥t ♥rs ♦ t P❲ ♦s s ♥ ♣♦tt s Φeq tr ♥ ♥♦r♠③t♦ ♥ t ♣tr ♣♦♥t ♦rrs♣♦♥s t♦ ♥ ♥ ♦ rrt t♣r♦t♦♥s ♥ s♥ ①♣♦sr t♦ ♥ ♥ ♦r♦r ♦r ♠sr♠♥t ts♠♣s r r♦t t♦ t s♠ ♥♥♥ stt ② t♥ t♠ ♦r ♠♥ts t♦ ❬♦❪

r♦♠ t s ♣♦ss t♦ s tt t rr♥t ♥rs s ♣r♦♣♦rt♦♥t♦ Φeq ♥ t r♥ r♦♠ 10 cm−2 t♦ 13 cm−2 ♥ tr 14 cm−2 ♥ t ♥tr♠tr♦♥ t ♠sr ∆ s ♠ r t rs♣t t ♦rs♥ ♥r ♦r s♠r rst s s♦ ♥ ♦♥ ♥ s♦♥ srs ♦ ♦s rrt t ♥tr♦♥st t t② ❬❪ ♦r Φeq < 13 cm−2 t ♦s ♥ ts s s ♦♥tr ♥ t s♠ ② ♦ t ♣rt tt♦r ♦s ♣rs♥t ♥ t ♦ r ♥② ♥r② tt ♦♥t♥♦s ♥ ♥ t ♣tr ♥t ♣r♦♣♦rt♦♥t② t♦r ∆Φeq s t t♦ ①−20 ·cm2

♦ t ♥ ♦♥♥♥t② s t♦ st♠t t s t♥ss ❲ ♦t P❲ s ♥ t ♣r♦t♦♥ ♠ ♥♣♥♥t ♣rt ① ♠sr♠♥tsr rr ♦t ♥ ♣r ② s♥ srs ♦ rt ♣rt tt♦r ♦s s s t ♦♠ ♦ ts rr♥ s s ♥♦♥ r♦♠ ts ♥♣♥♥t ♠sr♠♥ts ♦♥ ♥ ♦♠♣r ①♣r♠♥t ♦♥t♦♥s t s ♣♦ss t♦tr♠♥ rr♥t rt ♠ rt α ①10−17 ♠ ② ♦♠♣r♥ α tt t♦r t ♦r ♦r t P❲ ♦s t s t♥ ♣♦ss t♦ st♠t tP❲ ♦s ♦♠ ①−3 cm3 r♦r ♥♦♥ r♦♠ ❬♣❪ tt tP❲ sr s ♠2 t s ♥② ♣♦ss t♦ t t♥ss ❲ ♦t µ♠ s rsts t♦ ♥ r♠♥t t t ♦♥ r♣♦rt ♥ ❬❪

♥ t ♦ ❲ s tr♠♥ ♦r t P❲ ♦s t s st ♣♦ss t♦st♠t t ♠tr rsstt② ② s♥ t ♣t♦♥ ♦t tr♠♥ r♦♠ t ❱r ♦ ♥♦♥rrt P❲ ♦ s t ♦♥ ♣rs♥t ♥ ❬♦❪s rst ♣♣r♦①♠t♦♥ ♥ ♦♥t♦♥ ♦ ♣t♦♥ t s tt

Vdep =q

2ǫǫ0

NeffW

r ǫ0 ①−14 ♠ ǫ ♦r s♦♥ ♥ q t ♠♥tr② r s qt♦ ①−19 sr♥ ❱dep ❱ ♥ ss♠♥ ❲ µ♠ t s ♣♦sst♦ t ♥ t ♦♣♥ ♦♥♥trt♦♥ ♦ t s♦♥ ♠tr ♥t②♣ eff

rtr③t♦♥ ♦ ♣♥ ♦s

r P❲ rtrsts ♥ rrs s ♥♦r♠③ t♦ rr♥t♠sr♠♥t ♥ ♥rs♥ rrt♦♥ s t ❱ ♣r♦t♦♥s ♣t♥ ♠sr♠♥t ♦ ♥ ♥rrt ♦

×1012 ♠−3 ♦ ♥♦♥ t tr♦♥ ♠♦t② ♥ ♥t②♣ s♦♥ µn ♠2V −1s−1 t s ♥② ♣♦ss t♦ t t ♠tr rsstt②

ρ =1

qµnNeff

≃ 2.7 kΩ · cm

s ♥ ♥ ♦♦ r♠♥t t t ♦♥ r♣♦rt ♥ ❬❪ ♠ rtr ♦♥r♠t♦♥ ♦ t s ♥ stt ♥ r♥ t ♥②ss ♦ trt♦♥ rs♣♦♥s ♦r ♦ t P❲ ♦s ♦sr ♥

♦rr s ♠sr♠♥ts

rtr③t♦♥ ♦ t P❲ ♦s ♥ ♦rr s s ♥ ♦♥ ② ♠sr♥ t ♦ ♦rr ❱ rs ♦r s♠♣s rrt t♦ r♥t Φeq s t ❱ ♣r♦t♦♥s ♥ ♥ t ♥tr♦♥ ♦ t t♦t ♦ ♦s r①♣♦s t♦ ♣r♦t♦♥s ♥ ♦tr t♦ ♥tr♦♥s ♦r ♥ ♥ st♣ t♦ s r①♣♦s ♥ ♦rr t♦ t r♥♥② ♥ t rsts ♠sr♠♥ts r rr ♦ttr rrt♦♥ s♥ tst♥ s ♦♥ st♥♦♥ t② ② ♥t♥♥rs♥ ♠s rr♥ts ♣ss ♥ r♦r♥ t ♦♦♥ ♦rr ♦tsr♦ss t ♦ tr♠♥s t ①♣r♠♥ts r rr ♦t ♥ ttt ♦①

♥ s♣② t rsts ♦ t ♠sr♠♥ts ♦♦♥ ♣r♦t♦♥ rrt♦♥ ♥ ♦t ♥r ♥ ♦rt♠ s rs♣t② r ♦rrs♣♦♥s t♦t r ♦ t t♦ ❱ rs ♠sr ♦r t t♦ s ①♣♦s t♦ t s♠♥ ♦r Φeq < ①13 cm−2 t ❱ r ♦ t ♦ st ♥ t ♣♦st rt♦♥t ♥rs♥ ♣rt ♥ t r ♥s t r strt t♦ ♥ t♦rs♠r ❱F ♥ ♦rr rr♥ts ♥ t ♦rr ♦ ♠ r r r♦♠ tt ♣♦♥tt P❲ ❱ ss♠ t②rst♦r ♦r t♦t r♦r♦s ①♣♥t♦♥♦r ts ♣♥♦♠♥ s ♥♦t ♥ ♦♥ t s ♥ r♣♦rt ♥ trtr ❬♦❪ tt

♦♠♠r P❲ ♣♥ ♦s

r ♦rr ❱ rs tr ❱ ♣r♦t♦♥ rrt♦♥s ♥r s ♥ t ②①st rr♥t ♣♦♥ ♠s ♦rr ♦t s s ♣♦tt r ♦rrs♣♦♥s t♦ r♥t Φeq s ♥t ♥ t ♥

rt♦♥ ♥ ♥s ♥ s♦♥ ♦♥tt② ♥ t♦ t ♦r♠t♦♥ ♦ ♣♥♣♥t②rst♦r strtrs ♥ s ♣♦r ♥ ♦rr s s ♥ t s ♦ t s ♥rsts

st ♦ s rrt t ♥tr♦♥s ♥ ♦♥r♠ t ♦ ♦r♥ t ♥ ♥ t s♣ ♦ t ❱ r ♦r Φeq ①♥ ①13 cm−2 ♥st♦ ts ♦srt♦♥ t s ♣♦ss t♦ ♥ ♥ ♠ t ♣♣r ♠t ♦r t ♥t♦rr rr♥t t t P❲ ♦ ♥ s ♥ ♦s♠tr ♣♣t♦♥s

♦r t ♣r♦t♦♥ rrt s♠♣s s♦♥ ❱ r s ♠sr tr ♠♥ts♦ ♥♥♥ t t ♦ ♥ Φeq r♥s t t ♦ t ♥♥♥ trt♠♥ts r② ♦ ♦♥ t ♠sr t s s♦♥ ♥ ❱rt♦♥s ♥ t ∆❱F ♦♥ t♦rr ♦ t♦ ♥ ♠sr ♦r s♠♣s rrt t♦ ①12 cm−2 ♥①14 cm−2 rs♣t②

♥ t Φeq r♥ ♦ 13 cm−2 t t♥ ♦ t s♠♣s s ♥st r② t♥♥ r♦r ♦ t ❱ r ♦ ♠♦r t♥ s s♦♥ ♥

♦ ♥♥ ssts t♦ ♦ ♣rtr② ♥ t ♥ r♥ 13 cm−2 t♦t t ♦ s ts ♦ ♥♥ ♥♥♥ ♣♥♦♠♥ s ♥♥ ♥t②♦♥r♠s F ♠ s t ♣♣r ♠t ♦r t rr♥ts tt ♥ s ♥ t ♦sr♦t

♥ ♥t♦ ♦♥t t ♦ ♠sr rs t s ♦ ❱F ♦r tr strr♥ts ♥ ①trt ♥ ♣♦tt s ♥t♦♥ ♦ Φeq ♥ ♦rr t♦ tr♠♥ trt♦♥ ♦ t r♦♥ s♥stt② t r♥t ♦rr rr♥ts tr st

rtr③t♦♥ ♦ ♣♥ ♦s

r ♦rr ❱ rs tr ❱ ♣r♦t♦♥ rrt♦♥s ♦rt♠ s ♥ t②①s t rr♥t ♣♦♥ ♠s ♦rr ♦t s s ♣♦tt r ♦rrs♣♦♥s t♦ r♥t Φeq s ♥t ♥ t ♥

Φeq < 13 ♥ > 14♠−2 Φeq♥ t ♦ 13♠−2

r ❱ rs ♦r ♣r♦t♦♥rrt P❲ ♦r ♥ tr ♥♥♥ ♠♥ t

rr♥ts r ♠ s r♦t rr♥t ♠ ♠①♠♠ ♦ r♦♠t ♦srt♦♥ ♦ t ❱ ♦r ♥ ♠ s st s ♥ ♥t♥t♦♥②st ♥ t♥ t t♦ ① ♦r ♥ ♣♣r ♠ts ♦r♥ t♦ t tr♦♥st♥rs ♦r ♦♠♠r rr♥t s♦rs

♦♦♥ t t♦rt ♥t♦♥s ♦ t rt♦♥ rs♣♦♥s ♦ ♦rr

♦♠♠r P❲ ♣♥ ♦s

♦rr rr♥t ∆V/∆Φeq ∆V/∆Φeq ②♥♠ r♥♠ ①♣r♠♥t ♠❱♠−2 rt♦ t♦ ♠ Φeq♠−2

♠ ①−10 ≥ ①14

♠ ①−11 < ①14

♠ ①−11 < ①14

P❲ s♥stts ♥ ②♥♠ r♥s t r♥t ♥t♦♥ s

s ♣♥ ♦s t♦ ♣rt rrt♦♥ s ①♣t t♦ ♠♣r♦ t r ♥t♦♥s ♦r ts rs♦♥ ♦rr rr♥ts ♦r t♥ ♠ ♥♦t ♥ ♦♥sr ♥ts st②

s♦s t P❲ ♦rr ♦t sts ♦r t ♥t rr♥ts ♦ ♥ ♠ rs♣t② ♥ ts ♣♦ts ♦t t r♦♠ ♣r♦t♦♥ ♥ ♥tr♦♥ rrt♦♥ ♥ s ♣♦tt ♣♦♥ts ♥ ①trt r♦♠ t ♦♠♣t ❱ r♦ r t r♥t ♦s ♥ ♠sr ♦♥ tr rrt♦♥

♦r Φeq < ①12 cm−2 ♥♣♥♥t② ♦♥ t ♦rr rr♥t s t s ♥♦t s♦ s♥stt② t♦ st r♦♥s ♦r Φeq > ①12 cm−2 t ♥r ♣rt ♦ trtrsts s ♥ tt ♥ t s♥stt② ∆❱∆Φeq ♥rs t ♥ ♠ ♥ ♠sr t rs♣t t♦ t ♦♥ tr♠♥ t ♠ rsts ♦ tst♦♥ r r♣♦rt ♥

t t r rr♥t t ♥ ♥ s♥stt② s ♦r ♥r ts ♥t♦♥ ♦♥t♦♥s t ②♥♠ r♥ s r ② ♦t t♦r t♦ tr♦t rr♥t ♥ ♦s♥ ② t sr t♦ st t s♥stt② r♦♠ t♣rs♥t rsts t ♣♣rs tt ♠ r♠♥s t r♦t ♦♥t♦♥ tt ♥sr tst ♦♠♣r♦♠s t♥ t s♥stt② ♥ t ♠sr r♦♥ ♥r♥

♥②ss ♦ t ♦rr rr♥t ♣s

st② ♦ t t♠♣♦r ♦r ♦ t s♥ ♦ rrt P❲ ♦s s ♥rr ♦t ♦♥ tr s♠♣s rrt t ♥rs♥ q♥t ♣rt ♥s r♥♥r♦♠ ×1012 cm−2 t♦ ×1014 cm−2 s♠♣s ♥ ♠sr tr rrt♦♥r♦r♥ ♦♥ ♠s t♠s t s ♦ t ♦rr ♦t r♥ t ♥t♦♥♦ s♦♥s sqr rr♥t ♣s s s ♥ r③ ② ♠♥s ♦ ♦rt♦r②tst♥ s ♦♥ t② ♦rtr

♥ s♦ t ♦t♦♥ ♦ t ♦rr ♦t rt♦♥ t♥rs ♦ t ❱F t rs♣t t rst r♦r s t t ♣♦♥ ♦rr rr♥t♥t♦♥s ♦ ♠ ♥ ♠ rs♣t② ♠sr♠♥ts ♥ ♣r♦r♠rt② tr rrt♦♥ ♠♣t② ♠rrs s s tr r ♥♥♥ ♣r♦ ♦ ♠♥ts t ♠rrs ♦♥t♥♦s ♥s ♣rs♥t ♦♥ t ♣♦ts r tst t ♠ ♦♥ t t srs t ♦t ♥ ♥t♦ rts r t ❱F

r♦r t t t rs r♦r ♠♠t② tr rrt♦♥ ♣rs♥t ♦rt♠ ♦r

t t t♠ s rs r♦♠ t ①♣♥ ♥ r t ♥ ♦ t♦♥tt② ♠♦t♦♥ ♣r♦ss s ①♣t ♦r r♦r ♦r t P❲

rtr③t♦♥ ♦ ♣♥ ♦s

F ♠

F ♠

F ♠

r r♦♥ s♥stt② ♦ P❲ s t r♥t ♥t♦♥ s

♦♠♠r P❲ ♣♥ ♦s

Φeq ×1012cm−2

Φeq ×1013cm−2

Φeq ×1014cm−2

r ♥ r♦♠ rrt P❲ ♦s t r♥t t♠s tr ♥t♦♥ ♦rrrr♥t ♦ ♠

rtr③t♦♥ ♦ ♣♥ ♦s

Φeq ×1012cm−2

Φeq ×1013cm−2

Φeq ×1014cm−2

r ♥ r♦♠ rrt P❲ ♦s t r♥t t♠s tr ♥t♦♥ ♦rrrr♥t ♦ ♠

♦♠♠r P❲ ♣♥ ♦s

r♠♥ ♥st ♥ s♣ ♥ rtrst t♠ t rt♠ ♥stt② tt tss ♦s♠trs s ♥ s s t ♦rr stts ②♥ ♥t ♥st♦r ②r ♦ t ♣r♦ ♣♦t♥t rt♦♥s tt ♠♦② t t♠♣♦r♦r ♦ t s♥s♦rs ♦t

t♦ t ①t ②♦t ♦ t P❲ t s ♥♦t ♥♦♥ s♦♥ ♦① ♥ ♣rs♥t ♦♥ t ♦ strtr s ♣sst♦♥ ♦r s♦t♦♥ ②r ♦r♥ ♦ ts tr♠♥s ♥♥♦♥ ♦r s♦t♦♥ ②rs r ♣rs♥t ♦♥ t s r tr♣♣♥♣♥♦♠♥ ♥ t ♣ ♥ ♠② t② ♣r♦ ts ♦rt♠ ♥rs ♦ ❱F

♦r t♠r♦♠ t ♣rt ♣♦♥t ♦ ♦r t ♥♥♥ t ♦rt♠ r♦t ♦ t

♦rr ♦t rs t strt♦♥ ♦t s♦♥ tr t rr♥t ♣s ♥t♦♥♥ ♣rs♥t ss ♦ ♥ ♦r ♦t ♥stt rr♥ts tt♠ ♦r rr♥t ♥t♦♥ t s ♥♦t t♥ ♥t♦ ♦♥t t r♦t ♦ VF s ♥t t♦ t t ♠sr s ② ♦t

♣t♥ t ①♣r♠♥t tr ♥♥♥ ♥ s♦♠ ss t ♦rt♠ r♦t♦ t s♥ s r♣ ② ♠♦♥♦t♦♥ rs ♥ t ♦s ♦t ♦r t♠ s♣♦tt t ♠rrs ♥ rt t♦ t ①♣♦s t♦ ♥♦ ×1013 cm−2 s♥ strts t♦ ♦♥st♥t② rs ♦t ♦♥ s♦♥ tr trr♥t ♥t♦♥ t tt ts ♣♥♦♠♥♦♥ s ♥♥ t r ♦rr rr♥tss ♥ t♦ t♥ tt t strts t♦ t♣ ♥t rt♦♥♥ ts strt t♦ ♥♥ ♦ ♦ ts ♥♦♥♥♥ t s tssst t♦ ♣ t t ♦ t rr♥t ♣ss ♦r t r♦t ♦r t♥ s♦♥

r♦t ♦ ts s ♥ ts ♣r♦r♠ t rr♥t ♣ss tt ♦♥t t♦ ① ♦♥ s♦♥ s ♦r ♠t t rr♥t ♣s s t♦ ♦s♥ ♦r♥t♦ t rtrsts ♦ t tr♥s♠ss♦♥ ♥ r♦♠ t ♦ t♦ t s♦r tt ♣r♦st r♦t ♣s ♥ ♦rr t♦ ♣t t ♠♣♥ ♦ t tr♥s♠ss♦♥ ♥ rsts♣rs♥t ♥ t ♦♦♥ st♦♥s r ts ♦t♥ ② s♥ rr♥t ♣ss r♥♥r♦♠ ♠s t♦ ♠s

rt♦♥ rs ♦r P❲ s

♥ ♥t♦ ♦♥t t rstrt♦♥s ♥ t r♦t ♣r♠trs tr♠♥ ♥ t ♣r♦s st♦♥ t rr♥t ♣s ♦♣t ♦r t st② ♦ t P❲ ♣rt s♥stt②s st t♦ ♠ × ♠s ♦rr ♦t r♦t rs ♥ tr♦r tr♠♥ r♥ rrt♦♥s rr ♦t ♥ r♥t ♣rt ♠s t ♣rs♥t♥ ts st♦♥ ♦r t P❲ ♦s r r♦r ② ♠♥s ♦ t s②st♠ sr♥

s♦s t ♥rs ♦ t ♦rr ♦t rss t Φeq r♦r r♥ r♥t ♣r♦t♦♥ rrt♦♥ r♥s ♥ ♥ t ♥tr♦♥ ♥r♦♥♠♥t ♦ t t②t sr ♥ ♥ t s♠ ♣♦t t s♥stt② t♦ γr②s s s♦ ♥r♣♦rt t r♦ss ♠rrs ♦r t ♠♠ rrt♦♥ ♦r ♦s r ①♣♦s t♦♥rs♥ ♦ss r♦♠ t 60♦ s♦r ♦ t P❯ t② s ♦rs♠♣s r ts ①♣♦s t♦ ♦ ♥ ② rs♣t② s ♥t♥ t ♣♣r ①①s ♦ ♦♥rs♦♥ t♥ γ ♦s ♥ ♣♦t♦♥ ♥s ♥ ♦♥ t t t♦r ♦r ❱ ♣♦t♦♥s ♥ ♦♥ q t♦ ♣②·♠2 ♦r t ♣♦t♦♥ t t ①①s tr♦r ♦rrs♣♦♥s t♦ t ♥♠r ♦ γ

rtr③t♦♥ ♦ ♣♥ ♦s

r t♦♥ rs♣♦♥s ♦ P❲ ♦s ♦s ♦rr ♦t t ♠ s♣♦tt rss t Φeq t ♦ t r♦t rr♥t ♣s s ♦ ♠s ①♣r♠♥tt t♥ ♥ t ❱ ♠ ♦ t t② t s ♥ r♦r t r♥t♣r♦t♦♥ rts ×1011cm−2 · h−1 ×1012cm−2 · h−1 ×1012cm−2 · h−1 ×1013cm−2 ·h−1 ×1013cm−2 ·h−1 ♥ t ♣♣r ①①s t ♠♣♦② r♥ t①♣♦sr t♦ γr②s ♥ s♦ r♣♦rt ♦♥rs♦♥ t♥ γ ♦s ♥ ♣♦t♦♥ ♥s ♥ ♦♥ t t t♦r ♦r ❱ ♣♦t♦♥s ♥ ♦♥ q t♦ ♣②·♠2

♣♦t♦♥s♠2 ♥② ♥ ts rt♦♥ ♣♦t t rsts ♦ t♦ ♥♣♥♥t rrt♦♥srr ♦t t ❱ ♥tr♦♥s ❬❲❪ ♥ ♥ t r♦ ♥tr♦♥ s♣tr♠ ♦ t rt♦r t ❬r❪ s s♦ ♥ ♥

② tt♥ t r♥t t st t s t♥ ♣♦ss t♦ tr♠♥ t rt♦♥ t♦r ♦ t ♥r rt♦♥s♣ tt ♥s t r♦t ♦ t ♦rr ♦t ∆❱F t tΦeq s♦ tt

∆VF = c · k · Φ = c · Φeq r1

c= 9.1 × 109 ♠2/♠❱

st t ♦ t t s♦ t♦ ♥ r♠♥t t♥ ± t rs♣t t♦ t♠sr ①♣r♠♥t t ♦♥r♠ s♦ tt t P❲ ♦s ♦s♥ts♦ s♥stt② t♦ γr②s ♥ t ♥ r♥s ♦ ♥trst ♦r t

♦♠♠r P❲ ♣♥ ♦s

r ♥♥♥ ♣r♦t♦♦ ♦r P❲ s ♠ ♠♣♦② r♦♠ t s♦♥ t♦ r t tr♠ qr♠ ♥ r♥t t♥ ♦♥t♦♥ ①♣r♠♥t ♣r♦r♦♣t ♦r t ♥♥♥ ♦ t P❲ s

♦♥tr♠ ♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦rP❲ s

rst r♦♦♠ t♠♣rtr ♥♥♥ tst ♣r♦r♠ ♦ t P❲ s ❬❪s♦ tt tr t s♥ ♦ t rrt ♦s Φeq ×1014 cm−2rss ♦ ♦t ♦♥tr♠ ♥♥♥ ♦ ts s s ♥ s♦ ♦♥srs ♥ ss t♦ st ♥ t t♦ r♥t r ♠sr♠♥t t t P❲s

♦r strt♥ t ♥♥♥ st② ♥ ♥stt♦♥ ♦♥ t ♥♥ ♦ t♣♥ ♥ t tr♠ ♦r ♦ t P❲ ♦s s ♥ ♣r♦r♠ ♦r ts♣r♣♦s ♦♥ ♥rrt P❲ ♦ s ♥ s s tr♠♦♠tr ♥ t ♣♥ r♥t ①♣r♠♥t ♦♥t♦♥s r♥ ts ①♣r♠♥ts t ♦t♦♥ ♦ ts ❱ ♥ ♦rrs♣♦♥♥ r♦r ♦♥♥ rt♦♥ ♦ t ♦rr ♦t ♣♦♥ µ rr♥t ♥t♦♥ s ♥ ♦s♥ s r ♦ ♠rt s♦ tr♦r trt♦♥ ♦ t ♦s ♦rr ♦t s♣♣ t rr♥t ♦ µ s ♥t♦♥♦ t t♠ ♥ t ♣tr t VF rt♦♥ s ♥ ♦♥rt ♥ t♠♣rtr r♦t② s♥ ♥r s♥

♦♥t♥♦s ♥s ♥ rr t♦ t ♦ ♣t ♥ ♦♥tt t ♠t♣t t ♣ t♦ r♥t t♠♣rtrs r♥♥ r♦♠ t♦ s♥r♦♠ t P❲ s ♣♣rs t♦ r st② t ♥t t♠♣rtr t♥ t♦ ♠♥ tr t ♥♥♥ ♦ t t♥ ♣r♦r s ♦♥ t♠ ♥t♦ r t tr♠ qr♠ r② ♥ts tt t tr♠ ①♥ t♥t s♦♥ ♥ t ♦♥ ♥s t♦ ♠♣r♦ t♦ rr② ♦♥ ♣rs♥♥♥ st②

s♦t♦♥ s ♥ ♦♥ ② t♥ ♣ t ♦♠♣♦♥♥t t t sr ♥♥♥t♠♣rtr ② ♣tt♥ t ♥t♦ ♦♠ ♦ r♠ tr s s♦♥ ② t ♦tt ♥♥ ♥ t s ♦ t ts ♠t♦ t ♥♥♥ t♠♣rtr ♥ r t♦ s♦♥s tr t ♥♥♥ ♦ t tr♠ ②

rtr③t♦♥ ♦ ♣♥ ♦s

r♦r ♥ ♦rr t♦ r♥t t t♠♣rtr stt② ♦r t♠ ♥ t♦ t♦ ♣r♦r♠ r♣r♦t ♥♥♥ ♠sr♠♥ts t ♥♥♥ st② ♣rs♥t ♥ tsst♦♥ s ♥ ♣r♦r♠ ② ♦♦♥ t ♣r♦t♦♦ s♦♥ ♥ ♦r ♥t t ♠sr♠♥t ♣r♦r ♦♥sst ♦ tr ♣ss

• t♦ ♣ t ♦ ♥ tr t t sr ♥♥♥ t♠♣rtr ♥

• t♦ q② ♦♦ t ♦ ♦♥ ♥ tr t ♠t♥ ♦r s♦♥s

• t♦ ♣ t ♦ ♥ ♦♥tt t ♦♣♣r ♣t ♦r ♠♥t ♥ ♦rr t♦ r t r♦♦♠ t♠♣rtr ♦♥t♦♥s ♦r strt♥ t ♦s r♦t

srs ♦ rrt P❲ ♦s s ♥ ts s♠tt t♦ ts ♥♥♥♣r♦r ♥ ♦rr t♦ rtr③ t ♥♥♥ ♣♥♥ ♦ t ♦rr ♦t s♥t♦♥ ♦ t t♠♣rtr ♥ t Φeq P❲ s♠♣s s ♦r ts stsr rrt t ♣r♦t♦♥s t Φeq r♥♥ r♦♠ ×1011 cm−2 t♦ ×1014 cm−2 ♥t② r ♥♥ t ♦r st t♠♣rtrs ♥ tt ♦ sr ♣r♦r ♥ t tr ♣trs ♦ t ①♣r♠♥t tt t r♥t ♥♥♥ t♠♣rtrs r ♣♦tt t r♥t ♠rrs s st ♦♥♥♥ t s ♥ ♦t♥ ② r♥ ♦t t ♦ ♦ts t ♠s ♦rrrr♥t ♣ss

r♦♠ t s ♣♦ss t♦ s tt ♦r Φeq ♦r t♥ ×1012 cm−2 ts♥ ♦s♥t s♦ ♥② ♥ ♦ ♥♥♥ s ♦♥r♠ ② t ♠sr♠♥t t ♠♣t② sqr ♠rrs ♥ rr ♠rrs ♦r Φeq>×1012 cm−2r ♥♥♥ ♦r ♥st ♣♣r ♥ t t♠♣rtr r♥ r♦♠ t♦ t ♥♥♥ s t ♦♦♥ ♦r ♦r t rst ♠♥ts t ♦s♠tr s♥s♦ ♦♥② s♠ rt♦♥ ♦r t rtr t♥ ♠♥ts t rt♦♥ s♣♥rss s s♦♥ ♥ ♥ ♥ t ♥stt ♥♥♥ t♠♦ ♠♦r t♥ 5 ♠♥ts ②s ♥s ♦ strt♦♥ ♣♥♦♠♥ ♥♦t♥ ♦♥

♥ ♥♦② t♦ t s ♥ ♦♥ ♦r t rr♥t rt ♠ rt ♥s♦♥ ♣rt tt♦r strtrs ❬♦❪ t ♦♥tr♠ ♥♥♥ ♦ t ♦rr♦t ♦r t P❲ ♦s s♠s t♦ ♦♦ ♦rt♠ ♥t♦♥ ♦ t t♠s t ♥♥♥ ♦ VF t r♦♦♠ t♠♣rtr s s t r t♠♣rtrs s♦s♥ t♦ sr ② ♦♥ ①♣♦♥♥t ♥ ♦rt♠ tr♠ rst ♣rt ♦ t♥♥♥ rs ♠sr t ♦r t < ♦ ♠♥ts rs t rs♣t t♦ t♦♥ t ♦r t♠♣rtr ♦r ts rs♦♥ ♦♥② t t ♠sr r♦♠ t♦ ♥ ♦♥sr ♦r s ♣r♠tr③t♦♥ ♥② ♥ t s♠ ♥♥♥♥t♦♥ t t♠♣rtr ♣♥♥ s ♥ s♦ ♥tr♦ s♦ tt

VF (t) = A − α · exp

(

− t

τ

)

− β · ln(

t

t0

)

− (|Tc| × ∆T )

r ∆T = T − Tref

♦r t♠♣rtr ♥ ♦r Φeq t t r tt ♦r♥ t♦ q t t0 st q t♦ ♠♥ ♥ ref t♠♣rtr ♦♥t c s ♥

♦♠♠r P❲ ♣♥ ♦s

Φeq ×1011cm−2

Φeq ×1012cm−2

Φeq ×1013cm−2

r ①♣r♠♥t t s ♦r t ♥♥♥ ♣r♠tr③t♦♥ ♦ t P❲ ♦sr♦♠ t♦ t t rr t♦ ♦s rrt t ♥rs♥ ♣rt ♥s ♦♥t♥♦s♥s r t t ts ♦♥ t♦ ①trt t ♣r♠trs t♦ s ♥ q

rtr③t♦♥ ♦ ♣♥ ♦s

q s ♥ ♥st ♠sr r♦♠ r♥t st ♦ ♦s tt r rrt♥ ♥♥ ♥ r♦s ♦♥t♦♥s c ♦r t P❲ ♦s s ♥t♦♥ ♦Φeq ts ♦r rrt♦♥ s ♦ ♠❱ s t s tr♠♥ ② tt♥ t①♣r♠♥t ♠sr♠♥ts ♣rs♥t t ♠♣t② sqr ♠rrs ♥ Φeq ♣♥♥ ♦ ts ♣r♠tr s ♥st s♦♥ ♥ r t ①♣r♠♥tt ♥ tt t t ♦♦♥ ♥r ♥t♦♥

|Tc(Φeq)| = 8.315 × 10−13 cm2mV/ · Φeq + 2.3 mV/

♦tr ♣r♠trs α ♠♣t ♦ t ①♣♦♥♥t tr♠ ♥ β ♣rs♥t ♥q ♥ ♦♥ t♦ t♠♣rtr ♥♣♥♥t tr Φeq ♣♥♥♥ sr ② t ♦♦♥ rst ♥ s♦♥ ♦rr rt♦♥s

A(Φeq) = (1.99 ± 0.2) × 10−13 cm2V · Φeq − (0.46 ± 0.05) ❱

α(Φeq) = (4.23 ± 0.4) × 10−28 cm4V · Φ2eq + (4.51 ± 0.45) × 10−15 cm2V · Φeq +

+ (0.051 ± 0.005) ❱

β(Φeq) = (9.66 ± 0.5) × 10−29 cm4V · Φ2eq + (2.42 ± 0.12) × 10−15 cm2V · Φeq +

+ (0.003 ± 0.0001) ❱

♥② t rr♥s ♣♦t ♦ t t♠ ♦♥st♥t τ r tt

1

τ= k × exp

(

− EA

kBT

)

tEA = 0.236 · exp(1.966 × 10−14 cm2 · Φeq) ❱

k = 1.706 · exp(3.274 × 10−13 cm2 · Φeq) s−1

♥ ♣♥♥t ♦♥ Φeq t s t♦ ♥♦t tt t ♥ ♣r♠tr③t♦♥ ♦s♦♥② ♦r t t♠ ♥t ♥ t t srs ♦ ♦r t♠♣rtr r♥♥ r♦♠ t♦ ♥ ♥ t Φeq r♥ r♦♠ ×1012 cm−2 t♦ ×1014 cm−2 t②♦ t ♦ ♣r♠tr③t♦♥ s ♥ tst ♦♥ srs ♦ ♦s rrt ♥ ts♠ ♦♥t♦♥s t rs♣t t♦ t ♦♥s s ♦r t ♣r♠tr③t♦♥ s s♦♥ ♥ t t♦♥ s ♥ r♠♥t t♥ ± t rs♣t t♦ t r♥t①♣r♠♥t t sts ♥ t ♦ ♠♥t♦♥ t♠♣rtr ♥ ♥ r♥

s♥stt② ♣♥ ♦s r♦♠ P

s♥stt② P s t♦ rtr③ ♦r t ①♣r♠♥t ♥ ♦♣ ♥ ♠♥tr ② t ♥tr ♦r t♦♥ P②ss P♦ t ❯♥rst② ♦ ❲♦♦♥♦♥ str ② r ♦♥♠♣♥t ♣♥ ♦st s ♥t ♦ ♠♠ ♥ r♦ss st♦♥ ♦ ♣+ ♥ ♥+ ♦ ♠♠2 s sr rt r♦♠ ♣rt② ♥t②♣ s♦♥ ♦ ρ ∼ 10 kΩ·cm ❬ ♦s❪ ss s♦ ♥ ♥t ♦rr ♦t ♦ ♦t ❱ ♥ s t rr♥t♦ ♠

s♥stt② ♣♥ ♦s r♦♠ P

r ♣♥ ♦s t♠♣rtr ♦♥ts ♥ t ♥ t |Tc| ♥ r♣♦rt Prrrt♦♥ t♠♣rtr ♦♥ts ♦ ♣♥ ♦s P❲ P ♥ N Φeq ♣♥♥ ♦ t t♠♣rtr ♦♥t ♦r t P❲♦s ♦♥②

r ❱t♦♥ ♦ t ♥♥♥ ♣r♠tr③t♦♥ ♦r t P❲ ♦s

rtr③t♦♥ ♦ ♣♥ ♦s

rt♦♥ rs ♦r P s

s♦s t ♥rs ♦ t ♦rr ♦t rss t Φeq r♦r r♥ r♥t rrt♦♥s rr ♦t ♥ t ①♣r♠♥t ts sr ♥ ♣tr ♥ r♦♠ ❬ ❪ rs♣♦♥s r r♦♠ ❬❪ s ♥ ♠sr♥ t ♣tr♠ ♥tr♦♥ ♠ t t ① t♦r ♦ t r♦♣♥♦♠♠ss♦♥ ♦♥t sr ♥tr t ♦♥ r♦♠ ❬❪ s ♥♠sr ♥ t ❱ π+ ♠ π t② t t P rrr ♥sttt P❱♥ t③r♥ ❬❲❪ s t s ♥ s♦♥ ② ①♣r♠♥t ♠sr♠♥ts ♥ ❬❪ ♦r Φeq > ×1012 cm−2 t rs♣♦♥s ♦ t P s strt t♦ ♥rs①♣♦♥♥t② s t ♣♥♥ ♦ ❱F ♦♥ t s♦♥ rsstt② s q strts t♦♦♠♥t ♦r ♦ t ❱F r♦t s ♥t♦♥ ♦ Φeq ♥s ts t♦ t r♦♠♥rt② ♦r ts rs♦♥ t rs ♣rs♥t ♥ ts ♦r ♥ t t ♦ ♠♥t♦♥Φeq

② tt♥ t r♥t t r♦♠ ♥tr♦♥ ♣r♦t♦♥ ♣♦♥ ♥ ♠① rrt♦♥s♥ t ♦♣rt♦♥ r♥ ♦ t t s t♥ ♣♦ss ♥ ♥♦② t t s ♥♦♥ ♥ t s ♦ t P❲ ♦s s q t♦ tr♠♥ t rt♦♥ t♦r ♥ t ♥r rt♦♥s♣ tt ♥s t r♦t ♦ t ♦rr ♦t ∆❱F t tΦeq s♦ tt

∆VF = c · k · Φ = c · Φeq r1

c= 1.7 × 108 ♠2/♠❱

st t ♦ t t s♦s t♦ ♥ r♠♥t t♥ ± t rs♣t t♦t ♠sr ①♣r♠♥t t sts s t s ♥ s♦ ♥t ② t rr♦rrs ♦ ♠sr♠♥ts ♣rs♥t ♥ ts rt♦♥ ♣♦ts ♥ rr♦t t ♠ rr♥t ♣ss ♦ r t r♦♠ ♠s t♦ ♠s

♥ t s♥stt② t♦ γr②s s s♦ ♥ ♣♦tt t r♦ss ♠rrs tr ①♣r♠♥t ♣♦♥ts ♦rrs♣♦♥s t♦ tr ♦ss r♦♠ t 60♦ s♦r ♦ tP❯ t② s ♥ ② rs♣t② st t ♦ tst s♦ ♠♠ s♥stt② ♦ 0.014 mV/Gy

♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦r P s

♥♥♥ s ♥ ♠sr ♦♦♥ rrt♦♥ ♦ P ♦s s♦s ♦r ①♠♣ s♦rt ♥♥♥ ♣r♦ ∼ rs ♠sr t ♦r ♦rrt t t Φeq ♦ ×1012 cm−2 ♥ t ♥r♦♥♠♥t ❩ ♥ r ♠ s r♦r ♥♥♥ s ♦♥ t♦ ss t♥ ♦r s ♣r♦ s rst s ♥ ♦♥r♠ ♥ ①t♥ ♥t ♦rs tr ♥tr♦♥rrt♦♥ t♦ t ♠①♠♠ Φeq t t rt♦r t② ♦ ♥ ♦♥② ♥ t ❬r❪ ♣rs♥ts t ♦♥tr♠ ♥♥♥ ♦r ♦ tP s tr ♠♦♥ts ♦ r♦♦♠ t♠♣rtr ♥♥♥ tr rrt♦♥ t♦ t♠①♠ ♥ t ♦rr ♦t st ♦st ♦ ts ♥t s s ♥ t s♠ ♦rr ♦ t r② tr♠♥ ♥ t rt♦♥ rs ♣rs♥t ♥ ± tr♦r t ♥♥♥ ♦rrt♦♥ s♥t ♥ ♦♥sr s ♥ ss♦r ts s

s♥stt② ♣♥ ♦s r♦♠ P

♦rt♠ s

♥r s

r P ♦s rt♦♥ rs t ♠ ♥ r♥t r♦♥ s rr♥t ♣st r♦♠ t♦ ♠s tr♦♥ t r♦♠ r rt♦r ♥ t② P♦♥s t r♦♠ Pπ ①r♦♥ t r♦♠ t ♣♦tt ♥ ♦rt♠ s ♥ t r t s♥stt② t♦ γr②s s s♦ s♦♥ ♦♥rs♦♥ t♥ γ ♦s ♥ ♣♦t♦♥ ♥ s ♥ ♦♥ t t t♦r ♦r ❱ ♣♦t♦♥s ♥ ♦♥ q t♦ ♣②·♠2 t r♦♠ ♣♦tt ♥ ♥r s ♥r t s ♥ r♠♥t ② ± rr♦rrs t rs♣t t♦ t ①♣r♠♥t t

rtr③t♦♥ ♦ ♣♥ ♦s

♥♥♥ ♦ P ♥ ♦s ♦♥tr♠ ♥♥♥ ♦ P ♦

r ♥♥♥ ♦ P ♥ ♣♥ ♦ s ♥♥♥ ♦rs♦r ♦t P ♥ ♥ s t ♦rt ♦s ♥ ♦♠♣r t ♥♣♥♥t ♠sr♠♥ts r♦♠ t ♣r♦rr♦r tr ②n ♥tr♦♥ ①♣♦sr r♦♠ 252 s♦r ♦r♥ t ❬♦❪ ②n ♥ tss s q♥t t♦ Φeq ∼ ×1010 cm−2 ♦r Φeq ∼ ×1011 cm−2 ♥ s♦♥ ♦♥tr♠ ♥♥♥ ♦r P s ♠sr t t r tr ①♣♦srt♦ Φeq ×1012 cm−2 r♦♠ ❬r❪

t♠♣rtr ♣♥♥ ♦ t P s s ♥ tr♠♥ ♥ ♣♦tt♥ s ♦r t s ♦ t P❲ s ts ♠sr♠♥ts ♥ ♦♥ ② ♣♣♥ t ♣ s ♥t♦ tr t t t♦ r♥tt♠♣rtrs t ♥② t♠♣rtr t ♦s ❱F s ♥ ♠sr ② ♥t♥ ♠s ♦♥ rr♥t ♣s ♦ ♠ ♥t♥st② c ♦ ♠❱ s ♥ tr♠♥s s ♥ ♦♥ t♦ q② rs t t rrt♦♥ t♦ t st ♦t r♠ t♦ t ♥tr ♦ t s♠♦♥t♦r ♥ ♣ ❬♦s❪ ♥ t ♥sttΦeq r♥ ♣ t♦ ×1012 cm−2 ts s ♥ ♦♥ t♦ rss ♣ t♦ ♠❱

♣♥ ♦s

s♥stt② s ♥ ♠♥tr ② t ♥sttt ♦r srPr♦t♦♥ ♥ ♣♣t♦♥ ♦ ♦s♦t♦♣s P ♥ Pr ❬Pr♦❪ s sr ♣r♣r ② ♦♥ ♠♣♥tt♦♥ ♦ ♦r♦♥ ♥ ♣♦s♣♦rs ♥t♦ t ♥t ♥t②♣s♦♥ s♥ r②st s♥ t ♦t♥ ③♦♥ ♠t♦ s♣ rsst♥ ♦ t♥t ♠tr s ρ ∼ 100 Ω · cm ♦♠♣t st ♦ t♥ ♣r♠trs ♦r ♦t ♥ s s ♥ ❬♦♣ Pr♦ t❪

rt♦♥ rs ♦r s

s♦s t ♥rs ♦ t ♦rr ♦t rss t Φeq r♦r r♥t♦ r♥t rrt♦♥s rr ♦t ♥ t P t② ❱ ♣r♦t♦♥s ♥ ♥ t rt♦r sr ♥ ♣tr ♠sr♠♥ts ♣rs♥t ♥ tsrt♦♥ ♣♦ts ♥ rr ♦t t ♠ rr♥t ♣ss t t t ♦

♣♥ ♦s

sr♣t♦♥ ②♣ ②♣

t♦♥ tt ♥tr♦♥s t > ❱♠♥s♦♥s ×tbase ×× ♠♠ ×× ♠♠

tr♦♥ r♥ ② ②tr♦♥ ♥r② ♣♥♥ ss t♥ ±

st♥tr♦♥ s♥stt② ♠❱② ❱②γ s♥stt② < ♠❱② < ♠❱②♥s♥ ♣st

♥t ♦t t ♠ ❱ ❱

♥ ♣r♠trs ♦ ♥ ♦s r♦♠ ❬t❪ ♥tr♦♥ ♣♦tt ♥ ts t s rrr t♦ t ♦s r t♦ ♠♥ tss♦r♥ t♦ ❬♦❪ ②n ♥ ♠♥ tss s ♣♦s ② Φeq ∼ ×1010 cm−2 ♦❱ ♥tr♦♥s

♠s s ♥t ♥ t s t st st ♦ ♠sr♠♥ts s s♦ ♥ rr♦t ② ♥t♥ t ♠ s♥ rr♥t t ♣s ♥t ♦ ♠s s st♠sr♠♥t srs s♦s t♦ ♥ r♠♥t t t ♠s ♦♥s ♦r ♦t ♥

② tt♥ t r♥t t ♦ ♦r r♦ s♣tr♠ ♥tr♦♥s ♥ ❱♣r♦t♦♥s t s ♣♦ss t♦ tr♠♥ t rt♦♥ t♦r ♥ t ♥r rt♦♥s♣ tt♥s t r♦t ♦ t ♦rr ♦t ∆❱F t t Φeq s♦ tt ♦r t t②♣

∆VF = c · k · Φ = c · Φeq r1

c= 1.6 × 108 ♠2/♠❱,

♦r t ♦r t t②♣

∆VF = c · k · Φ = c · Φeq r1

c= 2.7 × 107 ♠2/♠❱.

st t ♦ t t ♦r t t♦ s s♦ t♦ ♥ r♠♥t t♥ ± t rs♣t t♦ t ♠sr ①♣r♠♥t t ②s r♦♠ t ①♣r♠♥t rs♦ t s ♣♦ss t♦ tr♠♥ t ♦♣rt♦♥ r♥ ♦ t t♦ s st ♠①♠♠ Φeq t t s rs♣♦♥s st ♦♦s ♥r ♦rr♦r Φeq r♥ ♦ ♦t ×1012 cm−2 ♥ ×1011 cm−2 s ♥ tr♠♥ ♦rt ♦s ②♣ ♥ rs♣t② s rsts r ♥ r② ♦♦ r♠♥tt t t ♦ r r♥ ♦ ×1012 cm−2 ② ♥ ×1011 cm−2

② s ♥t ♥ tr♠s ♦ ♥tr♦♥ ♥ tss

♥♥♥ ♥ t♠♣rtr ♣♥♥ ♦r s

♥♥♥ rs ♥ ♠sr ♦♦♥ ❱ ♣r♦t♦♥ rrt♦♥ ♦r t t♦t②♣s ♦ ♦s s♦s t ♠sr♠♥ts r♦r ♦r ♦t rs t r♦♦♠ t♠♣rtr ♦ ♦t ♦s ♥ rrt t♦ Φeq ×1011 cm−2 ♥ t s♠ ♣♦t ♥♥♥ t ♠sr ② t ♠♥trr tr①♣♦st♦♥ t♦ Φeq ♦ ×1011 cm−2 s ♥ s♦ r♣♦rt r♦r ♥♥♥ s

rtr③t♦♥ ♦ ♣♥ ♦s

r t♦♥ rs♣♦♥s ♦ ♦s ♦s ♦rr ♦t t ♠ s♣♦tt rss t Φeq t ♦ t r♦t rr♥t ♣s s ♦ ♠s ①♣r♠♥tt t♥ ♥ t ❱ ♠ ♦ t P t② t P ♥ r♦r t r♥t♣r♦t♦♥ rts ×108cm−2 · s−1 ×108cm−2 · s−1

♦♥s♦♥

♦♥ t♦ ♦t ♦r ♣r♦ ♦ rs s rst s ♥ ♦♦ r♠♥t t ❬Pr♦❪ ♥ ♦tr rr♥s t tr♥

t♠♣rtr ♣♥♥ ♦ t s s ♥ tr♠♥ t ts♠ ①♣r♠♥t ♣r♦r ♠♣♦② ♥ t ♣r♦s ss ♥ ♣♦tt ♥ ♠♣rtr ♦♥ts c ♦ ♠❱ ♥ ♠❱ ♥ tr♠♥ ♦rt ♦ ②♣ ♥ rs♣t② s s ♥ ♦♥ ♥ r② ♦♦r♠♥t t ❬Pr♦❪ tt ♠♥t♦♥s s♦t t♠♣rtr ♣♥♥s ♦ ♠❱ ♥ ♠❱ rs♣t② t ♥ r② ♦ ± s s r①♣t t♦ r♦② ♦♥st♥t ♥ t Φeq ♦♣rt♦♥ r♥ ♦ t s ♦r t ♥stt♦♥ ♦r t Φeq ♣♥♥ tr rrt♦♥ s♥t rr ♦t ♥ tr♠♦r ♦ ts tss ♦r

♦♥s♦♥

♥ ts ♣tr tr t②♣s ♦ ♣♥ ♦s ♥ ♥stt ♦r t ♥s ♦ t ①♣r♠♥ts

♦ ♦r t rqr r♦ ②♥♠ r♥ ♣ t♦ sr 14 cm−2 t ♦♠♠rs r♦♠ P❲ r② st ♦ ♣r♠♥r② ♥stt♦♥s t ♥ t ♥♥ts ♥ rtr③ ♥ t ♦r ♦s♠tr ♣r♣♦ss t srs♦ ♠sr♠♥ts rr ♦t t r♥t t②♣s ♦ ♣rts ♥ ♥rs ssts t♦s♣♣② ts s t ♦rr s rr♥t ♣s ♦ ♠ ♦ t tt ♦s♥t t♦ ① s rr♥t ♣ss r♦♠ ♠s t♦ ♠s r t ♦♣t♠♠ ♦ ♦r tr♦t ♦ s ♥ ts ② ♥♥ ♥♥♥ ♥ st♥ ♣♥♦♠♥r ♦ t♥ t ♦s ♦♣rt r♥ rt♦♥ rs ♣rs♥t rr tt t s s ♥♦t s♥st t Φeq s < ×1012 cm−2 s♥stt② ♦×109 cm−2/mV ±20% s ♥st ♠sr ♥ t ♦♦♥ ♣rt ♦ t rs♣♦♥s r

♦♥tr♠ ♥♥♥ ♦ t ∆VF s ♥ ♥t s t ♠t♥ t♦r ♦r s s ♦r ts rs♦♥ ♣r♠tr③t♦♥ t♦ ♦rrt t t♠ ♦r ♦ ∆VF s♥t♦♥ ♦ t ♦♣rt♦♥ t♠♣rtr ♥ t ♠t Φeq s ♥ r ♣r♦♣♦s♦r♦r t s♥ ♦ ♥♥♥ ♣♥♦♠♥ ♦r Φeq < ×1012 cm−2 s ssts t♦ ♣rrrt s s ♦r tr t③t♦♥ ♥ ts ② t ♥t♥s♥st r♦♥ ♥ ♠♥t t♦t tr♥ t rtrsts ♦ t ♦srt♦♥ rs♣♦♥s s t s ♥ s♦♥ ♥ ❬❪

♦ t②♣ ♥stt② ①♠♠ Φeq r♥ ♥♥♥

P ×108 cm−2/mV ± 13% ×1012 cm−2 < tr ×108 cm−2/mV ± 15% ∼ ×1012 cm−2 ∼ tr ×107 cm−2/mV ± 15% ∼ ×1011 cm−2 ∼ tr

♠♠r② ♦ t ♣r♦r♠♥s ♦ s♥stt② ♦rrs s♦♥ ♦s

♦ ♣r♦ t ①♣r♠♥ts t ♣♥ ♦ s♥s♦rs t ♥ s♥stt②tr s ♥ tst ♥ t r♠♦r ♦ ts tss ♦r tst ♦♥ tss s ♥ rr ♦t ♣♦r♥ t♠ t ♦rr rr♥t ♣ss r♦♠ ♠P t♦ ♠ ♥ ♦ t r♥♥ r♦♠ t♦ ♠s r ♥♥♥

rtr③t♦♥ ♦ ♣♥ ♦s

♦r s s tr t♠♣rtr ♣♥♥ ♥ s♦ ♠sr ♥ ♣rs♥t r s ♥ ♦r ♦ t ♠♥ rtrsts ♠sr ♦r ttr tst s

r♦♠ rsts tt t ♦ t②♣ s t st s♥stt② s ♦t t♦r rtr t♥ t ♦♥ ♦ t ♥ t P s♦r t rr♥t rqr t♦ ♣♦r t s t t ♠♦♠♥t ♦♥sttts ♠t♥ t♦r ♥ t ♥trt♦♥ ♦ s s ♥t♦ t P s♣♣ t ♠ ♦rr rr♥t tr♥ ♦t t♦ ♥st t s♠ r♦t♣r♦t♦♦ s t ♦♥ ♥ ♦r t P❲ ♦r♦r t t♦ s strt t♦strt ♦r r♥ t Φeq ♦ ×1012 cm−2 ♥ t♦ ② ♦r t ①♣r♠♥t r♥ ♦r ts rs♦♥s t P s r ♣rrr t♦ t ♦♥s ♥tr♦r ♥ st t♦tr t t P❲ ♦s s Φeq ♠♦♥t♦r t♦ t ①♣r♠♥ts ♥s

♣tr

♦s♠tr② ♦r t

①♣r♠♥ts

t♦♥ s♥s♦rs s♥ ♣t② t♠t ♠♥s♥ ♥ ♣rs♥t♥ ♣tr ♦♣♠♥t ♦ s s s ♦s t♦ rss t ♦♥r♥ ♦t ♦s ♠sr♠♥t ♦r s♣rts ❬s❪ s s♥s♦rs t♦♥ sr ♥ ♥ ①♣♦t t ♠tr ♦s♠tr② ♣r♦♣rts ♥ ♦rrt♦

• s♥stt② ♦ t ♦rr ♦ t ♠②

• ②♥♠ r♥ ♦ ♦r ♦rrs ♦ ♠♥t ♠② t♦ ②

• ♣♦r ♦♥s♠♣t♦♥ ♦s t♦ ③r♦ ①♣t ♦r t s♦♥s r♥ t♠

r♥ t r♥ ♣r♦ss t tr♣♣ rrrs r rs ♣r♦♥ rst♦ t s♥s♦r ts s ♦♥sq♥ t s ②s ♣♦ss t♦ ♦♦s r♥ ②tt ♣r♥ts t s♥s♦r r♦♠ strt♥ ❬❱❪ ♦ trs ♠ t ♥ ♥trst♥ ♥t ♥♦t ♦♥② t♦ ♠sr t ♦s r ♦rt②♦rt ♦rs♣rts t s♦ t♦ ♠♦♥t♦r t ♥r♦♥♠♥t ♥ r rt♦♥ ts rt♦rs ♥ ♣rt rt♦rs ♦r♦r ♠♦♥ t ♦tr ♥ts t ♦ t♥♣♥♥ ♦ ts rs♣♦♥s ♥ t ♦♥③♥ rt♦♥ t②♣ ♥ ♥r② ♠ r t♥trst ♦ s♥ t ♠tr ♥ ♠① rt♦♥ ♥r♦♥♠♥ts s t ♦♥ ①♣tt t ①♣r♠♥ts

♥ t♦♥ ♦ t ♠tr ♣r♦♣rts ♥ ♦ sr s s♥s♦r s♥ ts ♦♥t t s ♣rt ♦ ts tss ♦r ♥ t ♦♣ ♥ t♣rs♥t ♣tr ♠♥ t♦ ♠♦♥strt t st② ♦ ♥ rt♠ s②st♠ tt ♥♥trt s♦ t t♥♦♦② ♥ ♣rtr t ② ♥trt s②st♠ ♥♥s t ♦♥tr♠ ♦t ♦♥③♥ ♦s s ♠♦♥t♦r t s ♦rrs ♣♥ ♦s ♣r♦ ♥♦r♠t♦♥ ♦♥ t ♠t s♣♠♥t ♠ ts♥ t s♥s♦r rst tr r♥ s t♦ ♦♥trt t♦ t ♠sr♠♥ts ♦t ♣r♦ rt♦♥s ♦ t ♦s ❬❪

♥ ts ♣tr ♦r t rst t♠ t st② ♦ t s♥stt② ♦ t ♠tr♥r ❱ r ♣rts ♥ ♥tr♦♥s ♣rs♥t s s r♥t ♠t♦st♦ ♥♥ t ♠tr s♥stt② t♦ tr♠ ♥ ♥r② ♥tr♦♥s ♦r♦r

♦s♠tr② ♦r t ①♣r♠♥ts

r ttr♥s♠ss♦♥ s♣tr♠ ♦r µ♠ ♦ ♦ ♣t♦♥ ♠tr

t ①♣r♠♥t ♠♣♥s rr ♦t t t ♥ ts♦♥ ♥ ♥trt s♥s♦r ♦♣ ♦r s♣ ♣♣t♦♥s s♦ ♣rs♥t ♥② ♣r♠♥r② tsts t ♣r♦t♦t②♣ ♦ rt♠ r s②st♠ s♦sr ♥ ts ♣tr

♠♣s s ♦r sts

s♠♣s ♠♣♦② ♦r ts tss ♦r s t♦ st② t rs♣♦♥s ♦ ts♥st ♠tr t♦ r♥t ♥ ♦ rt♦♥s r ♦t♥ r♦♠ µ♠ t ②r ssr♥ ♣r♥t ♦♥ µ♠ t ♣t♦♥ ♦ s ♦s ♣r♣r t t❯♥rst② ♦♥t♣r r t ♥ s♠ sqrs t t s③ ♦ × ♠2 ♣t♦♥s ♥ ♦s♥ s sstrt ♦r t s♥st ♠tr s ♦ ts tr♥s♣r♥② t♦ t t s s r♦♠ t tr♥s♠ss♦♥ s♣tr♠ ♦ tt s ♥ ♠sr t ♦r t s♠♣s ♣r♦t♦♥ ♦r♦r ts s♠♣s r ♦♥ t♦ s② t♦ ♥ ♥ ♠sr t t ♦rt♦r② tst♥ sr ♥ ssr ♥ ♦r t r♦t t s♣♠♥s r ♣ ♥ t s♠♣s tr②t t ♣t♦♥ s ♥ t ♥ t ♠tr s ♥ t ♣♦t♦♠t♣r♥♦

s♠♣s s♦ ♣r♣r r s♦ s② t♦ ♣r♦tt r♦♠ t ②t s♥stt② st ♦ s♠♣s r tst ② ①♣♦s♥ t♠ rt② t♦ t t tr s♠♣sr ♥st ①♣♦s ② ♣♥ t♠ ♣s♦♥ s♦ tt t ♣t♦♥ ②r s ♥rt② t t tr ②s s♠♣s r ♠sr ♥ t rsts srs ♦s♠♣s s♦ ♠♥s♥t r♦♥ s♥ ♦t t♦r r t rs♣t t♦t s♦♥ srs tt s♦ s♥s ②♥ ♦s t♦ t ♦st ♦ t r♦t s②st♠

♥stt② t♦ ❱ ♣r♦t♦♥s

r ♠tr s♥stt② t♦ ❱ ♣r♦t♦♥s r♥t s②♠♦s ♥ t ♣tr♦rrs♣♦♥ t♦ r♥t sts r ♦t t r♥t t♠s t tr rrt♦♥ • s♠♣sr♦t ♠♠t② tr rrt♦♥ s♠♣s r♦♠ r♥t ts st♦r t ♥ r♦t t♥ ② s♠♣s st♦r t r♦♦♠ t♠♣rtr ♥ r♦t trrrt♦♥ s♠♣s st♦r t ♥ r♦t tr ♠♦♥ts

s tst ♦♥r♠s t ♦ ♦ s ♣r♣rt♦♥ ♠t♦ ♦r t ♠tr t♦ ♥stt

♥stt② t♦ ❱ ♣r♦t♦♥s

♦ tr♠♥ t s♥stt② ♦ t ♠tr t♦ t ♥r② ♣r♦t♦♥s r♥tsrs ♦ s♠♣s ♣r♣r s sr ♥ ♥ ①♣♦s t♦ ♥rs♥♣r♦t♦♥ ♥s ♥ t t② t t ♥② ♥ r♦♠ t♦ ♥t s♠♣s r rrt t t s♠ t♠ ♣r♦t♦♥ ♥ t ♥② st♣s tr♠♥ ② tt♦♥ ♦ ♦s t t s♠ ♠♥s♦♥s s t s♠♣s♥r tst ♥t♦♦s ♦♥rs♦♥ s ♥ ♦♥ s♥ q ♥ rsts rrt t♥ ±

rsts ♦ ts rrt♦♥ tsts r r♣♦rt ♥ rr♠rrs r t ♦♠♥ r♦♠ t s♠ st ♦ ♠trs ①♣♦s t♦ ♥rs♥ ♣r♦t♦♥♥ ♥ r♦t ♠♠t② tr ♣rt ①♣♦sr t ♠sr♠♥t♣♦♥ts ♦♦ ♥r ♦r ♥ t r♥ ② t ♥ r② ttr t♥ t r ♦ss t rs♣♦♥s ♦♠s s♥r t♦ strt♦♥ ♦ t tr♣♣r s rsts r ♥ r♠♥t t t t ♦ ♦tr ♥ ♠trsrrt t r ♣rts ❬s❪

♦ ♦♥r♠ ts rst t st ♦tr s♠♣s ♥ rrt t♦ ♥rs♥♣r♦t♦♥ ♥s ♥ r ♦t ♦♦♥ r♥t st♦r ♣r♦s t r♦s t♠♣rtrs

♦s♠tr② ♦r t ①♣r♠♥ts

r ①♣r♠♥t st♣ ♦r t rrt♦♥ tst ♦ t ♦♥♥ s♥s♦r ♦r s♣ ♣♣t♦♥s ♥ t s♠ts t s♥s tt r r♥ r♦♠t♦ t s♥s♦r r t s s t ♦t♣t ♠♣t♦♥ st

ts ♦♦♥ t ♣♦♥ts ♥ ♠sr r♦♠ r♦s s♥ s♠♣srrt s♣rt② t ♥② ♦s st♣ s ♠sr♠♥ts r s♦♥ ♥ ♣♦ttt r♥t ♠♣t② ♠rrs t♦t t s♣ ♦ t rt♦♥ rs♣♦♥s s ♦♥r♠t ①♣r♠♥t rr♦r tt ts t ♠sr♠♥ts ♠ ♠ r s s ♥t rt rr♦r rs ♦ ts t sts ♥ t ♥r r♦♥ r♠♥t ♦ t t♣♦♥ts ♦s ♦♥ t♦ ♦t ±

♥rs ♦ t ♥rt♥t② ♠♦♥ t r♥t ♠sr♠♥ts ♠② ♥t tt♦tr ♣♥♦♠♥ s ♦r ♥st♥ t ♥ ♦ t ♠tr s♦ t♥ ♥t♦♦♥t ♥ t r♦t s ♣r♦r♠ tr ♦♥ t♠s ♥ ♥ ♥♦t ♦♥tr♦t♠♣rtr ♦♥t♦♥s ♥ rs sss ♥ ♠♦r t ♥

st ♦ ♥ ♥trt s♥s♦r ♦r s♣ ♣♣t♦♥s

rst st♣ t♦r t ♦♥♣t♦♥ ♦ rt♠ s♥s♦r s ♦♥ ♦r t ①♣r♠♥ts s t♦ t t ♣r♦r♠♥s ♦ t ①st♥t ♥trt s♥s♦r♦♣ ♦r s♣ ♣♣t♦♥s t t ❯♥rst② ♦♥t♣r ♣r♦s② sr♥

s♥s♦r tst t s rs♦♥ t ♦♠♠r tr♦♥ ♦♠♣♦♥♥ts rt♦♥ r♥ ② ♦♠♣♥st♥ t rt♦♥♥ ♠ ♥t ♦♠♣♥st♦♥ ♦ t ♠ss♦♥ ♦ss s ♥ r③ ♦♦♣ tt ♥rss t ♦♣rt rr♥t t t ♠tt rss s♥s♦r rs♦♥ s ♠♥t t♦ s♥st t♦ ♦ss s ♦ s ♠② ♥ t s ♣r♦♥t♦ ♠♠♥ ♣ t♦ Φeq ♦ ①11cm−2 rrt♦♥ t ❱ tr♦♥s ❬❱❪ tst s♥s♦r ♠♦♥ts ♠♥s s ♥ ♠♠ts s sP♣♦t♦s♥s♦rs ♦r strt♥ t rrt♦♥ tst t s♥s♦r s ♦♥♥tt♦ ♥ ①tr♥ tr♥s♠♣♥ ♠♣r st t ♥ ♦ s ①tr♥ rts ♥ r③ ② s♥ t ♥♣t st q♠♣r q t♦ t♦♥ ♠♦♥t ♦♥ t s♥s♦r ♦r tt s s♦ ♣r♦♥ t♦ r♥ t t ♣rt♥ ♦ ♥trst ❬❱❪

st ♦ ♥ ♥trt s♥s♦r ♦r s♣ ♣♣t♦♥s

r ♥trt s♥s♦r rs♣♦♥s ♥ ♠① r♦♥ ♦ ♣tr ♥ rr♥t ♠♦♥t♦r♥ ❱led ♦♥ tr s r♦t r♦♠ t ♦s♦s♦♣ ♥ r♦r tr ② ①♣♦sr ♥ r♦r tr ②s ①♣♦sr

s♦s t ①♣r♠♥t st♣ s ♦r t rrt♦♥ tst s♥s♦r s♣ ♦♥ P ♦♥t♥♥ t ♠♣t♦♥ st t♦ ♦t t ♠♥s♥t ♣r♦♠ t ♠tr ❱osl r♥ t st♠t♦♥ st♠t♦♥ s ♣r♦② ♣♣②♥ ♦r rt♥ t♠ rr♥ ♦t ❱ref tt ♦rrs♣♦♥s t♦ ♦rrrr♥t ♥t ♥ t s♥s♦r ♣r♦s s♦ s♦♥ ♦t♣t ❱led tt ♥ s t♦ ♠♦♥t♦r t rt♦♥ ♦ t rr♥t s s♥s r r♥ t♦ tr♦t q♣♠♥t ♠tr tst♣rs

①tr♥ q♣♠♥t ♦♥sst ♦ ♥ ♦s♦s♦♣ t♦ ♠♦♥t♦r ♦t ❱osl ♥ ❱ref s♥s ♣♦r s♣♣② s t♥ ♥ t♦ s t tr♦♥s ♦♥ ♦rs ♥ t♦ trrt r♦t ❱ref ② s♥ ♠♥ ♥trr♣tr s s♦♥ ♥ t rt♥ ♦r♥r ♦ ❱ref ♦ ❱ s t♥ ♣♣ ♦r s♦♥s t♦ r♦t t ①♣♦s ♠tr s♥s♦r s ♥st ♥ t rt♦♥ ♥r♦♥♠♥t ♦ t t②t t t ♦t♦♥ ❩ ♠ ♥ r ♠ r φeq ♦ ♦t ①10 cm−2

♣r ② s ♥trt tr♦♥s ♣r♦t♦♥s ♥ r r♦♥s r ♥ ts♥s♦r ♦t♦♥ tt s r♦r ② ♠♥s ♦ P ♦s♠trs

r♥ t rst ②s ♦ ①♣♦sr t s ♥♦t ♣♦ss t♦ ♦sr s♥ ♠r♥r♦♠ t ♥♦s tt s ♦ s♦♠ ♥r ♦ ♠❱ rst ♠sr s♥ s♦sr tr ♦t ②s ①♣♦sr t♦ ♦s ♦ ♦t ② s s♥ ♣♦ ♦t ♠❱ s s♦♥ ♥ t rst ♦s♦s♦♣ tr ♦ t♠ss♦♥ ♦ t ❱led s ♠♦♥t♦r ♦♥ t tr ♥♠r ♥ t s q t♦ ❱

①♣r♠♥t s r♣t ②s tr tr ♦ ♦t ② t♦tsss s ♣ s r② st♥s r♦♠ t r♦♥♦ ♦t ♠❱ ♥ t ❱led st♠t♦♥ s♥ t♦ t s st ♦ ♦t ❱s t ② ♥♦s ♦ ❱ t tt ♣♦♥t t s♥s♦r s ①♣♦s t♦ ♣rt ♥ ♦t rtr t rs♣t t ♦♥ t♦ t ♥ tst ♦r s♣♣♣t♦♥s

♦s♠tr② ♦r t ①♣r♠♥ts

r ♥trt s♥s♦r rs♣♦♥s ♥ t ❱ ♣r♦t♦♥s ♦ ♥r♦r tr ♦♥ ❱ ♣r♦t♦♥ ♥ ♦♥♥ s♥ r♦r tr t ♥trt s♥s♦rr

♦ r② t s♥s♦r s st ♦♣rt♦♥ t s t♦ tst t rt② t ❱ ♣r♦t♦♥ rst ♥ t t② ♥ ts ♦♥t♦♥ t ♦s r t♦ ts♠♣ ♥ ♦♥ s♦t s ♦ ♦t ② ♥ ♦t ♠s t♠ rst ♦ ts tsts s♦♥ ♥ r ♦r t s♠ ♥t♥st② ♦ st♠t♦♥ ❱ ♣ ♦ ❱ s ♥ ♠sr s rst s ♥ r♠♥t t t ♣r♦s ♦♥ s♥ t s♥♦t♥ s ♦t tr t♠s r ♦r tr t♠s t ♣♦s

tr ts rst ♣r♦t♦♥ rrt♦♥ t s♥s♦r strt t♦ ♥rt ♣r♦t♦♥s ♣ss♥ tr♦ t s♥s♦r strtr r t♦ trr t r♦t sq♥ s♦s t t♦ ♠♥s♥t ♣s ♦rrs♣♦♥♥ t♦ t♦ ♦♥sq♥t ♣r♦t♦♥s♣s r♦r r♥ t rt♦♥ ①♣♦sr r♦r t ♠tr s r②♦♠♣t② rst ♥ t ①tr♥ trr ♦t ❱ref s ♥ tr t ①♣♦st♦♥t♦ t ♣r♦t♦♥ s♣s

rsts ♣rs♥t ♥ ts st♦♥ r♦t t♦ ♥ tt t tst s♥s♦r ss♠② t♦ t s ♦r♥ ♥ t ♦st ♥r♦♥♠♥t s ♥♦t t♦♣r♦♣r② ♦♠♣s ts ts ♥ ♠sr♥ t rt♦♥ ♦s t t ①♣t s♥stt② s rst ①♣r♠♥ts ♥r♥ srs ♦ ♦♥str♥ts tt t ♦♣♠♥t ♦ ♥trt s♥s♦r ♠st t♦ ♦♥t t s♣t② ♦ t ♥r♦♥♠♥t

s♥stt② ♦ t r♦t s♥ ♣♦t♦♦ s♦ ♠♣r♦

♦♥♦r s♥s♦r ♦t♣t st s ♥♦t t♦ r tr s♥s ♦t t♦♦♥ st♥s ♠ tr♦♠♥t ♣rtrt♦♥s ♥♥ ♥rs♦ ♠❱ ♦ ♥♦s ♦♥ t tr♥s♠ss♦♥ ♥ r t ♠♥ t♦r r♥ t ♥ ts t ♠♥♠♠ tt ♦s

rt♦♥ r♥ss ♦ t tr♦♥ ♦♠♣♦♥♥ts ♦♥♦r s t♦ ①t♥s♥ t s♥ ♠t ♦ t tst s♥s♦r ♦♣ ♦r s♣ ♣♣t♦♥s r

Pr♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r ♦r ♣♣t♦♥s

r♣② r ♦r♦r t rt♦♥ str♦♥② rs t♦ ts♣t ♦♥ ♥ rst t♦ ♠♦r t ♥ ♠♥ t s♥s♦rs tr♦♥s

♥ ♦ t ♠tr s ss♣t s♦ t♦ rs♣♦♥s ♦ t s♥stt② ♦ss s s ♥ t P t② t r♦t ②s r ♣r♦r♠ ♦r♦♥ t♠s sr ②s ♥ t ♦♣rt t♠♣rtr ♥ t ①♣r♠♥trs s r♦♥

♦♣rt♦♥ ♥ rt♦♥ ♥r♦♥♠♥t t ♣rts ♠② ♥ rr♥t s♣s tt ♥ tr♥ ♥ ♥t② trr t r♦t ♣r♦ss Pr♦tt♦♥♥st ts ts ♠② s♦ ♦rs♥ s ♣r♦♠ s ♥ ♥♦t ♥ts tss ♦r ♦r ♥ ♥ rs♦♥ ♦ t s♣ s♥s♦r s ♥ ♣r♦ t t ❯♥rst② ♦♥t♣r r ts ♣r♦♠ s ♥ s♦ ♥t s♥ ♦ t s♥s♦r ② ♥tr♦♥ t♦♥ st tt ♦s ♥tr♦ts ②s rtr ts ♦t ts ♥ s♥s♦r rttr ♥ ♦♥♥ ❬❱❪

Pr♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r ♦r ♣

♣t♦♥s

♥ ♦rr t♦ ♦♦ ♣ t rrt♦♥ tsts ♦♥ ♥ ♥trt s♥s♦r strtr ♥♣r♦t♦t②♣ ♦♣t♠③ ♦♦♥ t ♥t♦♥s st ♥ s t t ♣tr ♦ ts ♣r♦t♦t②♣ P ♦ ♥ ♥trt s♥s♦r s s♦♥ ♥ ♦♠♣♦♥♥ts r ss♠ ♦♥ tst P ♥ t s♥s r♦t ♦t ♣♥ ♥♥♦♥♣ tt ♦ t♦ ♦♥♥t t r♠♦t s♥s♦r ♦r t♦ rr ♥t ♣ t ♠st♥ r♦♠ t rrt♦♥ ♣♦st♦♥ s t♦ r t s♥ ♥s s st ♣♦r ♥s t♦ s♣♣② t ♦♥♦r tr♦♥ ♥ t♦ ♦♥tr♦ ♦ t ♦r t♦♣t st♠t♦♥

②st♠ sr♣t♦♥ ♥ ♣r♦r♠♥s

♦ rss t ♣♦♥t rs ♥ t r♦t s ♠♦ ② rt♣♦st♦♥ ♦ t♥ ②r ♦ ♠tr ♦♥ t s♥st sr ♦ ♠♠tssP s ♣♦t♦♦ t②♣ ❬♠❪ s s♥s♦r s ♣r♣r t t♦rt♦r② ♦ t ❯♥rst② ♦♥t♣r r s♦♥ ♥ t ♥ s♥ s ♥ ♦♣ ♥ ♦rr t♦ ♠①♠③ t t ♦t♦♥ r♦♠ tst♠t ♠tr ♠♠ts ♣♦t♦♦ s ♥ ♦s♥ s ♦ ts s♥stt② ♥ t s r♥ ♥ s ♦ ts ♦♦ t♦ ♥ t r♦♥ ♦t tr♦♠♥t s♣tr♠

s♥s♦r ♦r t ♣r♦t♦t②♣ s t♥ ② s♥ s s♥st♣♦t♦♦ ♥ ♦♣♥ t t♦ ♥ s ❬sr❪ ♦♣♥s ♥ r③ ② s♥ ♥ ♠♣t② ♠♥♠ ②♥r t♦ ♦ t rt ♥tr♥ ♦t ♦♣ ♣♦t♦♦ ss♠ s♥s♦r s s♦♥ ♥

r♦t rtr② ♠♣♠♥t ♦r t ♥trt s♥s♦r ♣r♦t♦t②♣ ss♦♥ ♥ rt s ♥ s♥ ♥ ♦rr t♦ tr♥s♠t t rr♥t s♥

♦s♠tr② ♦r t ①♣r♠♥ts

r ♣r♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r t t Ptr ♦ t♣r♦t♦t②♣ s ss♠ ♦♥ t tst P sP ♣♦t♦♦s t ♠tr ♣♦s♦♥ t s♥st sr

♦r ♦♥ st♥s r♥ t ts ♦ t tr♦♥ ♥♦s ♦♥ t tr♥s♠ss♦♥ ♥ ♦t♣t st ♦ t s♥s♦r s ♥ r③ t t♦ rr♥t ♠♣rs tt s♣t t♣♦t♦rr♥t ♥rt ♥ t ♣♦t♦♦ r♥ st♠t♦♥ t♦r tst ♣r t♦ t rr ♥t ♥♦s ♥rt ♥ t tr♥s♠ss♦♥ ♥s t♥ s♣t ♥t♦ q ♦♠♣♦♥♥ts ♥ s♣♣rss ♥ t s♥s r ♠r t tr♦t st

r♥t ♠♣r ♠♦♥t s ♥♣t st ♦ t rr ♥t r♦♠♥st ♠♥s♥t s♥ tt s t♥ trt ② ♣ tt♦r ♥ ♦rr t♦ ♠sr t ♣ ♠♣t tt ♦♥sttts t ♦s♠tr ♣r♠tr rt s ♥♠♥s♦♥ ♥ ♦rr t♦ t ♥r rs♣♦♥s ♦r r♦ rr♥t r♥ ♥rt ♥t ♣♦t♦♦ > ♦rrs ♦ ♠♥t strt♥ r♦♠ rr♥ts ♦ ♣ s s♦♥ ♥ tt r♣rs♥ts t ♦t♣t ♦ P s♠t♦♥ ❬❪

Pr♦t♦t②♣♦♥♥trts♥s♦r♦r

♣♣

t♦♥s

r tr ♠ ♦ t ♥trt s♥s♦r ♦♣ t ♥s ♣rt ♥ t t♥ s r♣rs♥ts trt ♠♦♥t ♦♥ t r♠♦t s♥s♦rs P s ♣♦t♦s♥s♦r s♠t ♥ t rt s r rr♥t ♥rt♦rr♣rs♥ts t s♥st ♥ ts ♣tr t ts ♦ t rt s t♦ ♣♦t t ♥ ♦♠tt r♠♥♥t ♣rt♦ t rt s ♥ ss♠ ♦♥ t rr ♥t ♣ ♠trs ② r♦♠ t ♥trt s♥s♦r ♥ ♥♦t ①♣♦s t♦ t rt♦♥

♦s♠tr② ♦r t ①♣r♠♥ts

r P s♠t♦♥ ♦r t ♦t♣t ♦ t ♥trt s♥s♦r

♦ ♠♥t♦♥ rtr② s♠ s ♠♣♠♥t t ♥ t s♥s♦r♣r♦t♦t②♣ s♦♥ s♥st ♠♦♥ts s♠♣ P❲ s ♣♦t♦♦ t♦ts♥st ♠tr ♣♦s ♦♥ t ♥ ♦rr t♦ t t ♦ss ♦ ♣r♦r♠♥s ♦ t s ♦r t ♦♣t st♠t♦♥

s♥stt② t♦ rt♦♥ ♦ ts ♥ ♣r♦t♦t②♣ s ♥ tst t ❳r②s ②s♥ t rrt♦r sr ♥ rrt♦♥ s rr ♦t t♥ ♦♣rt ♦t ♦ ❱p t t t♦♥ ♦ ♠♠ s♦rr ♥ ♦rr t♦ tt r②♦ ♥r② ♣rt ♦ t ♣♦t♦♥s s♣tr♠ < ❱ ♥ s ♦♥t♦♥s t♦srt t ♠ st♥ r♦♠ t t s ♦ ②♠♥

s♦s t rs♣♦♥s r ♦ t ♥t ♣ ♠♣t s ♥t♦♥ ♦t rt♦♥ ♦s ② s♥ st♠t♦♥ rr♥t ♦ ♠ ♣r♦t♦t②♣ s♦s s♥stt② ♦ ♠❱② s♦ tt t ♠sr♠♥t ♦ ♦ss ♥ t r♥ ♦ ② s ♣♦ss rs♣♦♥s ♦ t ♣r♦t♦t②♣ ♥r② ♣ t♦ ② t r ♦sst rs♣♦♥s ♠ q② s♥r s r② strt♦♥ t s ♥♦t ①♣t♥ s ♥ ♥t ♥ t ♠♦♥t♥ ♦ t ♣♦t♦♦ tt s ♥ ♦♥ t♦ts♥ t r♥ t ♠♥s♥t s♥ r♦t ♦♣rt♦♥ t tr ♠② ♥♥ r♦♠♥t♦♥ t ♥ ♥ tr♥ strt♦♥ ♦ t ♠♥s♥t s♥rs♣♦♥s

♦♣t♠③ ♣r♦t♦t②♣ s t♥ ♣ ♥s t rt♦♥ ♥r♦♥♠♥t ♦t t② ♥ ♦rr t♦ t ts ♣r♦r♠♥s ♥ r♦♥ ♥r♦♥♠♥t ♣r♦t♦t②♣ s ts ①♣♦s r♥ sr s ♥ ts r♦t s ♣r♦r♠②② sr t♠s ♣r ② t♦ t ♥ ♦t♣t st ♦s rt♦♥ ♦t ♥♦s ♦ ♦t t♦r ♦♥ t♦ t♥s ♦ ♠❱ t s t s♥ t ♥♥♥t♦ ♠sr r ♠♥s♥t ♣ ♦t ♦ t r♦♥ ♥♦s ♦♥ t tr♥s♠ss♦♥♥ ♦♣rt♦♥ ♦ ts s♠♣ ♣r♦t♦t②♣ ♦s t♦ ♥rst♥ tt t ♦ss ♦♣r♦r♠♥s ♦ t ♦r s②st♠ r ♠♦st ② ♦♠♥t ② q rs ♦t ♣r♦r♠♥s ♦ t ♦♣t ♦♠♣♦♥♥ts

Pr♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r ♦r ♣♣t♦♥s

r ♥stt② ♦ t ♥trt s♥s♦r ♣r♦t♦t②♣ t♦ ❱p tr ❳r②s

♦ r② t ♦ ②♣♦tss srs ♦ ♥ s ♣♦t♦♦s r①♣♦s t♦ r♥t s ♦ rt♦♥s ♥ ♦rr t♦ tr t♦r♥ t♦ t r♦♥♥r♦♥♠♥t rsts ♦ ts sts ♣rs♥t ♥ t ♥①t t♦♥

t♦♥ r♥ss ♦ ♥trt s♥s♦rs ♦♣t ♦♠♣♦♥♥ts

s s ♥ ♦t t♦ ♥trt s♥s♦rs ♥ ♥t s ♣♦t♦♦s ♠♠ts ♥ P❲ ♥ ①♣♦s t♦ r♥t rt♦♥ s ♥ t ♥r♦♥♠♥t t ❩ ♠ ♥r ♠ rrt ♦♠♣♦♥♥ts ♥ ①♣♦s t♦tr t P ♦s♠trss ♥ rrs s s♦♥ tt♦rs s ♥ ♦rr t♦ ♠srt rt♦♥ ♦s ♥ t Φeq rs♣t② ♥ ts ♣♦st♦♥ t ♠sr rt♦ ♦s ♥PΦeq s q t♦ ×109 cm−2Gy−1

s♦s t rrt♦♥ tst ♦ ♠♠ts sP ♣♦t♦♦ss t♦ t s♥st ♥ t ♥trt s♥s♦r ♣r♦t♦t②♣ ♠sr♠♥ts r ♣r♦r♠ ② ♠♥t♥ t ♣♦t♦♦s t ♥ ♥rs♥ ♥t♥st②♦ r t ♥♠ ♠tt ② ♥ r♦r♥ t ♦rrs♣♦♥♥ ♣♦t♦rr♥t♦r ♦ss ♦ ② rt♦♥s ♦ ♦t ♥ ♠sr s rt♦♥s♥ ♦♠♣r t t ①♣r♠♥t rr♦r tt ts t ♠sr ♣♦♥ts ♥ts tt t ♣r♦r♠♥s ♦ t ♦♠♣♦♥♥ts r ♥♥ tst ♦♠♣♦♥♥tss♦ ♥st rs ♦ ♥ tr ♣r♦r♠♥s ♥ t rt♦♥ ①s ② ♥ ♦t tr ② ①♣♦sr

♦r ts ♣♦t♦♦ ♠sr♠♥ts ♥ ♣r♦r♠ t ♥ t♦t t qrt③♥♦s tt ♣r♦tt t s♥s♦r ♥s t ♣ s ♠sr♠♥t s♦stt t rt♦♥ ♦r ♥ t s♥ t s♥s♦r ♥♦s ♦s♥t ♥ t♠sr rsts s♠ rsts ♥ ♦♥ ♦r t ♠♠ts

♦s♠tr② ♦r t ①♣r♠♥ts

r t♦♥ r♥ss tsts ♦ ♣♦t♦♦s s ♦r t s♥s♦rs ♥ t ♥r♦♥♠♥t ♠♠ts sP ♣♦t♦♦ P❲ s♦♥♣♦t♦♦

sP ♣♦t♦♦s ♠♦♥t ♥ t ♦♥t♣r s♥s♦r ♦♥r♠♥ ts t rsts ♣s ♥ ❬❱❪

r♥t s t stt♦♥ ♦r t P❲ ♣♦t♦♦ tt♦♥ ♦r ts ♦♠♣♦♥♥t rst t♦ r ♦ ♠♦r t♥ t ② ♥ ♦ ♦t t ② s t s s♦♥ ♥ ♦ rsts ♦♥r♠ t ♦ ♦s♥ sP ♣♦t♦♦s s s♥st ♠♥ts ♦r t ♥trt s♥s♦r

t♦ ♦♠♠r ♥♠ ♠♦♥t ♥ t s♥s♦rs ♥ r ♥t ♣rt ♦r tr ♣♥ t②♣ r♦r trrt♦♥ r♥ss ♥ r♦♥ s ♥ sts ② rrt♥ ♥ srs♠♣s ♦ ♦♥②

s♦s t ♠sr rsts ② ♠♥s ♦ rt ♦♣t tr♥sr♥s ♣♦t♦♦ tt s s t♦ ♠sr t ♠ss♦♥ r♦♠ t rrt rr♥t s s♥t t♦ t ② ♠♥s ♦ ♣s ♥rt♦r ♥ ♦rr t♦ ♦ ♣♦ssst♥ ♣♥♦♠♥ t♦ ♦rr rr♥t ♦ ♦r t t②♣ ♦♣rt♦♥rr♥t ♦ ♠ t ♠ss♦♥ s r② r ② t♦r tr t ♦s ♦ ② ♠♦st s♥st ♠♥t t♦ rt♦♥ ♠ ♥ r♦♥ ♥r♦♥♠♥t rstt♦ t ♦♠♠r ♦♠♣♦♥♥t s ♥ ♦t ♥trt s♥s♦r ss♠s srst s ♥ ♦♦ r♠♥t t t ♦♥ ♣s ♥ ❬❱❪ ♦r t ♦♥t♣rs♥s♦r

♦ r♣ ts rt♦♥ s♥st q♣♠♥t sr② s ♥ ♦♥ ♥ ♦rr t♦ ♥ ttr ♣t t♦ t rs r♦♥ ♥r♦♥♠♥t t t ♥ tr♠s♦ rt♦♥ r♥ss st ♦♠♣♦♥♥ts ♦r ts ♣♣t♦♥ ♥ ♥t♥ ♥sP s ❬s❪ s t ♣t① P♦r ♥sP ❬♣❪ s ♥ st s ♥t ♦r t ♥trt s♥s♦r ♦r♦rts ♠ts t ♥ ♥t ♥ ♦ ♥♠ tt ttr ♠ts t st♠t♦♥ s♣tr♠ s s♦♥ ♥ t r ♦

rsts ♦ sr rrt♦♥s ♣r♦r♠ ♦♥ t ♣t① ♦ s ♥ ♣♦tt ♥ r♥t ♣t① s♠♣s ♥ ①♣♦s t♦ t 60♦ ♠♠

Pr♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r ♦r ♣♣t♦♥s

r t♦♥ r♥ss tsts ♦ s s ♦r t s♥s♦rs rrt♦♥ tstrr ♦t t t t② s t①t

r t♦♥ r♥ss tsts ♦r t ♣t① P♦r ♥sP

♦s♠tr② ♦r t ①♣r♠♥ts

r ♥ rs ♦r t ♥♥♥ ♠♣♦② t

rt♦♥ t t Pr t② s t♦ t ♠① ♥r♦♥♠♥t ♦ t s s t♦ t rt ♣r♦t♦♥ ♠ ♦ rtr③t♦♥ ♦ ts♦♠♣♦♥♥ts s ♥ ♥ ♣r♦r♠ ② ♠sr♥ t t ♠ss♦♥ t ♥rs♥♣s ♦rr rr♥ts

s ♣r♦ t♦ ♥s♥st t♦ s ♣ t♦ ② ♣♦♥ ♠♠ rrt♦♥ ♥ t ♠① r♦♥ ♦ ♥ ♦r♥ t ♦rr rr♥t r t♥ ♠ t t ♠ss♦♥ rsts tt♥t ♦r ss t♥ tr ♦s ♦ ②♥ ♦ s ♥ s♦ ①♣♦s rt② t♦ t ❱ ♣r♦t♦♥ ♠ ♦ t t② ♥ ts ♦♥t♦♥ t t ♦t♣t ♦ t s ♥ ♦♥ t♦ tt♥t♦ ♦t t♦r tr ♣r♦t♦♥ s♣s ∼ 1011 p/cm2 tt ♣♦s ♦s ♦ ② t♦ ts ♦♠♣♦♥♥t s♦s ttr rt♦♥ r♥ss ♥ r♦♥ ♥r♦♥♠♥ts♣② ♣♦r t r ♦rr rr♥ts ts st rst r♥s t♦ ♥t s♥stt② ♦ ts ♦♣t q♣♠♥t t♦ s♣♠♥t ♠ ts

♠tr ♥

♥trt s♥s♦r ♣r♦t♦t②♣ t t s ♥ s♦ s t♦ q♥t② ♥ ♣r ♦♥③♥ rt♦♥ t ♥ ♦ t ♠tr s t ♥♦ t ♠tr rs t t t♠ t ♠♣t ♦ t ♠♥s♥t s♥ ♦r ♥ rt♦♥ ♦s r♦r t s rt ♠♣t ♦♥ t s♥stt② ♥ ♦♥ t♠♥♠♠ tt ♦s r♦♠ ♦s♠tr s②st♠s s ♦♥ t ♥ ♠sr♠♥ts r s♦♥ ♥ r t s♥ ♠♣t ♥♦r♠③t♦ t ♦t♥ t t s ♣♦tt s ♥t♦♥ ♦ t t♠ tr rrt♦♥

rst ♥♥♥ r t r♦♦♠ t♠♣rtr s ♥ ♠sr ♦♦♥ ♠♥ts rrt♦♥ t♦ ❱p ❳r②s t ♦srt ♦ ②♠♥ s r s ♣♦ttt rr ♠rrs ♥ s♦♥ ♥ r s ♥ tr♠♥♦♦♥ ♥♠ ❯❱ t rrt♦♥ ♦s ♣♦s ② ❯❱ t s ♥ ① ②①♣♦s♥ t ♠tr ♦r t♠ ♥♦ t♦ t s♠ ♣ ♠♣t t

t♠ ♠♦♥t♦r♥ t r s②st♠

t t rs♣t t♦ t ♣r♦s ❳r②s ①♣♦sr s♠ ♣r♦r s ♥ r♣t ♦♦♥ ❯❱ t ①♣♦sr t ♥

s ♥ rsts r♣r♦ t s ♠sr ♥ ❬s❪ ♦r s♠r ♠tr ♠♥s♥t s♥ r ♦t ♦ ts tr s♦♠t♥s ♦ ♦rs r♦♠ t rrt♦♥ s st s♥ s r str ♥ tt♠♣rtr ♥rss s ♣rt ♥

② ♠sr♥ s♠♣s t r♥t t♠ tr rrt♦♥ t ♠♣t ♦ ts♥ ♠② t ② s♥♥t rt♦♥s t♦ t ♥ s s t ♣♣♥♥ t tr♠♥t♦♥ ♦ t ❱ ♣r♦t♦♥ s♥stt② r s s♦♥ ♥ tr♥t t sts r ♥ r♠♥t t♥ ♦t ♥ t r ♠sr t♦♦rs tr rrt♦♥ s ①♣t ♦r t ♥ ♦ t ♠tr r t♦ r ♣r♠tr tt s t♦ t♥ ♥t♦ ♦♥t ♥ t s♥ ♦ ♥ ♥trt s♥s♦rs s ♥ ts rt♦♥ ♥ t③t♦♥

t♠ ♠♦♥t♦r♥ t r s②st♠

♥ t ♣r♦s st♦♥s t s ♥ s♦♥ tt t♦ t tr♦♥ rttr ♦t ♥trt s♥s♦r s ♥ ♠♣r♦ t s♥stt② ♦ s s♥s♦r ②♦ts ♥ t♦♣rt ♦♥t♦♥s t②♣ ♦ P ts s ♠♥② ♠t ② t♦ t♦rs

t rt♦♥ r♥ss ♦ t s s ♦r t st♠t♦♥ tt r♣②r ♥ r♦♥ ♥r♦♥♠♥t

t ♣r♦♣r ♥ ♦ t s♥st ♠tr tt q② rs t ♠♥s♥ts♥ ♦r ♥ ♦s

rst ss ♥ ♦r ♥st♥ ② r♣♥ t st♠t♦♥ s♦r t ♦♠♣♦♥♥t t ♥♥ rt♦♥ r♥ss s t ♣t① ♦s tst ♥ ♦r ts ♦♠♣♦♥♥ts ♥ ♠♦r ①♣♥s ♥ ♠♦r t t♦ ♣r♦r tt tst♥r ♦♠♠r ♠② t♦ rs ♥ t ♥trst ♦ s ♥trts♥s♦r s♠

s♦♥ ♣r♦♠ ♥ ♣rt② ♦♠♣♥st♥ t s♥ ♦ss ② ♠♣r♦♥t ♥② ♦ t tt♦♥ ♦r ② ♥rs♥ t st♠t♦♥ ♣♦r ♥ ♠t♦t♦ ♥rs t t ♦t♦♥ ♥② s ♦r ①♠♣ t♦ ♠♣r♦ t ♠tr♣♦st♦♥ ♦♥ t s♥st ♦♠ tsts ♥ ♣r♦r♠ ♥ tt rt♦♥s s♦♥ ♥ ♥ ts ♣♦t t s♥stt② t♦ ❯❱ t ♦r r♥t s♥s♦r s t ♦♥s s♦♥ ♥ s ♥ ♣♦tt ♥ ♥t♦♥ ♦ t①♣♦sr t♠ ② ♥rs♥ t r♥rt② ♦ t ♠trs t s♥stt② s♥ ♥♥ ② t♦r

s♦♥ ♠t♦ t♦ ♥rs t tt♦♥ ♥② ♦ s♦ t♦ r♣ t ♣♦t♦♦ t ♠♦r s♥st ♣♦t♦♠t♣r P ♦r ts st s♦t♦♥ ♥rs t ♥♠r ♥ t t ♦ t ♦r ♥trt s♥s♦r ss♠②

♥♦tr ♦♥♣t ♦ s♥s♦r strtr ♥ t ② r♣♥ t st♠t♦♥ t sr ♦r♦r t♦ ♦ t♦ ①♣♦s ts ♦♠♣♦♥♥t t♦ t rt♦♥♥r♦♥♠♥t ♥ ts t♦ ♦ ♥② rt♦♥ ♦ t st♠t♦♥ s♦r ♦r t♠ tt s♥ ♥ r♥ t♦ t r②st ② ♠♥s ♦ ♥ ♦♣t r ② ♦t♥

♦s♠tr② ♦r t ①♣r♠♥ts

r ♥stt② t♦ ❯❱ t ♦ t s♥st s ♦♥ ♣♦t♦♦s

t ♠♥s♥t s♥ s♥ t s♠ ♣r♥♣ s♦♥ ♦♣t r t tr♦♥♥ t♦ r♦t t ♠tr ♥ ♣t ♦ts t rrt♦♥ r r♦r P ♥ ♠♣♦② ♠①♠③♥ t t s♠ t♠ t st♠t♦♥tt♦♥s♦r ♣ts

♦♦♥ t ♦ ②♦t s♦ t s♥s♦r t ♣r♦t ♦ t s♥st s ♥ t ♥♦ r t♦ s♠ ♣r② ♣r♦ ♦ ♠♠trs t♦ ♦♣t rs t t t ♥ r②st r tr♦r t♦t ♠sr♠♥t ♣♦♥t t r♦t tr♦♥ ② sr ♠trs ② ♦r♠t rrt♦♥ st s ♦♥♣t ♦ rt♠ ♦s♠tr② s ♥ s♦ tst t ts ♦ t ♦♣ ♠sr♠♥t s②st♠ s s t rst rsts rsr ♥ t ♦♦♥ sst♦♥s

②♦t ♦ t s②st♠

t♦t t rt♦♥ r♥ss ♦ t r♦t tr♦♥s ♦s♥t ♦♥sttt ♣r♦♠t ts r♦t s♠ t♦ ♥sr r ♠sr♠♥ts t t rt♠ ♥ trs ♥r♦♥♠♥t t rt♦♥ t♦r♥ ♦ t ♦♣t rs tt rr② ♦tt sr ♥ t s♥s ♠ ♥st ♥♠♥t ♦r ts rs♦♥ t s②st♠s♥ t ts ♥t ♦♥ t ♣r♦r♠ ♥ ♦♣t rs s ♥ tP ①♣r♠♥ts ♦ t ❬♠ r❪

s♦s t ②♦t ♦ t rst ♣r♦t♦t②♣ ♦ rt♠ tst ♦r rt♦♥♠♦♥t♦r♥ ♥ r♦♥ ts ♦ qrt③ rs r♦♠ P♦②♠r♦ ♥♦♦s P♦♥① ❩ ❯ ♦ ♠ ♥t ♥ ♠♠ ♦r ♠tr r ♥srt ♥t♦ ttt ♣r② ♣♣ ♦ ♦t ♠♠ ♠tr t ♦♥ s s♥s♦r t rsr ♣♦s ♥ ♠ r②st s ♦♣ ② ♠♥s ♦ P ♦♣t t ♦ t ♦♣t s s ♥ t ♥srt ♦ ♥② t s♥s♦r

t♠ ♠♦♥t♦r♥ t r s②st♠

r Pr♦t♦t②♣ ♦ t♠ s②st♠ s♥ ♦r t ♠♦♥t♦r♥ ♥ P ts

s r♣♣♣ s♥ ttt ♠tr t t r♦t s ♦♥ r s♦♥♥t t♦ ♥♠ ♥s ♣♠♣ sr t♦ ♣r♦ t ♦♣t st♠t♦♥ t s♦♥ ♦♥ s ♦♣ t♦ ♣♦t♦♠t♣r t t♦ ♦t t s ♠ss♦♥♦r t ♣r♦t♦t②♣ s ♥ ts ♦r t ♦♣t st♠t♦♥ ♥ ♣r♦ ♥ ♣♦rr♥ ♣ t♦ ♠❲

t s t♦ ♥♦t r tt t ♠①♠♠ ♦♣t ♣♦r r t t ♠♦♥t ♥ t ♣r♦s ♥trt s♥s♦rs s s ♦t ♥ ♦rr ♦ ♠♥t♦r ♥ t r ♣♦r t♦ r② ♦rr rr♥ts t②♣② ♠♦♥sr♥ tt t♦ ♦ st♥ ♣r♦♠s ♥ ♦♣rt♦♥ t r s②♣♦r t ss t♥ ♦ t ♠①♠♠ rr♥t rt ts ♠ r t ♦ ♥t ♥ts ♥ s♥ sr st♠t♦♥ s♦r

♠♣♦② rs r s♣ ♦r t r♦♥ ♦rr ♦r♠tr ♦ t ①♣r♠♥t s ② r ♣r♦s② tst t t② s♥ ❱ tr♦♥s ♣ t♦ ② q♥t t♦ ∼ 1016 tr♦♥s ❬♠❪ ♥ t ❱ ♣r♦t♦♥s t t rrt♦♥ t② r♥ ② q♥tt♦ ♠♦r t♥ ×1016 p/cm2 ❬r❪ s rrt♦♥ tsts s♦ tt t rt♦♥♠ ①ts t s♠ ♦r ♦r ♦t tr♦♥s ♥ ♣r♦t♦♥s tsts ttt♥t♦♥ ♦ ♥♠ ♥ ♥ t ♥ ♥♠ ♦rt tt♥t♦♥ s ♥♦♥ ♥ t ♥ ♥♠ ♥ ♥♦ tt♥t♦♥ s ♥ ♥st ♠sr ♦ ♥♠ s♦ t ♦tt ♥s t r tt♥t♦♥ s♣tr ♦r tr①♣♦sr t♦ ② tr♦♥s r♦♠ ❬♠❪ ♥ t ♣tr t ♠ss♦♥ ♥st♠t♦♥ s♣tr r s♦ r♣♦rt

♦ ♠♥t♦♥ rt♦♥ r♥ss sts ♥ ♦♥ ♦r ♥ts λr♦♠ ♥♠ t♦ ♥♠ ♥ ts r♥ t rt♦♥♥ tt♥t♦♥ tr ①♣♦srt♦ ② s ♠♥♠ ♥ t r♦♥ ♥ t ♠①♠♠ ♦ t ♠ss♦♥ s♣tr♠s ♦ t r t ♥t r t♥ ♥♠ ♦r ♥ t♦t

♦s♠tr② ♦r t ①♣r♠♥ts

r t♦♥♥ tt♥t♦♥ ♥ t ♦♣t r s ♦r t rt♠ ♥ t ♣tr t s♣tr r rrr t♦ t t♥ s ②①s t tt♥t♦♥♥ t rs t tr♥s♠ss♦♥ ♠ r rrr t♦ t s♦♥r② ②①s ♥ t ♣trt ♠ss♦♥ ♥ st♠t♦♥ s♣tr r s♦ r♣♦rt tt♥t♦♥ s♣tr ♦ t♥♦trrt r t r tt♥t♦♥ ♥ r② s♠ ♦s t♦ t ①①s ♥s r② s

tt tt♥t♦♥ ♣ ♠t ♣♣r ♦r λ r♦♥ ♥♠ t ♣♦rr♥♦ t sr t ♥ ♦ t♦ ♥rs t st♠t♦♥ ♣♦r ♦r ♥rs♥ rt♦♥♦ss t♦ ♦♠♣♥st ♦r ♣♦ss rt♦♥ ♥ ♦sss

♦ ♦♥srt♦♥ ts ♥t t r s ♦♦ ♥t t♦rr② t s♥s ♦r t rt♠ s②st♠

Pr♦r♠♥s ♦ t r ♣r♦t♦t②♣

rst rrt♦♥ ①♣r♠♥t ♦r t ss♠ ♣r♦t♦t②♣ s ♥ ♣r♦r♠ ♥ t rt♦r ♦ t ♦③ t♥ ♥sttt ♥ ♥ ♦♥ sr♥ rt♠ s♥s♦r s rrt ② ♣♥ t ♥t♦ t rt♦r♦r tr♦ t rrt♦♥ t r ♠sr♠♥t ♣♦♥ts r t♥ ♠♦♥t rt♠ ② ♠ st♣s ♥s t rrt♦♥ ♥♥ ♥ ♦rr t♦ ♠srt ♦s ♣r♦ ♦♥ t

t t rt♦r ♣♦r ♦ ❲ t ♦srt s ♦ ♦t ②s t t strt♥♣♦st♦♥ stt ♥t ♥ t rt♦r ♦r ♠ ♥ t ts♠ ♣♦st♦♥ t ♥tr♦♥ ① r t♦ t s♥s♦r ♥ ♠sr ② ♠♥s ♦rrs s s♦♥ tt♦rs s ♦ ×1010 ♥♠2 ·s ♠sr♠♥ts r♣r♦r♠ r♥ ♥tr♦♥ rrt♦♥ ② r♦r♥ t ♠♣t ♦ t ♠♥s♥t♣ ♠tt r♥ s sr st♠t♦♥ ♦r r♦t ② t s♥s♦r s ①♣♦s ♦r s♦♥s t♦ t rt♦♥ ♥ ♦rr t♦ ♠t rs

♣r♦♠♣t ♦♠♥s♥ t ♠tt ② t ♠tr r♥rrt♦♥ ♥ s♦ s ♦r ♦srt t♦♥s ♥ t s♠ s♦♥ s t ♠

t♠ ♠♦♥t♦r♥ t r s②st♠

r t♠ ♠sr♠♥ts ♥ t rt♦r ♥ t ♣tr t ♥ ♠sr♠♥ts rr ♦♥ t t rt♠ ♥ ♦♠♣r t t ♦s♣r♦r♦r ♥♣♥♥t② ② ♠♥s ♦ s♠♦♥t♦r ♦s♠trs

♥s♥ r♦♠ s♥tt♦r ❬P♦❪ Pr♦r♠♥ ♠sr♠♥ts r♥ rrt♦♥ts ♠♦♥t ♦ t s t♦ t♥ ♥t♦ ♦♥t ♥ strt r♦♠ t ♣♠♣t ♥ t ♣rs♥t s t rt♦♥ ♦ ♠sr s♥ r♣rs♥ts ♦t ♦ t r♦r ♠♥s♥ s s♦♥ ♥

♥② ♦♠♣rs t ♦srt ♣r♦ ♠sr t t t♥qsqr ♠rrs t rr♥ ♠sr♠♥ts ♦t♥ s♥ s♦♥ ♦s♠trs rr ♠rrs ♠sr♠♥ts r ♥ r② ♦♦ r♠♥t t t rr♥ ♦♥s ♦r r♥ ♦ ♦r ♦srt s ♦r♦r t ♦r ♠tst ♦♥ ♦♥r♠♥ ts t ♣t② ♦ t rt♠ s②st♠ t♦ s ♦t ♠♥s♥ t♥qs ♦r rt♦♥ ♠sr♠♥ts r♥ ♥ tr rt♦♥①♣♦sr ❬③❪ srs ♦ ♠sr♠♥ts ♥ t r♥t ♥♥ ♣♦st♦♥sr r♣t sr t♠s ♠sr♠♥t r♣tt② ttr t♥ s ♥♦t♥ s s ♦♠♣r t t ♥rt♥t② ♥ t s♦t ♣♦st♦♥♥ ♦t s♥s♦r ♥s t rt♦r rrt♦♥ ♥♥ ♦r ♠sr♠♥t ♣♦♥t ♣rs♦♥ ttr t♥ s ♥ ♦t♥ tr t♥ ♦♥st ♠sr♠♥ts ♦tsts ♦♥r♠ ts tt t ♠♣♦② ♦♣t rs ♦♥t s♦ s♥♥t ♥s ♦rt♦♥ ♠ ♥ t ♥tr♦♥ ♥ r♥ ♣ t♦ ×1013 cm−2 t♦ t② r①♣♦s ♥ t♦t r♥ t r♥t rrt♦♥ tsts

s♥ ♦ t rt♠ ♣r♦t♦t②♣ s rr♥t② ♥r ♦♣t♠③t♦♥ ♥♦t t s♥s♦r ♥ t r♦t s t t ♦ t♦ ①t♥ t s♥stt② r♥♦ t s②st♠ ♦ t st ♦♥ ♦rr ♦ ♠♥t ♥ ♦s

♦s♠tr② ♦r t ①♣r♠♥ts

tr♦♥ tt♦♥ t ♠trs

♠trs ♥ sss② s ♦r P ♣♣t♦♥s t♦ ♠sr t ♦sr ② ♥r② r ♣rts s t s ♥ s♦♥ ♥ t ♣r♦s st♦♥s♥ tr s ♦ ♦♥♥ ♥tr♦♥ ♦s♠trs ♦r P ♣♣t♦♥s s♣② ♦rtr♠ ♥tr♦♥ ♥rs t ♣♦sst② t♦ ♠ ♠tr s♥st t♦ ♥tr♦♥s s r② ttrt ♣r♦s♣t ♦r t rs♣♦♥s ♦ ♣r t♦ ♥tr♦♥ rrt♦♥s st t♦ st ♥ t s ♣rrqst t♦ ♣♦ss s ♥ t rt♦♥ ♥r♦♥♠♥ts s t t♦♣ sss ♥ ts st♦♥ ♦r♦r ♥ tsst♦♥ ♦r t rst t♠ t ♠♥tr ♦ s♣② ♣r♣r ♠trs ♣rs♥t t♦tr t t qt♦♥ ♣r♦ss ♠♥ t♦ t tr ♥tr♦♥s♥stt② ♥ tr ♥r② ♣♥♥

tr♦♥s ♦ ♥♦t ♣r♦ rt ♦♥③t♦♥ ♥ ♠trs ♦r tt ♠♦♥t ♦♦♥③♥ ♥r② s ♣♦st s♦♥r② ♣rts ♥rt ② ♥tr♦♥ ♥trt♦♥s t♦t ♥tr♦♥ r♦ssst♦♥s ♦r t ♠♥ts ♦♥sttt♥ t s ♠tr r♥ t ♦rr ♦ r♥s ♦r ♥tr♦♥ ♥rs r♥♥ r♦♠ tr♠ t♦ sr ❱ rst♥ ♥r② ♣♦st♦♥ s ①♣t t♦ ♥♦t s♥t t♦ ♥rt ♠srq♥tt② ♦ tr♦♥♦ ♣rs ♥ ♣r

♦r ts rs♦♥ t♦ ♥rs t s♥stt② t♦ ♥tr♦♥s r♥t ts ♥ ♠① t t st♥r ♠tr ♥ ♣rtr ♦r♦♥ s t♦♥rs t s♥stt② t♦ tr♠ ♥tr♦♥s ♥ ♣♦②t②♥ P s ♦rst ♥tr♦♥ tt♦♥

♦r♦♥ s rs♣♦♥s ♦r tr♠ ♥tr♦♥ ♣tr t ♥r rt♦♥

10B + n →7 Li + α + γ + 2.3MeV.

s rt♦♥ s r② r r♦ssst♦♥ σr r♥s ♦r tr♠ ♥rstt rss ♦♥ t♦ r♥s ♦r ♥rs ♦ s♦♠ t♥s ♦ ❱ s s♦♥ ♥ ❬①❪ ♣ ♣rts ♥ t t♠ ♦♥s ♥rt ② t ♥tr♦♥ ♣tr ♦♦s tr ♥r② ♦♥③t♦♥ ♥ t s♥st r ♠tr r♥s ♦ tt♦ rt♦♥ ♣r♦ts ♥ t r r t t t s♦tr ❬❪ ♥♥t♦ ♦♥t tt t ❱ rs ♥ t rt♦♥ ♦♥trts t♦ t ♥t ♥r②♦ t t♠ ♦♥ ❱ ♥ t ♣ ♣rt ❱ r♥s ♦ µ♠ ♥ µ♠ ♥ r r t rs♣t② s s♦rt ♣t♥ts r♥t tt ♣tr tr♠ ♥tr♦♥s ♣♦st t ♦♥③t♦♥ ♥r② ♥ t ♠tr

P t ts ♦♥t♥t ♦ ②r♦♥ s t ♣rrr ♠tr t♦ tt st ♥tr♦♥ss ♦♥ ♣rt ♥ tr♥sr r♦♠ ♥♦♥ t♦ ts ♥r② t♦ t ♣r♦t♦♥ ♥ ♦♥st ♦s♦♥ r r♦ ♥r② ♦ t ♥t ♥tr♦♥ ♥r②②r♦♥ s r♦ssst♦♥ σs ♦ t ♦rr ♦ t♥s ♦ r♥s ♦r ♣tr♠ ♥tr♦♥stt s t♦ r♥s ♦r t ♥r② ♦ ❱ t rtr rss t♦ ♣♣r♦①♠t② r♥ ♥ t ♥tr♦♥ ♥r② rs ❱ s s♦♥ ♥ r♦ ♣r♦t♦♥ ♠♦ tr♦ t s♥st ♠tr t ♣t ♥t ♣♥♥ ♦♥ t ♥r②tr♥srr t♦ t ② t ♥♥t ♥tr♦♥

tr♦♥ tt♦♥ t ♠trs

r P♦ts ♦ t ♥tr♦♥ r♦ssst♦♥ ♦ ♥trst ♦r ♠trs

tr♦♥s♥st ♠trs

♣r ♠tr ♥ tr ♦♠♣♦♥s ♦ ♠tr ♦♣ t ♦r♦♥ ♥♠① t ♣♦②t②♥ r ♣r♣r ♥ rrt t♦ r♥t ♥tr♦♥ ♥s ♥r♥t rrt♦♥ ts ♦r r♥t t②♣s ♦ s♠♣s r s♦♥ ♥ ② s③ ♦ ① ♠♠2 ♥ r♦s t♥sss ♥ ♣rtr t s♠trs t ♦♦♥ rtrsts

st♥r ♠tr ♣r s♣♠♥s ♦t♥ r♦♠ µ♠ t ②r♦ r ssr♥ ♣r♥t ♦♥ ♣t♦♥ ♦ s s♦

♦♣ t ♦r♦♥ s♣♠♥s ♦t♥ r♦♠ µ♠ t ②r♦ r t ♦r♦♥ ♦♣ ssr♥ ♣r♥t ♦♥ ♣t♦♥ ♦ ♦r♦♥s ♥tr♦ ♥ t ♠tr tr♦ s♥tr♥ ♥ ssq♥t r♥♥♣r♦rs ♥sr♥ t ♦♠♦♥t② ♦ t ♦t♥ s♠♣s

♠① t P♦②t②♥ P s♣♠♥s ♥ r♦♠ r ♦♥ t r s ♠t t ♣♦②t②♥ t♥sss ♦ t s♠♣sr ♦ ♠♠

♠① t P ♥ ♦r♦♥ P s♣♠♥s ♦♥t♥♥ ♦tP ♥ ♦r♦♥ t♥sss ♦ ts s♠♣s r s♦ ♦ ♠♠

t②♣ ♦ ♠tr t♦ ♣s r s r♥ t rrt♦♥ tst ♥♦rr t♦ ♣r♦ t r♣r♦t② ♦ t rsts ② r ♣ ♥ rrt ♥ ♠r♦♥t ♠♥♠ ♦s ♥ ♦rr t♦ ♣r♦tt t♠ r♦♠ t ♦r rrt♦♥t s♠♣s r t t♦ ♦r ♦rs t♦ ♥♥ t r ♥ t tr♣s t♦ r t ♦s♠tr ♠tr

♦s♠tr② ♦r t ①♣r♠♥ts

r ♠♣s ♦ ♠trs r♦♠ t t♦ rt ♣r ♠tr ♦♣t ♦r♦♥ ♠① t P♦②t②♥ ♥ ♠① t P♦②t②♥ ♥ ♦r♦♥

①♣r♠♥t ♣r♦r t♦ rtr③ ♥tr♦♥s♥st ♠trs

♦ q② t r♥t sts ♦ ♠trs s ♥ ♥t♦♥ ♦ tr ♥tr♦♥s♥stt② ♥ ♥r② ♣♥♥ t♦ s♣ rrt♦♥ ts t ♦♠♣♠♥tr②♥tr♦♥ s♣tr ♥ ♦s♥

♥ t t② t t P rt♦r s t rrt♦♥s r ♣r♦r♠ ♥ t② t ♠ r♦♠ t ♥♥t ❱ ♣r♦t♦♥ ♠ ♥♦rr t♦ t ♥ ♠♦st ♣r r♦ s♣tr♠ ♦ ♥r② ♥tr♦♥s ♥ ts ♦♥t♦♥s r♥ss t♦r s ♥ t ♥ t r rt♦rt t rrt♦♥s r rr ♦t ♣♥ t s♠♣s ♥t♦ t rt♦r ♦rtr♦ t ♥♥ tt ♦♣s r♦ ♣♦st♦♥ ♥ ♥trs t rt♦r ♦rr♦♠ ♦ s sr ♥ ♥ ts ② t rrt♦♥ s ♣r♦r♠ ♥ tr♠♥tr♦♥s ♦♠♥t ♣rt s♣tr♠ ♥ ts t② r♥ss t♦r s ♥ tr♠♥ s♣tr ♦ ts t♦ ts ♥ ♣♦tt t♦tr♥

♥ t ♥ rt♦r srs ♦ ♠trs s ①♣♦s s ② ♠♥s♦ ♠♠ t ♠♠ ♦ ♥ ♦rr t♦ rrt t♠ t♦t t tr♠♥tr♦♥ ♦♠♣♦♥♥t ♦ t rt♦r s♣tr♠ s σc ♦r ♥ t♥ss s ♦s♥ ♦r♥ t♦ t tr♠ ♥tr♦♥ ♠♥r♣t tt s ♦ ♦t µ♠

♦tr t ♥tr♦♥s ♠♠ r②s r ♣r♦ ♥ ♦t rt♦♥ ♥r♦♥♠♥ts♠♠ r②s r♣rs♥t ♦♥t♠♥t♦♥ ♥ ♦t ♥r♦♥♠♥ts tt s ♣♥♥t ♦♥t ♦♣rt ♦♥t♦♥s ♥ ts ♥ t♦ ♠sr r♥ t rrt♦♥s r♦♠ ♠s s ♥ rrs s s♦♥ tt♦rss r s ♥ ♦t ts t♦ ♠sr t ♦t ♦♥③♥ ♦s ♥ t ♥tr♦♥ ♥ rs♣t② s♦s t rsts ♦ t ♠sr♠♥ts ♣r♦r♠ ♥ t t♦ ts ♥ t ♥ rt♦r t ♠sr♦r t s♠♣s rrt ♥ s♥ tr♥r ♠rrs s ♣rs♥t s♣rt②r♦♠ t ♥s s♠♣s sqr ♠rrs t♦ t ♠♠ r♦♥ ♥t ♥ rt♦r t rsts r ♦t t♦r r t♥ ♥ t

tr♦♥ tt♦♥ t ♠trs

r ①♣r♠♥t t② ♦r ♥tr♦♥ rrt♦♥ ♦ ♠trs tr♦♥ s♣tr♠ ♥ t t② s ♥ t♥ ②①s t ♠ r♦♠ ♠ ①s ♥♦r♠③ t♦♦♥ ♠♣♥♣♥ ♣r♦t♦♥ ♦♥t♥♦s ♥ t♦r ♥tr♦♥ s♣tr♠ s ♥ rt♥②①s s ♠sr r♦♠ tt♦♥ ♦s ♦tt ♥ ♠sr ♥ ♦t rrt♦♥ts ② ♠♥s ♦ r♦♠tr ♠s

t②

rst rrt♦♥ tst ♦ ♥tr♦♥s♥st ♠trs

♥ t t♦ ts t s♠♣s r ①♣♦s t♦ ♥rs♥ s ♦ Φeq ♥ ♦rrt♦ r♦r t s♥stt② rs ♦r t r♥t ♠trs s♠♣s r st♦rt r♦♦♠ t♠♣rtr ♥ ♠sr s tr rrt♦♥ s s♦♥ ♥ ♦r t ♣r r ♠tr t ♥ ♦ t ♠trs s ①♣t t♦ st③t t r♦t t♠ rr s ♦r t r♦t ♦ ts ♠trs s ttst♥ sr ♥

s♥ ♦t ♠sr t t r♦t s②st♠ s ♥ ♥♦r♠③ t♦ t♣r s♠♣s t ♥ ♦rr t♦ t ♥t♦ ♦♥t t r♥t s♠♣s ♦♠ s♦ trt s♥s ①♣rss ♥ ♠❱ ♥ ♣♦tt rss t Φeq ♥ r ♣rs♥t ♥ ♥

tr ♦t rrt♦♥s t s♥ t t ♣r ♠tr s t s♠st r♦r ♥ ♦r tsts ♥ s ss t♥ ♠❱ s s♦♥ ♥ ♥ t t② tr♥r ♠rrs ♦r s ♦ Φeq ♦ ①1011 cm−2 t s♥ s♦r t♥ t ♥♦s s♥ t ♥ ♦ t r ♦t s②st♠ s st t♦ ♠sr ♦ss ♦r t ♥ t② tr♥r ♠♣t② ♠rrs t s♥ s t♦r r t rs♣t t♦ t ♦♥ ♠sr t s s ♥ ♦♦ r♠♥t tt ♠sr♠♥ts ♣rs♥t ♥ s ①♣t t ♣r ♠tr ♠sr ts t ♦♥③♥ ♦♠♣♦♥♥t ♦ t ♥ s ss♥t② ♥s♥st t♦♥tr♦♥s

s♦s t rst rsts ♦t♥ ♦r t ♥ P ♠trs♥ t r ♥ r♥ strt♦♥ s ♦sr s s s♦ ①♣t ♦r t ♣r♠trs t ♥s r ①♥ t r♥ ♣rs♥t ♥ ♥ ts s

♦s♠tr② ♦r t ①♣r♠♥ts

r rst rrt♦♥ ♦r ♥tr♦♥s♥st s ♣r ♠tr rs♣♦♥s trrrt♦♥ t ♠rrs ♥ ♥ ♠♣t② ♠rrs ♥ P

♠tr rs♣♦♥s tr rrt♦♥ t ♠rrs ♥ ♥ ♠♣t② ♠rrs

tr♦♥ tt♦♥ t ♠trs

OSL+BOSLpure

OSL+PEOSLpure

♥

t s♥stt② ♦ s t♦ ♥tr♦♥s

r♠ ♣tr♠ st ♥r②< ❱ ❱ ❱ ❱ ❱ > ❱

♥

♣tr ♦♠♣♦st♦♥ ♥ t ♥ ♥ rt♦r♥tr♦♥ ts

r♠♥t t t ①♣r♠♥t t ♦r t r ♣rts tt ♥ ♣rs♥t♥ ♥ ♥ ❬s❪ ♦r ♦♠♣rs♦♥ t♥ t ♥tr♦♥s♥st ♥ t♣r ♠tr ♥r ts ♥ ♣♣ t♦ t t ♠sr ♥ t ♦ ♥ r♥ t♠s ♥rs s♥stt② s ♥ ♦♥ ♥ ts ② s ♣rs♥t ♥

ss♠♥ tt t t♦t ♥tr♦♥ s♥ s ♥ ② t s♠ ♦ t ♥ tP s♥s ♥ t ♥ t② ♦♥t♥♦s ♥s ♥ ♦r Φeq ×1011 cm−2 t ♠sr s♥s r♦♠ t sqr ♠♣t② ♠rrs ♥P r♦♥ ♠♣t② ♠rrs s♠♣s r♣rs♥t ♥ rs♣t② ♦t t♦t ♥tr♦♥ s♥ t ♦tt ♥s ♥ ♥ ♦r t s♠ ♥tr♦♥♥ t s♥s ♦t♥ r♦♠ t P s♠♣s r♦♥ ♠rrs r♣rs♥t♠♦r t♥ ♦ t ♥tr♦♥ s♥ s t sqr s♦ ♠rrs s♠♣s ♦♥② tt s♥ t ♦ rsts r ♥ ♦♦ r♠♥t ♦t t t s♣tr ♦♠♣♦st♦♥ ♦ t t♦ ♥tr♦♥ ♥r♦♥♠♥ts s♦♥ ♥ ♥ s♠♠r③ ♥

str♦♥② tt♥ s♥ ♦ t s♠♣s ♦t♥ t t t②♥ ①♣♥ s t② ♥ t ♠sr♠♥t ♦ s♥ tt s ♦s t♦ ttr♦♥ ♥♦s ♦ t r♦t ♣♣rts ♦r♦r ♦♥ ♦ t s♠♣s rrt♥ ♥ s♦ s♦s r rs♣♦♥s ♥ t s♠ ♥ r♥ s t sqr♠♣t② ♠rrs t ×1011 cm−2 ♦ ♥ ♥ ①♣r♠♥t ♣r♦♠ sss♣t rqrs r♦ss ♥ ♥ ♦rt♦♠♥ rrt♦♥

♦r t P ♦♥② t ♥ t r s ♠tr ts♠ rs♣♦♥s s t P tt s r② ♣♦tt ♥ ♠t♦ ♠♣♦② t♦ ♣r♦ P s♣♠♥s s t♦ ♣r♦♠♥♥t ♣♦②t②♥ rt♦♥♦♠♣r t♦ t ♦r♦♥ ♦♥ ♥ s ② t♦ ♦♥t ♦r ts t

♥② ♦r t ♥ s♠♣s ♥ ♥tr♦♠♣rs♦♥ ♦ ♥ Ps♠♣s rrt t ♥ t♦t t tr♠ ♥tr♦♥ ♦♠♣♦♥♥t ♦ t s♣tr♠ t♦t ♦r t s♥ s ♣rs♥t ♥ s ♥P s♠♣s s♦ r rs♣♦♥s ♦r ♦r♥ t♦ t♦♥ss♥ t r♦ssst♦♥s ♦ ♥ t ♥ ♥tr♦♥ s♣tr ♦ t s♥s ♦♠♥ r♦♠ t s ♥ P s♠♣s r ①♣t

♦s♠tr② ♦r t ①♣r♠♥ts

r rs ♦ s♠♣s rrt ♥ t ♥ rt♦r s♥ s♣♣rss t tr♠ ♥tr♦♥ ♦♠♣♦♥♥t ♦ t s♣tr♠ ♠rrs s♥s ♠sr♦r t s♠♣s rrt t t ♦ s♣tr♠ ♥s s♠♣s r s♦ s♦♥ ♦r♦♠♣rs♦♥ s ♥s

t♦ r ② ♦t ♥ ♣r♥t t rs♣t t♦ t ♥s ♦♥s t♦♥ ♦r t P s♠♣s t ♥t♦ ♦♥t tt r♦ ♣r♦t♦♥s ♦ ♥rs< ❱ rs ♥ ♠♦♥t ♦ ♥r② ♥ ♦♥③t♦♥ ♣r♦sss ♥t♦ t s♥st♠tr s♥ s♦♥t ts ♥ t ♦♥ t s♥ ♠sr r♦♠ tP s♠♣s s s s♦ ♦sr ♥ t ①♣r♠♥t t ♣rs♥t ♥ r t r♥ t♥ t s ♥ t ♥s P s♠♣s s t♥t rt rr♦rs ♦ t ①♣r♠♥t

♦r t rst ①♣t rt♦♥ ♦ t s♥ ♦r t s s♠♣s s ♥♦t ♦sr s ♦ t♦ t ♠♥ ts ♥ t r③t♦♥ ♦ tt s♥ s♥ ♠♠ t ♦ ♥ ♥ t♦ r ♥ tr ①♣r♠♥t

♠①♠♠ rt rr♦r t ♦♥ ♦t ♠sr♠♥t ♦ s♠♣s ♦ ts♠ t②♣ ①♣♦s t♦ t s♠ rrt♦♥ ♥r♦♥♠♥t s② t♦ s♠♣s s♣r t ♣♦♥t s sr ♥ ♦r srs ♦ rrt ♠trs s ♥ ♦r t ♥ ♥ ♦r t s♠♣s rs♣t② ♣r♦♥ ♦♦ r♣r♦t② ♦ t ♠sr rsts

♥ rr♦r s♦r t♦ t ♥t♦ ♦♥t ♥ t ♣rs♥t ♥tr♦♥ ♠sr♠♥ts s ♣r♦② ♠s♥♠♥t tt ♥ ♦r r♥ t ♣♦st♦♥♥ ♦ t rrt s♣♠♥s♥ t s♠♣s ♦r ♦ t tst♥ ♦r t r♥ ♥ tr ♠♥tr ♥♦t s♠♣s r tt♥ t s♠♣s ♦r ♥ t s♠ ②

❱t♦♥ tsts ♦r ♥tr♦♥s♥st ♠trs

rrt♦♥ tsts ♣rs♥t ♥ t ♣r♦s t s♦♠ ♦♣♥ qst♦♥s ♦tt rs♣♦♥s ♦ t ♠trs t♦ ♥tr♦♥s ♥ ♣rtr

tr♦♥ tt♦♥ t ♠trs

r ♦♠♣♠♥tr② rrt♦♥s ♦r ♥tr♦♥s♥st s t ♦ tr ♥♣♥♥t rrt♦♥ ♦♥ ♣r ♠trs ♠♣t② ♠rrs ♦rrs♣♦♥ t♦ t rrt♦♥♦ t st♥r ♠tr t ♦♥s r t rsts ♦ rrt♦♥s ♦r ♥ srs♦ ♣r♦ ♥ ♥ t ♣♦r s r♥ t♦ r♥ s③ ♦r t♥ µ♠ ♥s ♥ ♣♦tt s ♥s t♥ r♥t t sts ♥♣♥♥t ♠sr♠♥ts ♥ t ♥ rt♦r rr ♦t t ♠ P ♥ t 7 ♥ 6 ♣ss ♦s♠trs

t rs♣♦♥s ♦ t ♣r ♠tr t♦ ♥tr♦♥s s ♥♦t ♥stt t Φeq srtr t♥ ×1011 cm−2

t rtr③t♦♥ ♦ t rs♣♦♥s ♦ t ♠tr s t♦ t ♥♦rr t♦ ttr ♥rst♥ t r♦ ♦ t ♦r♦♥ ♦♣♥ ♥ s ♠trs

♦ ♥sr t♦ t rst qst♦♥ tr ♥ srs ♦ ♣r ♥ ♥♣♥♥t② rrt ♥ t ♥ rt♦r ♥t Φeq ♦ ♦t ×1012 cm−2 ♠sr♠♥ts ♦ ts s♠♣s ♣r♦r♠ t t s tst♥ ♥ tr sr s ♦ st♦r tr rrt♦♥ ♥ ♣♦tt ♥ ♠♣t② ♠rrs ♥ ♣r rs♣♦♥s r ♦♦s ♥r ♦r ♣ t♦ Φeq ♦×1011 cm−2 s t s ♥ r② s♦♥ ♥ t r ♥s t s♥s♦ strt♦♥ ♣ t♦ ♦t ×1012 cm−2 tr ts ♣♦♥t t s♥ strt t♦r♦t ♥r② ♥ t r♥t s♦♣ t rs♣t t♦ t ♣r♦s ♦♥ ♥ ♠sr♠♥t rsts ♣rs♥t ♥ ts st♦♥ t ①①s rr♦r rs ♥t t rr♦r♥ t ♥ ♠sr♠♥t tt s ♥ q♦t t♦ r♦♠ t r♦t ♦ rrss s♦♥ tt♦r strtrs ①♣♦s t♦tr t t s ②①s rr♦r rsr♣rs♥t ♥st t r♥♦♠ rr♦r t ② r♥ sr s♠♣s ①♣♦st♦ t s♠ ♣rt ♥

s ♠sr♠♥ts ♥ ♦♠♣r t st ♦ ♥♣♥♥t ♠sr♠♥ts♣r♦r♠ ② ♠♥s ♦ ♣ss ♦s♠trs s s♦♥ ♥ t♦ tr ♦tr♠♥tr♦♥ s♥stt② t ♠ t P ♥ t 7Li s s r s♣♣♦s t♦ ♠sr ♠♥② t rt♦r ♣♦t♦♥ r♦♥ ♥ t st♥tr♦♥ s t ♣r ♠tr ♦s ♣♦s ② tr♠ ♥tr♦♥s s ♥st ♥ ♦rr ♦ ♠♥t r s s♦♥ ② t r rrs tr♥r ♠rrs ♣♦tt ♥

♦s♠tr② ♦r t ①♣r♠♥ts

r s♠♣s ♣r♣r ♦♥ t ♥ ♠tr ♦r ♠trs ♥ ♠ ② ♦r r♥t ♦r♦♥ ♦♣♥ ♥ r r♦♠ t♦ s ts ♥t t①t ♦r ♥② ♠trs t♦ ♥♣♥♥t st ♦ s♠♣s ♥ rrt ♥ ♣♦ttt ♠♣t② ♥ ♠rrs rs♣t② ♥s ♥ ♣♦tt s ♥s t♥r♥t t sts

tt r♣rs♥t t r♥t ♦s ♠sr ② ♠♥s ♦ s 6Li ♥7Li ♠sr♠♥ts ♣rs♥t r rs tt ♥ t r♦♥ ♦ ×1011 cm−2 ♥ t rt♦r r ② tt s ♥ ♥t s t strt♦♥ ♠t ♦t s ♠tr tr r ♣rt rrt♦♥s s

♦tr t t rst rs♦♥ ♦ ♣r ♠tr ♥ r ♠tr s♥ ♣r♦ ♥ ② t ❯♥rst② ♦♥t♣r ♥ tst t t ♥ rt♦r s ♣♦r s ♥ r♥ t♦ r♥ s③ ♦r t♥ µ♠ ♥ t s ♥ ♣r ♥ t ♦♦♥ ♣♦ts r♦♠ ts ♥ s♣r♦t ♦r r♥t s♠♣s ♥ ♣r♦ ♥ tr s♥stt② t♦ t♠① γ♥tr♦♥ s♦ ♥ ♠sr ♦r t rst t♠

s♦ t ♠rrs t s♥stt② ♦ t♦ sts ♦ t ♠tr ♥ t rt♦r s ♥ s♦s r s♥stt② ♦ ♦t t♦r ♥ ♦s♥t s♦ ♥ ♦ strt♦♥ ♥ t ♥stt Φeq r♥ ♦r s♥stt② s ♠♦st ② t♦ t ♦r r♥ s③ ♦ t ♣♦r

r♦♠ ts ♥ ♣r ♦r ♦r♦♥♦♣ s♠♣s ♥ ♣r♣rs s♠♣s r♦♠ t♦ ♦♥t♥ ♥ t♦ ♦r♦♥ rs♣t② ♦r♦r t ♠tr s s♠tt t♦ ♦ tr♠② r♥ t s♥tr♥ ♣r♦r rsts ♦ t ①♣♦sr ♦ ts ♠trs♥ t rt♦♥ ♦ t rt♦r r s♦♥ ♥ ♦ r♥tsts ♦ ♠trs ♥ ①♣♦s ♥ t② r ♣♦tt ② ♥ ♠♣t②♠rrs ♥ t r

t♦t ♠♦r rt rt♦♥ ♦ ts ♠trs s t♦ ♣r♦r♠ ts rstrrt♦♥ tst ♦ t♦ ♥r♥ t ♦♦♥ ♣♦♥ts tt s♦ t♥ ♥t♦ ♦♥t♥ t tr ♣r♣rt♦♥ ♦ ♥ srs ♦ tr♠♥tr♦♥ s♥st ♠trs

♦♥s♦♥

• s♥stt② ss t t ♦r♦♥ ♦♣♥ ♦r t ♠trs ♣r♣r t t s♠ ♣r♦r s s s♦♥ ♥ r t ♠trs ♥ r♦s ♠rrs ♥ t ♦tt ♥s s♦ ♥ ♥rs♥ s♥stt②s t ♦♣♥ ♥rss r♦♠ t♦

• ♥ r ♦r♦♥ ♦♣♥ ♥ t♦ t ♣♣r♥ ♦ s♥ strt♦♥ tt s♠ s♦♥ ♦ t ♣r ♠trs s ♦sr ♥

• ♣r♦ss♥ ♦♥t♦♥s ♥ t t s♥stt② s s♦♥ r♦♠ t ♦♣ tt tr ♥ s♠tt t♦ s♣♣♠♥tr② tr♠ ② rsts♠♦r s♥st t♥ t ♠tr ♦♣ t ♦ ♦r♦♥ ♦♥♥trt♦♥

• ♠♣t ♦ t s♥ ♠sr t t② ♦♣ s♠♣s t♦ s ♦r t♥ t ♦♥ ♠sr t t ♣r ♠tr t♦rtr tsts r ♥ t♦ ♥rst♥ t ♦r♥ ♦ ts ♣♥♦♠♥♦♥ t ts♠♦♠♥t t s ♥♦t ♣♦ss t♦ ① ♣♦ss ♥♥ ♦ t ♦r♦♥ ♦♣♥ ♦♥t s ♥ ♦r

♦♥s♦♥

♥ ts ♣tr ♥ t♦♥ ♦ t ♠tr rs♣♦♥s t♦ r♦♥ ♥r♦♥♠♥tss ♥ rr ♦t s s tsts ♦ r♥t t②♣s ♦ s ♥trt s♥s♦rss♠s

rs♣♦♥s ♦ t ♣r ♠tr s ♥ st ♥ t s s ts♥tr♦♥ s♥stt② ♥ ♦ t ♠tr s ♥ ♠sr t r♥t t♠♣rtrs ♥ t s ♥ ♦♥ t♦ ♣♦ss ♠t♥ t♦r ♥ t ♦♣rt♦♥ ♦ ♥♥trt s♥s♦r ♥ ts r t♠♣rtrs ♥ ① ts ♦♥ t ♣♦sst② t♦ ♥♥ t ♥tr♦♥ s♥stt② ♦ t ♠trs ♥ rr ♦t♣② ♣r♣r s♠♣s ♠① t ♣♦②t②♥ ♦r ♦♣ t ♦r♦♥ r♠♥tr ♦r t ♠sr♠♥t ♦ st ♥ tr♠ ♥tr♦♥s rs♣t② t♦t s ♣♦ss t♦ ♠sr ♥ sr♠♥t t ♦♦ r② t♥ ♦t t♦ ♦♠♣t r♥t ♥tr♦♥ s♣tr ts ♥ ♠trs r st ♥ t ♦♣♠♥t♣s ♥ t r♣r♦t② t♥ t r♥t s♥s♦r ts s st t♦ ♠♣r♦♥ ♣rtr t rs♣♦♥s ♦ t ♦r♦♥♦♣ s r② ♣♥♥t ♦♥ t s♠♣s♠♥tr♥ ♠sr♠♥ts ♣rs♥t r s♣♣② sr rsts tt r ♥ ♥t♦♥s ♦r t ♣r♣rt♦♥ ♦ ♥ ♥rt♦♥ ♦ ♦r♦♥♦♣ s♠♣s

rtr③t♦♥ ♦ ♥trt s♥s♦rs s ♦♥ ♠tr ♥ r♦♥ ♥r♦♥♠♥ts s s♦ sss ♥ ts ♣tr ♥trt s♥s♦r ♦♥sr rs s ♦♥ s♥ ♣♦t♦♦ ①♣♦s t♦tr t ts r♦t tr♦♥s t♦ t rt♦♥ t♦ ♠sr s ss♠② ♣r♦ r② t♦ ♦rsss② ♥ s♣ ♣♣t♦♥s s s♥s♦r s♠ s ♥stt t tt ♠ t♦ ♥ t ♥ ② ♥trt s②st♠s t♦tr t t s ♥ ♣♥♦ t s st ♥ ts tss ♦r ❯♥♦rt♥t② t r♦♥♥r♦♥♠♥t rsts t♦ r② t ♥ ♠♥ t ♦♠♠r tr♦♥s rqr♦r t r♦t r ♠♣r♦♠♥ts ♥ r③ ♦♥ t tr♦♥ s♥

♦s♠tr② ♦r t ①♣r♠♥ts

♥ ♥ t ♦♠♣♦♥♥t st♦♥ ♦r t s ♥♦t ♣♦ss t s r♦ts♠ ♥ t♥ ♥t♦ ♦♥t ♠♥s♦♥s t ♥ ♣♦r ♦♥s♠♣t♦♥ ♦♥str♥tst♦ ② ①♣♦t t s♥stt② ♣r♦♣rts ♦ t ♠♣♦② ♠tr

② s♥ ♥♦tr s♥s♦r ♣♣r♦ t rt♦♥ r♥ss sss ♥ ② ♠♦♥ t r♦t tr♦♥ ♦t r♦♠ t rt♦♥ ♥r♦♥♠♥t ♥r ♠srs s ♥ r③ ② ♠♥s ♦ rt♦♥ r♥ ♦♣t rs tt r s t♦♦t t t s♥s r♦♠ s♠ r②st s r♦t s♠ ♦♣♥s t ♣♦sst② t♦ t t③t♦♥ ♦ ♦♣ ♦ ♦♠♠r srP s ♦r t r♦t ♥② ♥ t ♦♣t st♠t♦♥ ♥ ♥ t t ♦t♦♥ st♦ t rst ♣r♦t♦t②♣ tst t s♥stt② t♦ ♦♥③♥ ♦ss ♦♥ t♦ t ♠②r♥ s s♥s♦r ♣♣r♦ ♠ tr♦r ♣r♦♠s♥ ♣♦sst② ♦r t rt♦♥♠♦♥t♦r♥ t t ①♣r♠♥ts

♣tr

♦s♠trs ♦ ♦srt rs♣♦♥s ♥

♠①r♦♥ ♥r♦♥♠♥t

t♦ s ♥ ♥ t t♦ ♣♥ ♦ P❲ ♥P s♠♦♥t♦r ♦s♠trs st ♦r t ①♣r♠♥ts s ♣tr ♥ ♣tr ♠♣♦② t t ①♣r♠♥ts ♦ t rt♦r♥ r♥t ♦♥t♦♥s t rs♣t t♦ t ♦♥s ♥♦♥tr r♥ t rtr③t♦♥♣s

rt♦♥ rs ♣rs♥t ♥ t ♣r♥t ♣trs ♥ ♣r♦ ♥rt rt♦♥ tsts rr ♦t r♥ ②s tt r♥ t s♥s♦rs t♦t ♥ ①♣♦sr ♥ r② s♦rt t♠ t rs♣t t r ♦♣rt♦♥ sr ♥ Φeq ♥trt ♦r ②rs t♠ r♥ rt♦♥ r♥s t♣rt t②♣ ♥ ♥r② t rt♦♥ ♥t♥st② s s t ♥r♦♥♠♥t ♦♥t♦♥r ♣t ♦♥st♥t② ♥r ♦♥tr♦ ♥ t ♦tr ♥ ♦♥ ts s♠♦♥t♦r s♥s♦rs ♥st ♥ tr rr② ♣♦st♦♥s t t ①♣r♠♥ts t② ①♣♦st♦ ♥♥ ♦♣rt♦♥ ♦♥t♦♥s ♥♥

• ♣rt r♥s ♦ r ♥t♥st② t ♠♦♥t② st♦♥ ♣r♦s s

• rt♦♥ ♦♠♣♦st♦♥s r②♥ t t st♥ ♥ t ♥ t rs♣t t♦t ♥trt♦♥ ♣♦♥t

• r♥t ♦♣rt♥ t♠♣rtr ♥ r♥t ♠sr♠♥t sts

♥ ts ♦♥t♦♥s t s♥s♦r stt② ♥ rt② sss ♦♠ ♥♠♥t t♦♣r♦ ♣rs rt♦♥ ♠sr♠♥ts ♦r t♠

♥ ♦♠♣r♥s s♠t♦♥ ♦♥ t ②rs ♦ s r② ♥♦t ♣♦ss t♦ ♦ ts ♣tr s t♦ t t ♣r♦r♠♥s ♦ t ♦ ♦r s♠♦♥t♦r s♥s♦rs ② ♣♥ t♠ ♥ ♦ ♦srt ♠①♣rt rt♦r ♥r♦♥♠♥ttt s ♦s t♦ t ♦♥ ①♣t ♥s ♦r♥ ♣rt tt♦rs

♦ ♦ ts t s♥s♦rs r ①♣♦s ♦r tr ♠♦♥ts ♥ t s♦♥r② ♥r♦♥♠♥t♦ t t② tt ♣r♦s ♠① ♥r② ♣rts t ♦ rts② ♦r♥ ♦①s ♥ t ❱ ♣r♦t♦♥ ♠♥ rt t♦ t stts②st♠ s sr ♥ P♥ t s♥s♦rs t r♥t st♥s r♦♠ t♠ ①s r♦s rts ♦ ♥r② ♣♦t♦♥s ♥tr♦♥s ♥ r ♣rts ♥ t

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

r ②♦t ♦ t ♥ ts t t P rt♦r

❱ ♥r② r♥ r tr♦r s♠t♥♦s② ♦r♦r ♥s ♦ ♠♦♥t♦♥s ♥ t tr♥t♦♥ ♦ ♦♣rt♦♥ ♥ st♦♥ ♣r♦s ♠ ts t② ♥ tst♥ t♦ t t s stt② ♦r t♠

rsts ♦ ts ♦♥tr♠ rrt♦♥ ♠♣♥ r ♣rs♥t ♥ t ♦♦♥st♦♥s ♥ r sss ♥ ♦♠♣r t ♠sr♠♥ts ② ♦tr ♦s♠tr ♠♥ss s ♦♥t r♦ s♠t♦♥s

①♣r♠♥t st♣ ♦r t tst

rrt♦♥ ♦♥t♦♥s

♥ t ♠♥ ♦ t st ①♣r♠♥t r ♦ t P ♦♠♣①♣r♠r② ❱ ♣r♦t♦♥ rsts ♦ ①11 ♣rts r r t♦rs ♠rs♦rr ♣ ♥ r♦♥t ♦ st r♦♥ ♠♠♣ s s♦♥ ♥ ♥ tt ♦t♦♥r t t② s ♦t s ①♣♥ ♥ t ♣r♦t♦♥s ♣r♦ ♥♦r♠ rrt♦♥ s♣♦t ♦r sr ♦ ♦t ① ♠2 ❬❪ ②♣② r♦♠ t♦ ♣r♦t♦♥ rsts ♣r ♠♥ ② ♦ s r ①trt r♦♠ t P rt♦r ♥ r t♦r s rrt♦♥ ②♦t rrr s Pr♠r② ♠ ♦♥t♦♥s♥ t ♦♦♥ r♥ t ♦♣rt♦♥ ♦ t ❱ ♣r♦t♦♥ ♥trt♦♥s ♣r♦ ♥ t srr♦♥♥ r rt♦♥ ♠♥② ♦♠♣♦s ② ♥tr♦♥s ♣♦t♦♥s♣♦♥s ♥ ♣r♦t♦♥s s st♣ s ♥ sr rr ♥ ts ♦r s t t② s rtr ts ♥

♦♥ ♦♥str♠ ♦♥ t ♠♥ ♥♦tr tst♠ t② s♦♥r② ♥ r♥ ♥ ♦rr t♦ ♣r♦ t srs t ♥♦♥s♣rt ♦r♥r②

①♣r♠♥t st♣ ♦r t tst

r r r P ♦

❩ ♠ r ♠

♦t♦♥ ♦ tst s ♥

s♦♥r② ♣rt ♠ ♦♠♣♦s ② ♣+ π± ♥ ± ❬♠❪ s s♦♥r② ♠s ♣r♦ ② ♥srt♥ t trt ♥ t ❱ ♣r♦t♦♥ ♠ ♥ ♠♦②♥ t♠♥t ♦ t ❩ ♠♥t s ♥ ts ♦♥t♦♥s ♣rts r♦♠t trt t st ♠♦♠♥t♠ r ♥t ♦r t ♠♣♣ ♦t ♥ trt♥ s t rs♣t t ♣♦st♦♥ ❲ t s♦♥r② ♠ s tsr t♦ t srs ♦ s♦♥r② t t② ♥ ♦♥sq♥t② t ♥r♦♥♠♥t s r ② r ♣r♠r② ♣r♦t♦♥ ♠ s rrt♦♥st♣ rrr s ♦♥r② ♠ ♦♥t♦♥s ♥ t ♦♦♥

♥str♠♥tt♦♥ ♥ t r ♦♥sst ♦ ♦♥r② ♠ss♦♥ ♠r ♥ tt ♣r♦s ♠sr♠♥t ♦ t ♥t♥st② ♦rt ♣r♠r② ♣r♦t♦♥s r t♦ ❬r❪ ♥ ♦♥③t♦♥ ♠r P ♥ s s♦ ♥st ♦♥ t ♥ ♦ t rrt♦♥ r ♦r ♠sr♥ t ♦srt t♦ ♥ tt② r♥ ♠♥t♥♥ ♦♣rt♦♥s

t♣ ♦ t s ♥r tst

♦r ts rrt♦♥ tst t ♥ ♦s♠trs r ♥♣st♥ s ♠t ♣s ♥ t r♦r s♥s r ♦♥rt t♦ ♦s ②♦♦♥ t ♣♦r♦ rt♦♥ r ♦ q rr s s♥t t♦ ♣tr ♦rt ts ♦t t rr♥ts tt t♦ ♣♣ ♦r t s r♦t s st ①♣r♠♥t rt♦♥ ♣r♠trs ♦r t t♦ s ♥r sts

s s♦♥ ♥ ♣tr ♥♥♥ ♣♥♦♠♥ tt t t s st ♦rt ①♣r♠♥ts ♦ t r ♦ t ♦rr ♦ ♣r♥t ♦r ②rs t♠s ♦rts rs♦♥ t t ♣rs♥t ♥ ts ♣tr r ♥♦t ♦rrt ♦r s ♥ t

♦ ♠sr t Φeq t t♦ st ♣♥ ♦s r♦♠ P ♥ t P❲r ♥st s ♦r ♦t s t r♦r ♦s♠tr ♣r♠tr s t st♦ t ♦rr ♦t ❱F tt ♥rss ♥r② t t Φeq ♦♦♥ q ♥q ♥r ♠ ♦rr rr♥t s P❲ r ①♣♦s t♦ t rt♦♥ t♦t ♥ ♣rrrt

♦t s ♥ ♣♥ ♦s r ①♣♦s ♥ ③r♦ s ♠♦ ♥ t ♦s♠tr♣r♠trs ♦ts r r♦t ② ♦r♥ r♥t ♣s rr♥ts tr♦ t♠ ②s♥ t s②st♠ sr ♥ s②st♠ s st t♦ ♣r♦②r♥ t s♥s♦rs r♦t sq♥ ♥② ♦r ♦♥rt♥ t ♦ts t♦ ♦s♠trq♥tts t r♦r s♥s r♦♠ t s♥s♦rs r ♦rrt ♥st t♠♣rtrrt♦♥s s♥ t st ♦ c r♣♦rt ♥ ♣tr ♥ ♣tr

♥ ♣♥ ♦ s♥s♦rs r ♣ t ♠sr♠♥t ♣♦♥ts ♥ t r ♥ t st r♦♥ ♠♠♣ s ♥t ♥ tst ♠sr♠♥t ♣♦st♦♥s s s tr ♥ s ♥ t sss♦♥ ♦ t rsts ♦♦r♥t ❩ s t st♥ r♦♠ t ♠♠♣ t ♦♥ t ♠♥

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

r ♥t♥st② ♦ t ❱ ♣r♦t♦♥ ♠ r t♦ ♦r t rrt♦♥ tst

r s t r st♥ r♦♠ t ♠①sr ♠sr♠♥t ♣♦st♦♥s r ♦s♥ t r♥t r ♦s t♦ t ♠r

s♦rr r r ♥ r t ♦tr t♦ r ♥ ♣r♦①♠t② ♦ t♠♥ ♠♥t ♥♠ ♥ t P ♦♥③t♦♥ ♠rP ♦ r♣rs♥t s ♦t ♥

s♥s♦r s t♥ ♦♥♥t t♦ t r♦t s②st♠ ♠ ♦① s ♥ ♦t P ♥ P❲ ♣♥ ♦s r ♥st ♥ tr rr② ♣♦st♦♥s r♦♠ t ♥♥♥ ♦ t rrt♦♥ tst s r ♥st t♦t st♣ r♥ ♥ rt♦r st♦♥ ♣r♦ ♦rs tr t ♥♥♥ ♦ t①♣r♠♥ts

sts ♥ sss♦♥ ♦ t ♠sr♠♥ts

rrt♦♥ ♣r♦ st ♦t tr ♠♦♥ts ♦rs ♥t♥st② ♦ t♣r♠r② ❱ ♣r♦t♦♥ ♠ r t♦ t rrt♦♥ r ♥ ts ♣r♦ ♥ tr♠s♦ ♦♥ts r♦♠ t s s♦♥ ♥ r♥ t tsts t ♠ ♦♥t♦♥s ♥t r r st sr t♠s r♦♠ Pr♠r② t♦ ♦♥r② ♠ ♥ ♦r♥ t♦ ♣r♥ s r♦r t♦ s♠♣② t sss♦♥ ♦ t rstst ♥ r♦♣ ♥ t♦ s♣rt r♥s

• rst rrt♦♥ ♥ r♦♠ t♦ ♦rs tr ♦t ♦rs ♥ t P♠ s ♥♦r♠② ①trt ♥ rt t♦ t rrt♦♥ r ♦ ♥t♥st②Pr♠r② ♠ sr ♠♥ r ♦rr ♥ t ♠♥ sst ♦♥ ♦r ♦t ♦rs ♠ ♥ tr ♦t ♦rs r♦♠t r♦r② ♦ t ♠ ♦rs ♥ t ♠♥ s st♣♦r t r② ♦ t ♦♥r② ♠

sts ♥ sss♦♥ ♦ t ♠sr♠♥ts

t♦♥ ♦s

q♥t ♥

r t♦♥ ♠sr♠♥ts r♥ t rst rrt♦♥ r♥

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

• ♦♥ rrt♦♥ ♥ r♦♠ t♦ ♦rs st♣ ♦r t ♦♥r②♠ s ♠♥t♥ ♦r t rst ♦rs ♦r ♥♥ t♦ t Pr♠r②♠ ♦♥t♦♥s ♥t t ♥ ♦ t ①♣r♠♥t r♥ ♥ ts st ♣rt strt♥r♦♠ ♦rs t ♣r♦t♦♥ ♥t♥st② s ♦t t t ♣r♦s ♦♥ ♥t♥st② Pr♠r② ♠

r t♠♣rtr r♦r ♥ t tst r s ♦ ± s s♦♥♥ t s♦♥r② ②①s ♦

rst rrt♦♥ ♥

sr♠♥ts

s♦s ♠sr♠♥ts r♦r r♥ t rst rrt♦♥ r♥ ♥ t ♦ss ♠sr t t s ♥ ♣♦tt t r♥t ♥s ♦rt r♦s ♦t♦♥s ♦s r♦r t t t P ♦t♦♥ s♦♠♣r t t ♦♥ rt② ♠sr t t P ♦♥③t♦♥ ♠r rr♠rrs ♥ r♠♥t ♦ t t♦ ♠sr♠♥ts s r② ♦♦ ♦rs♦r ♦ss < ②

t s t♦ ♥♦t tt ♥ t ♦♣rt♦♥ t ♣r♦t♦♥s s ss♣♥ r♥t ♣r♦ r♦♠ t♦ ♦rs t s♥s♦rs r ①♣♦s t t P ♦t♦♥ t♦ r♠♥♥t ♦srt ♦ ♦t ♠② t♦ sttr ♣rts r♦♠ t ♥♦r♥s♦♥r② ♠♥s r♥♥♥ ♥ t P st r♥ ts ♣r♦ t s♥ ♦ t s ♦♥t♥ t♦ ♥rs ♥ t ts r② ♦ ♦srt ♠♦♥strt♥ t s♥stt② ♦ s s ♥ t ♦♣rt♦♥ t ♣r♦t♦♥s rstrt t ♦srt ♥ t r ♥rs t♦ tt strts t P r♦t tr♦♥s > ♠② ♠♥ rtr s ♦ ts s♥ s rr♥ ♦r t s ♥r tst♠♣♦ss ❬❱♥❪

♥ t Φeq r♦r ② t P s ♥ ♣♦tt t ♦♣♥♠rrs ♦ r② t ♥rt② ♥ t rs♣♦♥s ♦ ts s t ①♣r♠♥t tr ♥r② tt ② s♥ t ♣r♦t♦♥ ♠ ♥t♥st② ♦ t srs ♦♦♥rs♦♥ t♦rs ♠i ♦♥ts 7→ Φeq ♦r ♥② ♥ ♠sr♠♥t ♦t♦♥s rsts ♦ ts t♦♥s r ♣♦tt t r♥t ♥s ♥ ♦r Ps t ♠sr♠♥ts t t t ♦r t ♥tr r♥ ♥ Φeq s ♦r t♥t s♥s♦rs ②♥♠ r♥ < ①12 ♠−2 ♥ ♦r t ♦t♦♥ ♥ t♣rt ① s t ss ♥t♥s ♣♦tt t ♠♦♥ ♠rrs ts♥s♦r s ♥r② t t t♦♥ ♣r♦♥ tt ♥♥♥ ♣♥♦♠♥ tt♦ t s s r ♦r t♥ t ♠sr♠♥t rr♦r

♦r t ♠sr♠♥t ♣♦st♦♥ r ♦♥ ♥ t ① ♦ ♣rts t st r♦r t s♥ ♦ t P❲ ♦ s ♥ ♣♦tt t rr ♠rrs s s♥ s ♥ ♥♦r♠③ t♦ t st ♠sr♠♥t ♣♦♥t ♦t P t Φeq ①12 ♠−2 P❲ s♥ s ♥ r♠♥t t tt♦♥ ♦tt ♥ t♥ t rt♦♥ rr♦r % r② ♦r ts rt ♣rt ♥t♥st② t r t r ♦rrt ♥st ♦t s♦rt ♥ ♦♥tr♠♥♥♥ ♣♥♦♠♥ ♦r ♦♥rt♥ t ♦rr ♦t st t♦ Φeq ∆❱F s♥ ♦rrt ♦r t ♦♥tr♠ ♥♥♥ ② s♥ t ♣r♠tr③t♦♥ sr ♥

sts ♥ sss♦♥ ♦ t ♠sr♠♥ts

r ♦♥t r♦ s♠t♦♥s ♦r ♦♣rt t Pr♠r② ♠ ♥ ♦♠♣rs♦♥ t P ♠sr♠♥ts

♣♣ ♦rrt♦♥s ♦♥t s♦ ♦r t t♠♣rtr rt♦♥s ♦r t①♣r♠♥t ♣r♦ s♣② ♥

♦♠♣rs♦♥ t ♦♥t r♦ ♠t♦♥s

♦ t t s♦t Φeq ♣rs♥t ♥ t P rsts ♥♦♠♣r t t♦ sts ♦ ♦♥t r♦ s♠t♦♥s ♣r♦r♠ ♦r ❬r❪ t♦ s♠t♦♥s ♠ ♥ ♠ r ♥ t ♥♠r ♦♥rt ♣r♠r② ♥ts ①4 ♥ ①5 ♣r♠r② ❱ ♣r♦t♦♥s rs♣t② ♥st② ♥ t ②♦t ♥ ♠trs s t♦ ♠♦ t r ♦r♦r t♠ s ♥ r♥ ♦r r♥t ♣rs ♦ ♦♦r♥ts r ♥ ❩ t ♠ ♣rts♦♥② t rt♦♥ ♦ t rt♦♥ ♦♥ t rs r♦♠ t ♠ ①s t ①❩ ♦ ♠

♦ ♦♠♣r ♣rt ♥ ♠sr♠♥ts ♥ s♠t♦♥s t st ♦ s ♣r♠trs♠i ♣r♦s② t ♥ t♦♥ ❱eq ♣rt♠2 × ♦♥ts r ♥♦r♠③ t♦ t ♥t♥st② ♦ s♥ ♣r♠r② ♣r♦t♦♥ rst ❱eq ♣rt♠2 × s♣♥♦♥ t r♥ss t♦r ♦r t r t s t♥ ♣♦ss q t♦①♣rss t ①♣r♠♥t t ♥ tr♠s ♦ ♣rt♠2 × s♣ ♥ ♣r♦ t t♦♠♣rs♦♥

♦ s♦ t ♣rt s♣tr ♣rt t t ♠ ♦rt ♠sr♠♥t ♣♦st♦♥ r ♥ ts ♦t♦♥ t ♥tr♦♥ ♦♠♣♦♥♥t ♣♣rsr② t♦ ♦♠♥t t rs♣t t♦ t r ♣rts tt r♣rs♥t ♦♥② ♣r♥t ♦ t t♦t ♥♠r ♦ ♣rts r♥ss t♦r s t t♦ ± % ♦♥ t ♥tr♦♥ s♣tr ♦ t ♥♦♥ ♥tr♦♥

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

r♠ t♦rs ❬❪ rr♦r t ♦r ts ♥t♦ ♦♥t t ♦♥trt♦♥ ♦t r ♣rts t♦ ♥ t ♥r② rt♦♥ ♥ t s♠t ♥tr♦♥ s♣tr♠♦♥ ♥ ♦r♠ ♠ t♦ ♠ ♥ rs r♦♠ t ♠ ①s

s♦s t ♦♠♣rs♦♥ t♥ t ♠sr♠♥ts rr ♦t s♥ t♦s ♦♣♥ ♠rrs t t t♦ s♠t♦♥s ♠rrs rr♦r ss♦tt♦ t ♠sr♠♥t ± % ts ♥t♦ ♦♥t t ♥rt♥ts ♥ t P ♦srt♦♥ s s s t ♦♥ ♥ t t♦♥ ♦ t t♦r t♦ t ♠ tr♥ ♠rrs ♥ r ♦♥② ♦r ❩ t♠ s ♥ r♥ ♦r r♥t ❩ s r♦♥ ♠rrs t ♣♦st♦♥s ♦sst t♦ t♠ ①s t ♦♥t r♦ s♠t♦♥s ♦rst♠t t ①♣r♠♥t ♠sr♠♥tss ♥♥ s ♥ r♠♥t t ❬❪ r s♠r rsts r ♦♥ ② ♠♥s♦ ①♣r♠♥t ♠sr♠♥ts s♥ tt♦♥ ♦s ❬❪ ♠ r s♦♥t♦ ♦rst♠ts t rs♣t t♦ t ①♣r♠♥t ♠sr♠♥t ♣ t♦ ♠♦r t♥ % ♦r t ♦sst ♣♦st♦♥ t♦ ♠①s r t r ♣rt r♥t ♠② ♥♥t rr♦rs ♦r ♦t ♠sr♠♥ts ♥ s♠t♦♥s ♠ s♦ ♥st ♥r♠♥t ttr t♥ % t t ①♣r♠♥ts s t♦ rsts ♦♥r♠ ts tt② ♦ P ♦ ♠sr♠♥ts

♦♥ rrt♦♥ ♥

s♦s ♠sr♠♥ts r♦r r♥ t s♦♥ rrt♦♥ r♥ ♥ t rsts r♦♠ s ♥ ♦♠♣r t t ♠sr♠♥ts rr ♦t t P♦②♠r♥♥ ♦s♠trs P ❬♦♥❪ ♥ t r tP ♠sr♠♥ts r t ♠rrs t ♦rs t ♥s r t s♥♦ t ♦s r♦♠ Ps s♥ t ♣r♦t♦♥ ♥t♥st② ♣♦tt ♥ s ♠sr r♦♠ s r ♦r ♣♦st♦♥s t P ♠sr♠♥ts t♥ ♥①♣r♠♥t rr♦r ♦ ± % ♦ ♦ P ♦s♠trs t♦ t t ♠sr♠♥t r♦♠ s ♦♠ r t ♦♥trt♦♥ t♦ t ♦ ♣♦t♦♥s γ♥tr♦♥s ♥ ♥ r r♦♥s ♥ t ♠① rt♦♥ r ♦♥srs♣rt② s s♦♥ ♥ q ♥ q ♥ t ♦r♠s Kj

i r t r♠t♦rs ❬ ❪ r γ ♥ ♦r ♥ P ♦r P ♦r ♦r s Φ r ♥st t r♥t ♣rt ♥s t ♥♠r t♦rs t♥t♦ ♦♥t t rt s♥stt② ♦r ♥tr♦♥s ♦ t t♦ ♦s♠trs t rs♣t t♦t ♠♠ r②s

DPAD = KPγ × Φγ + (0.2) × KP

n × Φn + KPCh.H × ΦCh.H

DREM = KRγ × Φγ + (0.6) × KR

n × Φn + KRCh.H × ΦCh.H

r♦♠ t Kji t♦rs ♦ t s s② t♦ r② tt ♥ t ♥r② r♥ r♦♠

❱ t♦ sr ❱ ♥ r♦♠ t s tt ΦCh.H ∼ ×Φn ∼ ×Φγt r ♣rt ♦♠♣♦♥♥t rs t♦ ♦t P ♥ ♦t t♦ ♦rr♦ ♠♥t r t♥ t ♦♥ ♣♦s ② ♥tr♦♥s ♥ ♣♦t♦♥s ♥ s ♦♥t♦♥sP ♦s♠trs r ①♣t t♦ ♦♦ ♥♠r ♦r t ♦s♠trs

❲t r♥t ♠rrs s♦s t Φeq ♠sr♠♥ts r♦r ②t P❲ ♦s s♥ ♦ t ♣r♠r② ♠ ♥t♥st② ♦r ♥② ♠sr♠♥t

sts ♥ sss♦♥ ♦ t ♠sr♠♥ts

t♦♥ ♦s

q♥t ♥

r t♦♥ ♠sr♠♥ts r♥ t s♦♥ rrt♦♥ r♥

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

♦s♠tr t♦rs ♣②×♠2γ ♥

P → → ∼ 4 → Ps → → ∼ 4 → Ps

t♦r r♥s r♦♠ ❬ ❪ ♦r t rt♦♥ t②♣s ♥ ♥rs♦ t t② t P

♦t♦♥ s t ♥ t♦♥ s ♥ ♥ ♣♦tt t ♥s ♦r ♦♠♣rs♦♥t t ①♣r♠♥t t s ♣r♦s② ♣♦♥t ♦t t t ♦♣♣♦rt♥ ♥♥♥♦rrt♦♥ t s♥ ♦ s s ♠t ♥ ss t ♣rt Φeq t♥ t♥rt♥t② ♦ ♦t ± % tt ts t rt♦♥ t

sss♦♥ ♦ t rt♦ rs♣♦♥s rs♣♦♥s

♥ t s♦♥ rrt♦♥ r♥ t rs♣♦♥ss r♦♠ t s r② ①♣♦st♦ ①♥ s♦♠ t♥s ♦ ② r♥ t rst r♥ r ♦ ♥trst ♦r ♦ss①♥ ② tr rs♣♦♥s r ♦♠s str♦♥② s♥r ♥s t♦ strt t♦ t rs♣♦♥ss ♦ s ♥r ③r♦ s r ②s str♦♥②s♥r ❬♦ ❪ t s t t s♠ t♦t ♦s r ♥♦t strt♥ ♥ ts ② strt♦♥ ♠♥s♠ s ♥♦t ♥♦♥ t t s r tt rtrtr♦♥ s♣ ♠t rtr ② t♥ ♦① s t♦ ♦①tr♣♣ ♣♦str ❬ P❪ t ♦ ② t strt♦♥ ♦ s s ♥r②♦♠♣t s ♥ ♥st ♣r♦♥ t♦ s♠♦♦t② rs♥ rt♦♥rs♣♦♥s rs ♦r r♥ ♦ sr t♥s ♦ ② ♥r ①♣♦sr t♦ ♠♥② r♥tt②♣s ♦ rt♦♥ ❬❪

♥ s♦ t rt♦ t s♥stt② ♦ t s trs♣t t ♦♥s r♥ t s♦♥ rrt♦♥ r♥ Pr♠r② ♠ rstrs rt♦ ♦ t ♦♥r② ♠ rstrs t♦r ♦ ♥ ❱ ♣r♦t♦♥ ①♣r♠♥tst ♠② ♦ ♣rt ♥t t♦ ♠♦♥t♦r t rt♦ s ①♣♥ tr

s t t strt♦♥ ts ♥ ③r♦s ss t ①t ♠♥s♠ ♦ t rt♥ ♥ rt♦ s ♥♦t r ①♣♥t♦♥ s ② t♦ rs r♦♠ t ♣♥trt♦♥ ♦ s♦♥r② sttr ♣r♦t♦♥s ♥ ♦tr r ♣rts ♥ t s♦♥ ss s s t ♦♥r② ♠ s ♥ sttr r♦♠ t trt ♣ ♥t ♣r♠r② ♠

♥♠r ♦ s♦♥rs ♥ t r s ♥♦♥ t♦ s t t ♥♠r ♦♣rts rt t♦ t ♠♠♣ ♥ ts r ② ♦♥t ② t ♦r♠♥② s♣ts ♦ ♠ ♦s♥ r tr s♦ tt t ♠s♣♦t ♦♠tr② ♥s♥② ♥ ♣♦ssts ♦ ♥rt♥ ♥tr♦♥s ♥ ♣♦t♦♥s t t ♠sr♠♥t ♦t♦♥s♥ r rt ♥ t♦♥ t ♣r♦t♦♥ ♥rs r t♦ st tr♦♥ r ♣r♦s ♦rrs ❬P r♦❪ s♦r sr ♣♥♥ ♦ t rs♣♦♥s ♦♥ ♣rt ❬❪

rtr ♦r s ♥ t♦ tr t rt♦ ♥s ♠♦r t♦ r♣r♦t♦♥ ♦ ts s♦t♥♥ ♦ t ♣r♦t♦♥ ♠ ♦r t♦ t t♦♥ ♦♣♦t♦♥s ♥ ♥tr♦♥s t♦ t ♠ ♥ tr s ❬♦❪ ♦

♦♥s♦♥

r ♥stt② rt♦ ♦r s ♥ r♥ t s♦♥ rrt♦♥r♥ P♦t rt t♦ t ♦♣ ♦ s♥s♦rs ♥st t r

sr s t♦♥ ♦ t ♠s ♥♥ ssts s♥ ts s t t t♦ ♠♦♥t♦r t

s♥ rt♦ t♦ ♥♦r ♠♣♦rt♥t rt♦♥s ♥ t ♦♠♣♦st♦♥ ♦ t ♠ rtr♠♦r r♥ ♣rt ①♣r♠♥ts ♠♦♥t♦r♥ t ♠② t♦ sr♥♥s ♦ ♣rt ♠ ♦ss ♦r ♠ t♥♥ ♦♥t♦♥s

♦♥s♦♥

♦r s♠♦♥t♦r s♥s♦rs tst ♥ r t ss ♦ t rtr③t♦♥ sts rr ♦t ♥ ♣tr ♥ ♣tr ♦ ts tss ♦r s s♥s♦rs ♥ r♦♠♠♥ ♦r t rt♦♥ ♠♦♥t♦r♥ tr♦♦t t ②rs ♦ ①♣r♠♥ts s s♥s♦rs ♦ ♣ t♥ t tt♦rs srr♦♥♥ t ♦r♥trt♦♥ ♣♦♥ts t t st ♦ ♦r s r s ♠♥tr ② ♥ ♥ ♣♥ ♦s r♦♠ P ♥

rt ♥ t ♣rt ♠① sr ♦r t rrt♦♥ tst t t t② ♥trt ♦ss ♦ sr ♥r ② ♥ ♣rt ♥s ①♥13 cm−2 ♦r ♦rs s rrt♦♥ s t♦tr t s♦♠ rt♦♥s ♦t ♣rt ♠ ♥ t♠ ♥ ♥ ts t♥♥ r r② t s s♠t♦♥ ♦ t ♦r♥ ♦♥t♦♥s ♦ ♠♥t♦♥ rt♦♥ ♠♦♥t♦r♥ s ♦rsss② ♥ t s♠t ♠①♣rt ♥r♦♥♠♥t

r② ♥ t ♠sr♠♥t ♦ ♦s ♥ Φeq s t♥ t

♦s♠trs ♦ ♦srt rs♣♦♥s ♥ ♠①r♦♥ ♥r♦♥♠♥t

①♣r♠♥t rt♦♥ rr♦rs % t♦ % ♦r ♥ P sPr♦s rt♦♥s ♦ ts s r tsts ♥ rt② rt rrt♦♥♥r♦♥♠♥ts r ♥♥♥ ♣♥♦♠♥ ♥♦t ♥ ①♣t② ♦♥sr ♥ ts ♦ t P❲ ♦s t ♠sr♠♥t ♥ ♦♥ t♦ ♥ r♠♥t t♥ % ♦♥② ♦♣♣♦rt♥ ♥♥♥ ♦rrt♦♥s r s

♥② ♥ ts ♣tr ♥ ♦♥♣t ♦ s♥ t♦ s♥s♦rs t r②r♥t ♦① t♥sss s ♥ s♦r r s♥s t > ② ♥ rt② s s ♦♠♣♠♥tr② ♥♦r♠t♦♥ t♦ tt ♥s ♥ t rt♦♥ ♦♠♣♦st♦♥ s tr s t♦t t♦ ♥t♦♥ ♦ ♥t♥t♦♥ ♦r♥t ♥s ♥ t ♠ ♦♥t♦♥s ♥ ② r♥ ♦r t② t♥♥♦ t ♣r♠r② ♠s

♣tr

♥trt♦♥ ♦ t rt♦♥ ♠♦♥t♦rs

t t

t♦♥ ♠♦♥t♦r♥ t t ①♣r♠♥ts

♥ t ♣r♦s ♣trs t s ♥ ♦♥ ♦t tt t r♥t ♦s♠tr t♥♦♦s ♥stt ♥ ts tss ♦r ♥ ♣r♦ ♦♠♣t ♥ q♥ttt ♠♣ ♦ t①♣t ♦♠♣① rt♦♥ ♥r♦♥♠♥t ♦ t ①♣r♠♥ts ❲ t ♠♣♠♥tt♦♥ ♦ t s ♥ t ♣♥ ♦s s♠♦♥t♦r s♥s♦rs s strt ♦rrt ♥trt♦♥ ♦ t s st ♥s s♦♠ ♦♣♠♥t ♦r♦r t t t stt♦trt t rsts ♣rs♥t ♥ ♣tr sst t♦ ♣s t ♦♣♠♥t ♦ s♥rt♠ s♥s♦r ♣r♦ s ♦♥ r s②st♠ ♥ ♦ rt♦♥ ♠♦♥t♦r♦♠♥s t ♥ts ♦ t ♠tr s♥stt② s♥ ♦ strt♦♥s♠ ♠♥s♦♥s t t t ♣♦sst② t♦ ♣r♦r♠ r♠♦t ♠sr♠♥t t♦tr♥ tr s♥s ♦r ♦♥st♥s ♥ t s ♦ t ①♣r♠♥ts ♦ t ts ♠ ♥ ♠♣♦rt♥t ♦♥str♥t ♥ t rt♦♥ ♠♦♥t♦r♥ s t♦ ♣r♦r♠t♥ ♣rts tt♦rs tt r r② ss♣t t♦ t ♥t♦♥ ♦ ①tr♥ tr♦♥♥♦ss

st ♦ t ♦r r♦♠♠♥ s ♥ ♣♥ ♦s ♦rs t ♥s♦ t ①♣r♠♥ts ♥ tr♠s ♦ s♥stt② ♠②♠❱ ①8 ♠−2♠❱ ♥②♥♠ r♥ > ② ①14 ♠−2 ♦ s♥s♦r st ♥ r ♦t ② rr♥t♥t♦♥ s♦ tt tr r♦t ♦♥sst ♥ s♠♣ ♦♠ ♠sr♠♥t ♦r♦r t♦r t②♣s ♦ s♥s♦rs ♠♥s♦♥s ♥ t r♥ ♦ sqr ♠♠trs ♥ ♥ r ♦t ♦r ♦♥ st♥s ts rs♦♥s st② tr♦r t ♣r♦t♦♥ ♦♥ ♥trt s♥s♦r P t t ♠ t♦ s♠♣② t ♥♥ ♦ t rt♦♥ s♥s♦rst s t② ♥ ♥trt ♥t♦ ♦s♠tr Pr♥t rt ♦r P s t rqr♠♥ts ♦r t rt♦♥ ♠♦♥t♦r♥ ♦ t ①♣r♠♥ts

s♥ ♦ ♥ ♥trt s♥s♦r rrr ♦r ♥ ♠sr♠♥t

♦ ♦ s② ♥♥ ♥ t♦ ♣r♦ st♥r ♦♥♥tt② ♦r ♣r♦♣♦s s♥s♦rs♥ ♥trt P rrr s s♥ ♥ ♣r♦ t s s♦♥ ♥

♥trt♦♥ ♦ t rt♦♥ ♠♦♥t♦rs t t

s rrr s ♠ ♦ t♥ µ♠ ♦s P t ♥ ♦st ♣ t♦ ♣♥♦s ♥ t ♣s r♦♠ t♦ ♥ ♥ t ♠ ♦ t s♥s♦r ♠♦♥t t t t♦♣ s P ♦ t ♦tt♦♠ ♦♥ s P❲♦ s ♥ ♣

P r♦♥ts t ♣♥ ♦s ♥ s ♦♥♦r

P s t ①tr♥ ♥

r ♥trt s♥s♦r rrr ♦r t ①♣r♠♥ts

P rrr ♥ s♦ ♦ t r♦t ♦ ♦tr s ♦st ♥s ♣r♦♣r ♣♥ t t ♠♦♠♥t srs ♦ ♣s ♦♥t♥♥ ♦r s s♥ s♥ ♥ ♣r♦ ♦r t ①♣r♠♥ts s t s ♥ ①♣♥ ♥ ♥ ♦ ts ♥ s♥ ♠♦♥t ♦♥ t s♥s♦r P ♦♥ t rt♥ s♦ t♠♣rtr ♣r♦ s ♥ s s♦ ♣r♦ s ♠♦♥t ♦♥ t ♥trt s♥s♦r P ♥ r ♦t ② t ♦r s♥s♦r s♥s ♥ ♦♠♠♦♥ ♦♥♥t♦♥ s s♦♥ ♥ t t♥ s♦ ♦r ♠♥s♦♥s ♦ t ss♠ P ♥♥ t ♦♥♥t♦r♣ r ♦ ♦t × × ♠♠3

t s ♥ s♦♥ ♥ ①t♥s② sss ♥ tt t strt♦♥ ♥♦♠♣♦st♦♥ ♦ t ♠trs r♦♥ s ♥ str♦♥② ♥trr t ♠sr♠♥ts s♣② ♥ rt♦♥ s ♦♥t♥♥ ♥tr♦♥s ♥♦r ♦ ♥r② ♣♦t♦♥s♦s ♥♥♠♥t ts r ts ♥ ss ♦r♦r t s♣ ♦r t ♥stt♦♥ ♦ s ♥ ♦ s♥s♦rs s ♥♦tr ♠♣♦rt♥t ♦♥str♥t ♥ t s ♦ t ♦r

①♠♣ ♦ rt♦♥ ♠♦♥t♦r♥ s②st♠s t

ts rs♦♥ ♠♥② ♦ t ♣ ♣s s ♦r s ♥ ♦tr ♣♣t♦♥s ♠② ♥st ♦r rt ♣♣t♦♥ t t tr♦r t s♣ r♠ rrr♦r t ♥ s♥s♦rs s s♥ t♦ ts sss ❬♣❪ ♥ t s♠② t t♥ss µ♠ ♥ t ♠tr s ♦r t ♦♥strt♦♥ ♦ t♥trt s♥s♦r P ♥ st t♦ ♠♥♠③ ts ♥trt♦♥ ♥s t rt♦♥♥r♦♥♠♥t ♦r♦r ♥ ♣♦ss t ♠tr t s ♥ r s t ss ♥ t r t ♥♥ssr② P ♠tr s ♥ r♠♦ ♥♦rrs♣♦♥♥ ♦ t rrr ♣♥

s♥s r♦♠ t ♥trt rrr ♥ r♠♦t② r♦t ♣ t♦ r② ♦♥st♥s s♥ r ♦♥♥t♦♥s t t ♥ t ♦♥♥t♦r ♣ ♦r ss ♠rs♦♠ ♠t♦ s t♦ rt② s♦r t t t♦ t P s♥ t♣s ♦t ♥r t ♦♥♥t♦r ♣ s♦♥ ♥ ♦r♦r s ♠♦♥ts♥s♦rs ♣ st♦r t ♦s♠tr ♥♦r♠t♦♥ ♦r t♠ t ♥trt P ♥ s♦s ♥ ♣ss ♠♦ ② ①♣♦s♥ t t♦ rt♦♥s t ♦♥♥t♦♥s r♦♥ ♦rts ttr ♣♣t♦♥ t ♥trt s♥s♦r ♠st r♠♦ r♦♠ t ♠sr♠♥t ♥ ♣ ♦♥ ♦rt♦r② tst♥ t♦ ♣r♦r♠ t r♦t ②

❲ t ♣rs♥t rrr s ♦♣t♠③ ♦r t t ♦ trs ♠s tst③t♦♥ s② ①t♥ t♦ ♥② ♣♣t♦♥ ♥ ♠♦♥t♦r♥ ♦ ♠t ♦s♥ ♣rt ♥ s ♥

①♠♣ ♦ rt♦♥ ♠♦♥t♦r♥ s②st♠s t

♦♥♣t♦♥ ♦ t rt♦♥ ♠♦♥t♦r♥ s♥s♦rs r♦t tr♦♥s ♣t t♦ t♥s ♦ t ①♣r♠♥ts s ♦t ♦ t s♦♣ ♦ ts tss ♦r s s♦ s♥② ①♣r♠♥ts ♥ t ♠♥ r♥t rqr♠♥ts t♦ ♦♥t ♥s t② s t ♦♣rt♦♥ ♥ t ♥str♠♥tt♦♥ ♦♥tr♦ ♦♥ r♥t tr♦♥st♥rs ♦r t② ♦ ♦♠♣t♥ss ♥ ts st♦♥ t sr♣t♦♥ ♦ t ♣♣t♦♥♦ t rt♦♥ ♠♦♥t♦r♥ s♥s♦rs ♥ t s ♦ t ①♣r♠♥t ♥♥ ♦r ♦♥ t ♦① tt ♥st ♥ t t♥♥ ♥ tt♠♦♥ts s♦♠ ♦ t s♥s♦rs ♦♣ r ♣♥ ♦s P❲ s♦ ♥

rt♦♥ ♠♦♥t♦r♥ s②st♠

♥ r♦♣ t♦♦ r t♦ s♥ ♥ ♣r♦ ♥ ♦♥♥ rt♦♥♠♦♥t♦r ♦r t ①♣r♠♥t s ♦♥ t s st ♥ ts tss ♦r ♣r♣♦s ♦ t rt♦♥ ♠♦♥t♦r s t♦ ♣r♦ ♦♥♥ ♥♦r♠t♦♥ ♦t t ♥ t Φeq t r♦s ♦t♦♥s ♥ t ①♣r♠♥t ❬r❪ ♥ t♦♥ t♦ ttt rt♦♥ ♠♦♥t♦r r♦r t rt♦♥ ♦ rr♥t ♥ ♥ t ♣♦rtr♥sst♦rs s ♥ ♠♦♥strt t♦ ♥♦r♠t♦♥s ♦t t ♦ tr♠♥tr♦♥ ①♣♦sr ❬♥❪

rt♦♥ ♠♦♥t♦r ♠st ♠sr ♦ss ♥ r♥s r♦♠ ② t♦ ♥rs ♦ ②♥ r♦♠ 1011 cm−2 t♦ 1014 cm−2 ♣rt ♦r t ♣♥ ♦ s rtr③ ♥ tsst② t rt♦♥ ♠♦♥t♦r ♠sr Φeq r♦♠ rr♥t ♠sr♠♥t♦ rrs s ♦s

♥trt♦♥ ♦ t rt♦♥ ♠♦♥t♦rs t t

r Pr♦t♦t②♣s ♦ t t♦♣ s ♦ t ♣♦♣t ②r ♦♥♥t t♦ P r♠ ♥ t ♦tt♦♠ ♣rt ♦ P ♣st ♦s♥ ♦tr ♠♥s♦♥ ♦t ♦s♥ ♦① ♦r t ×× ♠♠3 ②r s ♣♦♣t t t ♣ ♦♥t♥♥ s P ♦ P❲ ♦ ♣t① ♦ t♦ tst strtrs ♥ t♠♣rtr s♥s♦r ♦r st ♦ ♦ ♦t♦♥s

♠♥ ♣rt ♦ t ♦♥♥ rt♦♥ ♠♦♥t♦r s tt♦♥ ♦♥t♦r ♥s♦r ♦r ♥ ts ♦r rt♦♥ s♥s♦rs ♥ t♠♣rtr s♥s♦r ♠♦♥tr t♦ t②♣s ♦ s ♥ ♦ ♦♥ s ♥ t ♥♥rtt♦r s♦♥ ♥ ♥ t ♦tr ♦♥ ♦tr ♠sr♠♥t ♦t♦♥s ♦s t s s♦♥ ♥

qr♠♥ts ♦r t ♠♦♥t♦r♥ ♥ t r r② ♠♥♥ s ts♥s♦rs ♠st ♦r rst r♥ ♦ ♦ss ♥ s ♦ r② ♠t ♣♦sst② ♦rss ♦r ♥t ♥tr♥t♦♥s r♦r s ♥ t ♥♥r tt♦r ♦st ♥♠r ♦ rt♦♥ ♠♦♥t♦rs ♦r r♦ ♦sr♥ ♥ ♣r♦ ♦ r♥♥② s ♦ r② ♥rt♥ t♠♣rtr ♦♥t♦♥s t s♦♠ ♦t♦♥s♥ t ♥♥r tt♦r ♦ r② t♥ ♥ t s ♠♦ r♠s ♥ q♣♣ t tr ♥ t♦ ♣ t ♦r t♦♥st♥t t♠♣rtr rs ♦

♦r ♦t♦♥s ♥ t st ♦ ♦ t s s♠♣ P t♠♥s♦♥s ♦ × ♠2 ♦st♥ t s♥st ♣♥ ♦ P t♠♣rtrs♥s♦r Ω ♥ r♠ ♣ ♦♥t♥♥ ♦♥ t ♦① ♦ tr♦r ♦♥♥t t rs ♦♥ ♦r s♥s♦r ♣s rtr♥ r

s r ♦t s♥ st♥r tr♦♥s ♥s♦rs r ♦t s♥ s ♦♥ ♦rs ♦♠♠♥t t t tt♦r♦♥tr♦ ②st♠ ♦r t s rr♥t ♣ss ♦r s♥ ♦ s♥s♦rs

♠ ♦ ♦♥t♦r ♦r s ♥r♣r♣♦s ♣♦♥ ♠♦ ♦r t♠♦♥t♦r♥ ♥ ♦♥tr♦ ♦ stt♦r r♦♥t♥ q♣♠♥t s s ♦♥ t ♥str②

①♠♣ ♦ rt♦♥ ♠♦♥t♦r♥ s②st♠s t

r rt♦♥ ♠♦♥t♦r ♦r s ♥ t t♥♥ t ♥rr♦♥ rs ♥ ♦♥t r♥ s ♦① r♦t tr♦♥s ♦① ♥ ts ♠♥♠s♥

♥ ♦♥rt t♦ ♦t rsst♦rs ♣r♦ ② ♦rs ♣ ♥t♦ ♦rs ♦r ♣r♦s ♥♥s ♦r t♥♥r tt♦r ♦♥ ♦r sr ♦♥ rs ♦r t rst ♦ ♣t♦ s ♦ ♦♥♥t t♦ ♦♥ ♦r ♥♥r tt♦r ♥s ♥♥s st ♦ ♥s ♥♥s ♦r s♥s♦rs ♦r rr♥t ♠♦♥t♦r♥ ♥ ♦r t♠♣rtr ❬r❪

t♦♥ ♠♦♥t♦r♥ ♥ t t♥♥ ♥ ①♣r♠♥t rs

rt♦♥ ♠♦♥t♦rs r s♥ t♦ ♠♦♥t♦r rt♦♥ s t t ♦t♦♥ ♦ q♣♠♥t ♥ t t♥♥ t ♥rr♦♥ rs ♦♥ t s ♦ t①♣r♠♥t r♥s ♥ t rt♦r t♥♥ ♥ ♦♥ t r♥ s ♥ ♦♣♣♦st♦♥t♦ t s ♥ sss ♥ t ♣r♦s st♦♥s ♦r t ①♣r♠♥ts tr r♥♦ strt s♣ ♠tt♦♥s ♥ t rt♦♥ s r ♦r t♥ t ♦♥s ♦rs♥ ♦rt ①♣r♠♥ts t♠ss s r♦r t ♥ts t ts♦t♦♥s ♥ ♦st t r♦t tr♦♥s ♥ t s♠ s♥s♦r ♦t♦♥ ♥ ♣r♦ ♦♥♥ t③ ♠sr♠♥ts ♦ t ♦s ♦s rt ♥ r♦♥ ① t ♠①♠♠ ③ ❬❲❪

s t②♣ ♦ s ♦r s s♦♥ ♥ ♥ t② r ♣♥ ♠♥♠ s♥ ♦ ×× ♠3 s t s s♦♥ ♥ rt♦♥♠♦♥t♦r♥ ♥ts ♣r♦ ♦♥♥ ♠sr♠♥ts ♦ t ♦♦♥ ♣r♠trs

♥ s♦♥ ♠sr ② s

Φeq♥ s♦♥ ♠sr ② t P❲ ♣♥ ♦s

st♥r s ♥ ♦♣♥ tt s ♥ ♠♣♠♥t s ♦♠♠♥t♦♥ ♣r♦t♦♦rtr ts ♦♥ tt♣♠r♥♦♠t♠

♥trt♦♥ ♦ t rt♦♥ ♠♦♥t♦rs t t

r♦♥ ♥ t > ❱ ② ♠♥s ♦ ♦s t♦ ♦♥t ❯s

♠♦♥t♦r♥ s②st♠ ♥t♦♥ ♦①s strt ♥ t t♥♥♥ ♥rr♦♥ rs ♠①♠♠ ♥♠r ♦ rt♦♥ ♠♦♥t♦r♥ ♥ts tt ♥ tt t♦ s♥ ♥t♦♥ ♦① ♦r t rst ♣rt r♥s ♦ t rt♦r t♦t ♦ rt♦♥ ♠♦♥t♦rs tt s t s♠ tr♦♥ s♥ ♥st ♥② rt♦♥ ♥ t rt♦♥ t♦r♥ ♦ t ♠♦♥t♦rs tr♦r ♠♥♠③ t♦ t ♦tt♦♦t rt♦♥ ♦ t ♦♠♣♦♥♥ts t ♦ ts ♠♦♥t♦r♥s②st♠ ♠ s ♥ t ♦♥tr♦ r♦♦♠ r♣ ❯sr ♥tr ♥tr s♦ ♦ ♦♠♥♥ t r♦♠ t ♠ ♦ss ♠♦♥t♦r♥ s②st♠ ♥ tq♥ ♣r♦tt♦♥ s②st♠ t♦ ♣r♦ ♦r♥t ♦ t rt♦♥ s r♦♥ tr♥ t♦ t ♥♥r ♥ r ❬❲❪

♣tr

♠♠r② ♦♥s♦♥

♠ ♦ ts tss ♦r s t♦♦ ♥ t ♦♥ ♥ srs ♦ rt♦♥ ♠♦♥t♦r♥ s♥s♦rs r rtr③ t ♣rtr rs♣t t♦ t ♣rt② ♦ t ♥r♦♥♠♥t tt t② ♦ t♦ ♠♦♥t♦r t t ①♣r♠♥ts rtr③t♦♥sts ♦ t ♥stt s s ♥ ♣♥ ♦s s♠♦♥t♦r s♥s♦rsr rr ♦t ♦r tr st♦♥ ♥ t♦ tr♠♥ t ② ♣r♠trs tt ♦tr t③t♦♥ t t rtr♠♦r sss rr♥ t s♥s♦r ♥♣st♦♥ ♥♥trt♦♥ r rss ♥ ♦rr t♦ ♦♥t ♦r t s♣t② ♦ t ♥r♦♥♠♥t ♥ t♦ ♠ t♠ r② ♦r tr ♥stt♦♥ ♥t♦ t ①♣r♠♥ts ♥ t♦tr ♥ ♦tr ♦s♠tr ♣r♥♣s ♥ ♥stt t♦ t tr ♣♦ss♣♣t♦♥ t t s s t s ♦ t ♠trs tt ♥ st♥ ♣rt s ♦ ♥trst ♦r ♣♣t♦♥s trt♥ r♦♠ t t♦♥ ♦ ts♥st ♠tr r♥t ②♦ts ♦ s ♥trt s♥s♦rs ♥ tst♥ tr ♣r♦r♠♥s ♠sr ♥ sss ♥ ts ssrtt♦♥

♦♠♣① rt♦♥ ♥r♦♥♠♥t ①♣t t t ①♣r♠♥ts ♦ t ♦♥sttt ♠♥② ♦ ♣♦t♦♥s ♣r♦t♦♥s ♣♦♥s ♥ ♥tr♦♥s ♠ ts ♠♦♥t♦r♥ ♥♥❱r② rt♦♥ s ♥trt ♥ rt♥ ♦t♦♥s t t rqr♠♥tt♦ s♥stt② ♥ ♦tr ♦t♦♥s r t rt♦♥ ♠ ss♥t♥s ♦r♦r t ♣rt s♣tr r r s ♥t♦♥ ♦ t ♥ t rs♣tt♦ t ♥trt♦♥ ♣♦♥t q♥tt② ♦ ♥trst t♦ ♠♦♥t♦r ♥ ts rt♦♥ r t ♦t ♦♥③♥ ♦s ①♣rss ♥ ② ♥ s♦♥ ♥ t ❱ ♥tr♦♥q♥t ♣rt ♥ Φeq

♦ rtr③ s st ♦r t ♦ ♠♥t♦♥ ♦♠♣① rt♦♥ r♥t rrt♦♥ ts r ♥ ♦r t rrt♦♥ ts tt ♣r♦ ♦♣t♠③ rt♦♥ s ♦r t rtr③t♦♥ ♦ t s♥s♦rs ♦r t ①♣r♠♥ts ♥ t s♥s ♦ ♣rt t②♣s ♥ ♥rs r t ♦♥s t t Prt♦r ♦r ts rs♦♥ ♥ t r♠♦r ♦ ts tss ♦r sr ♠sr♠♥t♠♣♥s ♥ ♦♥t tr ♥ ♦rr t♦ ♠♣r♦ ♦s♠tr ♠t♦s ♥ ♠♥s♥ s♣♣② r ♠sr♠♥ts t♦ s ♦r t rt♦♥ s♥s♦rs rt♦♥

❱ ♣r♦t♦♥ ♠ ♦ t t② t rs ♣r♦t♦♥s ♥s♣s ♦ ×1010 cm−2 ♣rts ♣r♦t♦♥ ♥ s s② ♠sr ② ♠♥s♦ tt♦♥ ♦s t♥qs t ♠ ♣r♦s r ♦t♥ t r♥t t②♣♦ ♦s♠tr ♠s r♦♠ ♥ ❲t ts t♥qs ♥ r② ♥ ttr♠♥t♦♥ ♦ t ♣r♦t♦♥ ♥ ♦ ± ♥ ♥ ♠ ♣r♦s ♥

♠♠r② ♦♥s♦♥

♣rs♦♥ ♦ ♥r ♦ µ♠ ♥ ♦t♥ ♥ ♠ ♣r♦♥ rst ①♣r♠♥t♠ t♦ ♣r♦ t ♣r♥♣ ♦ ♦♣rt♦♥ ♦ ♥ ♦♥♥ ♠ ♣r♦ ♠♦♥t♦r s ♦♥ t♠ss♦♥ ♦ s♦♥r② tr♦♥s r♦♠ t♥ ♠♥♠ ♦ s ♥ s♦ ♣rs♥t♥ ts tss ♦r ♥tr♦♥ ♥ ♥ t ♠① γ♥ ♥r♦♥♠♥t ♦ t t② s ♥st s② ♠♦♥t♦r ② ♠♥s ♦ ♣rt tt♦r ♦s t s ♠sr t r♥t ♣ss ♦s♠tr② P P ♥ ♦s♠tr ♠s ♥ts ♥r♦♥♠♥t ♦ ② ♥ s♦♥ s ♣♦s ② Φeq ♦ ×1011 cm−2 ♦♠♣rs♦♥ ♦ t ♠sr♠♥t t ♦♥t r♦ s♠t♦♥s s♦s ♥ r② ♦ ♥ t Φeq ♠sr♠♥t ♥

♥ t ♦♦♥ t ♠♥ ♦♥s♦♥s ♥ t rtr③t♦♥ ♦ t r♥t rt♦♥ ♠♦♥t♦r♥ s♥s♦rs ♦r t ①♣r♠♥ts r♥

• ♦s♠trs r♦♠ t s st♦♥ ♣r♦r t rst tt t♦ s r ♥ t♦ t rt♦♥ ♠♦♥t♦r♥ rqr♠♥ts ♦ t ①♣r♠♥ts tox µ♠ ♦r t ♠sr♠♥t ♦ ♦ ♦ ♥t♥st② s ♥ r s♥stt② ♦r t tr♠♥t♦♥s rqr ②♣ t tox µ♠ r ♥st ts st ♦r t ♠sr♠♥t ♥ ♥t♥st② s rt ts ♦ t ♥t r♦♠♥t♦♥ ♥ ② ♥r② r♦♥s t♥ ts♦♥♦① ②r ♦ t s t♠ss t♦ ♠♥♠③

s t tr ♥t s♥stt② ♦ ♦t ♠❱② ♥ tr②♥♠ r♥ r♦♠ ♠② t♦ ② r tr♦r t st ♦ ♦r t♠♦♥t♦r♥ ♦ t ♦tr stt♦r r♦♥s ♦ t ①♣r♠♥ts r t①♣t rt♦♥ ♦♠♣♦s ♠♥② ♦ r♦s♣tr♠ ♥tr♦♥s ♥♥rt ♣♦t♦♥s tt t♦ ♠t ♦ss ♦ t♥s ♦ ② ♦r t ②rs t♠ rrt♦♥ tsts rr ♦t t t t② ♣r♦♥ tt ♦srts ♦ ♠② ♥ tt ② ts s♥s♦r ♥♥♥ sts ♥ rt ♠sr♠♥ts ♦♥ ts s s♦ tt s♣♠♥t♠ ts ♥ ♣♣r ♥ ts s♥s♦rs r ①♣♦s t♦ rt♦♥ s♥ rt♦♥ t s♠r rtrsts t rs♣t t♦ t ♦♥ ①♣tt t ♦r t r♥t ♥♥♥ ♥stt♦♥s ♣r♦♥ tt ♥tr ♥ ♦r①♣♦sr t ♥♥♥ ♦ t ♦s♠tr ♣r♠tr s s ♦ s ♦r ♠♦r t♥ ♦♥ ②r t♠ ♥ t ②♥♠ r♥ ♦ ♥trst ts s s♦ ♣r♦♥ t♦ ss♥t② ♥s♥st t♦ st♥tr♦♥s s ♣r♦r♠♥s♥ r♥t ♥ r② ♦ ± ♥ t ♠sr♠♥ts ♦r t♠

s t tr ♥t s♥stt② ♦ ♦t ♠❱② ♥t② ②♥♠ r♥ r♦♠ ♠② t♦ s♦♠ t♥s ♦ ② r ♥st t st ♦♦r t ♠♦♥t♦r♥ ♦ t ♥♥r stt♦r r♦♥s ♦ t ①♣r♠♥ts r t①♣t rt♦♥ ♦♠♥t ② ♥♠♠ ♦♥③♥ Prts Pstt t♦ ♠t ♦ss ♥ t ② ♦r ②r t♠ rrt♦♥ tsts rr ♦t t t t② ♣r♦♥ tt t② sss②♦r ♥ ♥r♦♥♠♥t t ♦ ♦srts ♥ ♦♠♥t ② r r♦♥s♥♥♥ sts ♥ rt ♠sr♠♥ts ♦♥ ts s s♦ tt ♥ tr ♦ ♠♦r t♥ ② ♥ Φeq rtr t♥ ×1013 cm−2 t ts♦♠♥t ♥ t s rt♦♥ rs♣♦♥s ♥ ♥ s♥s ♦ s♣♠♥t

♠ ts r ♦♥ s♦ ♥ ts s t r♥t ♥♥♥ ♥stt♦♥s ♣r♦♥ tt t ♥♥♥ ♦ t ♦s♠tr ♣r♠tr tr ①♣♦sr t♦ ②♦ss s s ♦ s ♦r ♠♦r t♥ ♦♥ ②r t♠ ♥ ♥ t t♠♣rtrrt♦♥s ♦r t♠ r r t♥ ❯s♥ r♦t rr♥t ♥♦t ♦rrs♣♦♥♥ t♦ t ♣♦♥t ♦ t s t t♠♣rtr ♦rrt♦♥s ♦r t∆❱th s ♥t♦♥ ♦ t ♥ tr♠♥ ♥ ts ♦r s P ♥ ♥ s ♥ r♦ t♠♣rtr rt♦♥ ♦rs r♥ ♠sr♠♥ts♥ t ②♥♠ r♥ ♦ ♥trst ts s s♦♥ ♦♥st♥t s♥stt②t♦ st♥tr♦♥s ♦r ② t♦r ♦ t rs♣t t♦ t ♦♥ tr♠♥ ♦rt rt② rt♦♥s ♦ ♠♥t♦♥ ♣r♦r♠♥s ♥ r♥t ♥r② ♦ ± ♥ t ♠sr♠♥ts ♦r t♠

• ♣♥ ♦ s♥s♦rs P❲ ♦♠♠r ♣♥ ♦s r ♦♥ s ts♦t♦♥ t♦ ♠♦♥t♦r t Φeq tt ♥trt ♦r t ②rs ♦ ♥ t ♥♥r stt♦r r♦♥s ♦ t ①♣r♠♥ts sts rr ♦t♥ ts tss ♦r s♦ tt t ♦♣t♠③ ♦♥t♦♥s ♦r tr r♦t rr ♥ t rr♥t ♦ ♠ s r t ♣s ♦ ♠①♠♠ st ♦♣rt♦♥ t r ♥t♦♥ s r ♦rr rr♥ts s ♥♦tr♦♠♠♥ s ♠♣♦rt♥t st♦rt♦♥s ♥ t ♠sr ♦rr ❱ rs r♦♠♦t ♠ t♦ ♠ ♥ ♦♥ ♥ Φeq r t ♦ 1013 cm2t ♠ r♦t rr♥t ts s ♣r♦ s♥stt② ♦ ×109 cm2/mV♥ Φeq ①s ×1012 cm2 ♥ ♦r ♥rts strt♥ r♦♠ ♦t 1011 cm2/ht ♦r ♥t Φeq t s ♥♦t s♦ s♥stt② t♦ st r♦♥s s♦t♦♥t♦ r♥ t s t♦ tr s♥st ♦♣rt♦♥ r♦♥ s t♦ ♦♣rt ♦♥♣rrrt♦♥ r♥ ♦♥ t s rrt♦♥ tsts rr ♦t t t t② ♣r♦ tt ♦r ♥rts ♦r t♥ 1011 cm2/h t♥♥♥ ♦ ts s s t♦ ♦rrt ♥ ♦rr t♦ ♣ t r② ♦t ♠sr♠♥ts t♥ ± ♦r ts rs♦♥ ♣r♠tr③t♦♥ ♦r t♥♥♥ ♦rrt♦♥ s ♣r♦♣♦s ♥ ts ♦r tt ♦♥sst ♥ ♦♠♥t♦♥ ♦ ♥①♣♦♥♥t ♥ ♦rt♠ tr♠

VF (t) = A−α·exp

(

− t

τ

)

−β·ln(

t

t0

)

−(|Tc|×∆T ) s q ♣

tt s ♦r t t♠ ♥ t t♠♣rtr r♥ sr ♥ ♦♠♦ t ♣r♠trs s ♥ t ♦ qt♦♥ s♦ ♣♥♥ ♥ ♦t Φeq ♥ ♥t t♠♣rtr

s♥stt② P ♣♥ ♦s r ♦♥ ♥st t♦ t s♦t♦♥ t♦♠♦♥t♦r r② ♦ Φeq s s t ♦♥s tt ♥trt ♦r t ②rs♦ ♥ t ♦tr stt♦r r♦♥s ♦ t ①♣r♠♥ts rtr③t♦♥ sts rr ♥ ts tss ♦r s♦ ♦r t ♦rr ♦tr♦t ♥r s♥stt② ♣♥♥ ♦ ×108 cm2/mV ♥ Φeq s ♦rt♥ ×1012 cm2 r♥t rt♦♥ rs r ♥ r♠♥t t♥ ± t r s ♦ Φeq t rs♣♦♥s rtrsts ♦♠s s♣r♥r♦♥ q② t♦r r♦♥ r♦♥ rrt♦♥ tsts rr ♦t t t t② ♣r♦ tt ♥ ♦r ♦srts ♥ t ♦rr ♦ 109 cm2/h

♠♠r② ♦♥s♦♥

t ♥♥♥ ♦ ts s s ♦r t♥ t ♠sr♠♥t rr♦r s s ♥♣r♦♥ ② rt ♥♥♥ ♠sr♠♥ts ♦r♦r ts s s♦ t♦ t♦ ♠sr t ♣rt ♥s ♥ t r♥t ♦t♦♥s t ♥r♠♥t ♦ ± t rs♣t t♦ t ♣rt♦♥s ♦ ♦♥t r♦ ♠t♦♥s ts ♥② t t♠♣rtr ♣♥♥ ♦♥ ♦r s t②♣

Pr♠♥r② rrt♦♥ tsts r s♦ rr ♦t ♦♥ t♦ ♠♦s ♦ ③ s♦♥♣♥ ♦s t②♣ ♥ tsts ♣rs♥t ♥ ts tss ♦r ♥ rr ♦t ♥ ❱ ♣r♦t♦♥ ♠ ♥ ♥ ♥r rt♦r ♥tr♦♥♥r♦♥♠♥t s ♣r♦ts t♦ r ♦t t ♦rr rr♥t ♣s ♦ ♠ s rr♥t r♣rs♥t t t ♠♦♠♥t ♠tt♦♥ ♦r t ♥trt♦♥♥ t st♥r ①♣r♠♥ts r♦t tr♦♥s t s ♥t♦♥ st ♣r♦r♠♥s ♦ t ♠♦ r ♦♥ t♦ ♦♠♣r t♦ t ♦♥ ♦t P s s♥stt② ♦ t ♠♦ r ♥st ♦♥ t♦ ♦×107 cm2/mV ♥♠② t♦r r t♥ t ♦tr s ♥ ♥♥stt♦♥ ♦ tr ♣r♦♣rts t ♦r ♥t♦♥ s ♠ s st t♦ ♦♥ t② ♣♣r s ♦♣t♦♥ ♥ t r♣♠♥t ♥♦r ♦♠♣♠♥t♦ t P ♦s rr♥t② s

• ♠trs t♦♥ ♦ ♠tr ♥ r♦♥ ♥r♦♥♠♥t s ♥rr ♦t ♥ ts tss ♦r rs♣♦♥s ♦ t ♣r ♠tr t♦ ❱♣r♦t♦♥s s ♥ r st ♥ t s♦♥ tt t ♦ ts ♣rt s♦rrt② tt ♦r t ②♥♠ r♥ ♦ t ♠tr ♣ t♦ ② ♦rt ♥ ♦ t ♠tr s ♥ ♦♥ s ♣♦ss ♠t♥ t♦r s♣②♥ t ♦♣rt♦♥ ♦ s ♥trt s♥s♦rs ts ♦♥ t ♣♦sst② t♦♥♥ t ♥tr♦♥ s♥stt② ♥ sss② rr ♦t ♣②♣r♣r s♠♣s ♠① t ♣♦②t②♥ ♦r ♦♣ t ♦r♦♥ r ♠♥tr ♦r t ♠sr♠♥t ♦ st ♥ tr♠ ♥tr♦♥s rs♣t② t♦t s ♣♦ss t♦ ♠sr ♥ sr♠♥t t ♦♦ r② r♥t ♥tr♦♥ s♣tr t♥ ♦t ts ♥ ♠trs r st ♥ t ♦♣♠♥t♣s ♥ t r♣r♦t② t♥ t r♥t s♥s♦r ts s st t♦ ♠♣r♦

rtr③t♦♥s ♥ r♦♥ ♥r♦♥♠♥t ♦ r♥t ♥trt s♥s♦rs s♦♥ s♦ ♥ sss rst ♥trt s♥s♦r ♦♥sr ss ♦♥ s♥ ♣♦t♦♦ ①♣♦s t♦ t rt♦♥ t♦ ♠sr t♦tr t ts r♦t tr♦♥s s ss♠② ♣r♦ r②t♦ ♦r sss② ♥ s♣ ♣♣t♦♥s ❯♥①♣t② t r♦♥♥r♦♥♠♥t rsts t♦ r② t ♦♥ ♠♥ t ♦♠♠r tr♦♥s♦r t r♦t r ♠♣r♦♠♥t ♥ r③ ♦♥ t tr♦♥s♥ ♥ ♥ t ♦♠♣♦♥♥t st♦♥ ♦r t s ♥♦t ♣♦ss t♦ ② ①♣♦tt s♥stt② ♣r♦♣rts ♦ t ♠♣♦② ♠tr ② s♥ ♥♦trs♥s♦r ♣♣r♦ t rt♦♥ r♥ss sss ♥ ② ♠♦♥ tr♦t tr♦♥ ♦t r♦♠ t rt♦♥ ♥r♦♥♠♥t ♥r ♠sr s s♥ r③ ② ♠♥s ♦ rt♦♥ r♥ ♦♣t rs tt r ♥ ♦t

t t s♥s t♦ ♥ r♦♠ s♠ r②st s r♦t s♠ ♦s s♦t t③t♦♥ ♦ ♦♣ ♦ ♦♠♠r srP s ♦r t r♦t ♥② ♥ t ♦♣t st♠t♦♥ ♥ ♥ t t ♦t♦♥ t♦ t rst ♣r♦t♦t②♣ tst t s♥stt② t♦ ♦♥③♥ ♦ss ♦♥ t♦t ♠② r♥ s s♥s♦r ♣♣r♦ ♠ tr♦r ♣r♦♠s♥ ♣♦sst② ♦rt rt♦♥ ♠♦♥t♦r♥ t t ①♣r♠♥ts

♥② ♥ ts tss ♦r t ♥trt♦♥ ♦ ♦r ♦ t s♥s♦rs ♣rs♥t ♦ P P❲ ♥ ♥q P rrr s ♥ ♦♥ ♥trt♦♥ rs ♦♥ t t tt t r♥t s s♠r r♦t ♣r♠trs ♥ ♦r r ♥ t♦ ♥sr ♦♠♣t ♠♦♥t♦r♥ ♦ t ♥♥ rt♦♥ ①♣t t t rs♣♦♥ss ♦ t t♦ ♦s♠trs ♥ r t ♠♦st t ② t ♠trs tt srr♦♥ t ♠sr♠♥t ♣♦♥t ♦r tsrs♦♥ t ♣ rrr s ♥ s♥ ♦r t♠ ♦ t t ♦ ♦t rrr s ♠tr ♥ s ♥ t ♥r♦♥♠♥t ♦♥t r♦♠♦ s ♥ t ♥ ts rst t♦♥ tsts ♥ ♣rs♥t ♥ ts tss♦r ♥ ♣rtr t t♦♥ t ❱ ♣r♦t♦♥s s♦ tt t ♠♦ ♥ r② s t♦ tr♠♥ t t♥ss ♦ t rrr ②♦t ♥ t s rs♣♦♥ss♦r r♥t ♣r♦t♦♥ ♥rs s ♣♥ t♦tr t t t♦ ♣♥♦s P ♥ P❲ ♥ ♦st ♦♥ t ♥trt P rrr tt ♦s s♠♣ ♥♥ ♥ r♦t ♦r t ♦r ♣r♦♣♦s s♥s♦rs rtrsts ♦ trst ♣r♦t♦t②♣ srs ♣r♦ t ♥ ssss ①t♥s② ♥

❲ s♦♠ ①♣r♠♥ts r r② ♥st♥ s♥ s♥s♦rs ♦♣ ♥ tstss ♦r t♦r ♥ ♣r♦♣r r♦t s②st♠s s ♦trs ①♣rsstr ♥trst ♥ s♥ t ♦ P ♥trt rrr ♣rs♥t r ts ♥stt♦♥s ♥ ♦rs♥ r② ♥ t ②r t♦ r② ♦r t ♠sr♠♥t ♦ t rt♦♥ r♥ t rst ♥♥r♥ r♥ ♦ t ♠♥ s t t ♥ ♦

♣♣♥①

Pr♦r♠♥t s♣t♦♥ ♦r

s

s ♣♣♥① s♣s t ♣r♦r♠♥t ♥ t tst♥ ♣r♦r tt s ♥♦♣t ♥ t st♦♥ ♦ t r♠♥♥ st♦ ♦ ♣s r♦♠ t r tst♥ ♣r♦r tt s ♥ rr♦t t♦ ♣r♦r t ♠♦rt② ♦ s st♦ ♦ t r ♥ st t♠ t rtrsts sts② ♣♣t♦♥s t r

r♠♥♥ st♦ s ♦♥t♥♥ st② ♦r ♣s ♥t r♣r♦ tst s ♦♥② ♣rt ♥ t♦♦ ♣ sr ②rs ♦ s q♣♣ t♦♣r♦ s♥ ♥ r q♥tts ♠♥♠③♥ t rs ♦ tr♦stt ♠ tt ♥♦r r♥ t ♥♥ ♣r♦r s ♥ ♥t srs ♦ tsts ①tt ♣r♦stt♦♥ t t ♠ t♦ st t strtrs st ♦r ♣r♣♦ss♥ t s ♥ st st ♥ r♦♥ ♥ ♣r♦♣r ♣ ♣♥rtr tr tsts ♣r♦r♠ t t ♠ t♦ t s qt② ♦rt t ss♥♠♥t ts ♦t t st♥r s rrr t② s♣ ♦r t♦s♠trs t♦ ♥st t t r ♥ ♣tr

tst ♣r♦r

tr s♣t♦♥s r♥t ♦r t ♣r♦r♠♥t ♦ t ♦♦ strtrs♦ ②♣ ♦r t r r ♥ ♥ s ♥st t♣r♠tr r♥t ♦r qt② st♦♠r② ♣rt♦♥s ♥st tr♦stt♠ s ♦sr ♥ ♥♥ ♣r♦rs st♦♥ ♣r♦rs ♥ rr ♦t s ♦♦s

t s♥ s ♣r♦ s♥ ♣r♦r s♥ ♦r t ♠s srs t ♣rtr rs♣t t♦ t t♦ ②♣ strtr

♦♥ t ss ♦ t ♣r♠trs ♥ ♥ t ♦♦ ②♣ s ①trt r♦♠ t st♦ ♥ ♠ ♦r t③t♦♥

♣t ♦r ♥ t st ♦♥ ♦ t t♦ ②♣ strtrs♦♥ s ♥t♦ t ♥ ♣r♠trs r♥ ♦

tst ♣r♦r

t st ♦♦ ②♣ strtrs ♠♦♥t ♦♥ ♣ rrr t♦ ttr qt② ♦r tr t③t♦♥ ♦♦♥

P ❯❨

rtr ♦ ♦♦ ♣♥ ♠♥② ♦♥ ts ♥t♦♥t② ♥ ♠sr♥ rt♦♥ ♦s ♦♦♥ ♦rr♥ ♦♥srt♦♥s ♠st ts t♥ ♥t♦ ♦♥t srrs ♣r♦r♠♥

♥ ❱ r st t t♠ t t♠♣rtrs ♦

♦♠♦♥♦s ♥t trs♦ ♦t

Idss ss t♥ ♦ t ♥♦♠♥ r♦t rr♥t

♠♦rt rt ♦r ♥ tr rrt♦♥ tt

P♥tr♦ ♦t ♦♠♣r t t rqr r ♦t tr rrt♦♥

♥ t ♦tr ♥ ♦♥srt♦♥s ♦ ♦♠♣♠♥tr② ♣r♠trs

tst♦r② tsts

♠ rt② ♥ C rr♥t t

♥s ♥ t t♦♥ ♦ t qt② ♦r ts rs♦♥s rtr ♥ tst ② ♥ ♦♥sr ♥ t ♥r ♣tr ♦ qt②♦r ♦r t s♦rt♥ ♥ t② ♥♦t ♥t♥ s rtr ♦r rt♥ ♦rs s rt♦♥ tt♦r

♦♥t♥s t rs tt ♦♥sr s ♣trt s t s♥② ♦ t ♥t r② ♦ rt ♦♥trt② ♥ ♦ts t ♥♣r♠trs r♥ s rs r s ♦♥ ♦rt♦r②♦♦ t ② ♦r ♦♥ ts r ♦t ♦r t ♠sr♠♥t ♦ ts ♣r♠trs t ♣rt♦♥s strt② ♦sr ♦r ♥♥ ♣r♦rs ♥s ♠ s r♥♣r♦♥ ♦ ♥♦t s ♦r rt♦♥

♣r♠trs Vth,0, dutti, Idss ♥ Id−Vds s ♣r♠trs s♣ ♥ r ♥t♥ t♦ ♠sr ♦♥ t s t ♣r♦ stt♦♥ ♦r rrt♦♥♦r t BVdss t ♠♦st r tst s t ♠sr♠♥t ♦ t r♥s♦r ♦t tr ② rrt♦♥ ♥ ♥ Ids rr♥t s ♦r tr♦♦t t s ♦r tsrs♦♥ strtr ①trt ♦r♠ t t ♦ s ♦♦ s ♣r♠trs ♠♦♥t r♦♥ ♥ rrt t♦ ② tst ♣ss tstrtrs ♦r ♣ t♦ t ♠♥♠♠ ♦t rqr s s♣ ♥ ♥ss r t tst strtr ♣t ♦♥ t ss ♦ t ♦r s ♣r♠trss♦s ♥①♣t r② r♦♥ ♦t ♠srs t♥ ♥ r♠♥t tt ♣r♦r t♦ ♦♠♣t t ♣t♥ ♣s

♦♥t♥s rs tt s s ♥t♦rs ♦ qt② ♦r t ss♥♠♥t s ♣r♠trs ♠② s ♦r t s♦rt♥ s s ♥ st♥ s

r♦♥②♠ tt st♥ ♦r rt♣ ♥ ♥② t♦♦ t♠ ♥tr

Pr♦r♠♥t s♣t♦♥ ♦r s

♦r st②rs ♥ ♦st②rs rs ♦ ♦r ts rs t s♣t♦♥r s♦♠t♠s s ♦♥ st♠ts ♥ ♥ ts st t♦ rtr ♠♦t♦♥sr♥ t ①t♦♥ ♦ t ♠sr♠♥ts

P

❱ rtrsts

❯s♥ t ♦♥♥t♦♥ ②♦t s♦♥ ♥ t tr♥sr rtrst Id − Vgs ♦t s ♦r ♦♥ ♦ Vds ♥ t r♥ r♦♠ ❱ t♦ ❱ s ♥ ♠sr r♦♠t Id − Vgs rs t trs♦ ♦t VT ♥ t r♥♦r rr♥tIdss ♣r♠tr s ①trt ♦r♦r t ♦t♣t rtrst Id − Vds s ♥r t r♥t s ♦ Vgs t②♣② ♦r r♥♥ r♦♠ Vgs <VT t♦ ❱

r s ②♦t ♦r s ♥ t st♦♥ ♥ ♣r♦r ②♦t ♦r t❱ rtrsts ♠sr♠♥t ♦♥♥t♦♥s ♦r tst

s ♠♣rtr trss

♦ r② ♥② ♠♦♦♥ ♦♥t♠♥t♦♥ s ♥ ♥tr♦ ♦♥ t ♦① ♠sr♠♥ts rr♦t s♥ t ♦♦♥ ♣r♦t♦♦

♦♥♥t t t♦ t ♣t♥ ♠tr s s♦♥ ♥

♣r♦r♠ ♥ ♥t ❱ tst t r♦♦♠ t♠♣rtr s♣♥ t ♦t r♦♠ ❱t♦ ❱ r♦r♥ t ♣t♥ r

rrs t s♣

♣♣② ♣♦st ♦t tr♦ t t t♦ sts ♦ ❱♠ t②♣② ❱ ❱ ♥ t t s♠♣ t ♦r ♠♥ts t♥ t♠ s♦s♥ t♦ r tr♠ qr♠ s t tt t tt st t s tst ♠♦♥t ♦♥ ♣ rrr

♠♥t♥ t ♦t t s♠♣ s ♥ ♦♦ ♦♥

s♦♥ ❱ tst r♣t♥ st♣s ♥

tst ♣r♦r

♣♣② ♥t ♦t tr♦ t t ♥ t t s♠♣ t ♦r ♠♥ts

♠♥t♥ t ♦t t s♠♣ s ♥ ♦♦ ♦♥

♥ ❱ tst r♣t♥ st♣s ♥

r rt ②♦t

t ♣r♠trs r♥t ♦r t ♦s♠tr ♣♣t♦♥ ♦ t strtrs rtr♠♥ ♦♥♥t♥ t s ♥ t s♦ r rt ♦♥rt♦♥ s♦r tr♠♥ s ♦♥♥t t♦ t ♦② tr♠♥ ♥ s♣♣ t Ids t ♥ r♥r ♥st s♦rt

Pr♦r♠♥ts♣

t♦

♥♦rs

P ❨ ❨P ❳ ❯ ❯

r rt ♦♥rt♦♥ st ①t

♥t trs♦ Vth,0 ± ❱ t Ids µ ♦♥ ♣r♦stt♦♥

❱♦t(a) ❯♥rrt

r rt ♦♥rt♦♥ s ♦ st ①t

tt② ♦ Vth tt ± ♠❱ Vth ♠sr ♥ s tr tr♥♥ ♦♥ ♣r♦stt♦♥

t t♠ t rr ♦♥ ❯♥rrt

Id − Vgs rt ♦♥rt♦♥ st ①t

r♥s♦r Idss ∼µ t ♦ Ids t Vgs ♥ ♦s♥ Vds ♦♥ ♣r♦stt♦♥

rr♥t Ids t rr ♦♥ ❯♥rrt

rs t r♥t Vgs strt♥ ♠♠♥ t♦ ♥ ts

r♥ Id − Vds r♦♠ Vgs < −VT ♥ ♣rst

rtrst ❯♥rrt ♣♦r s♥trs

r rt ♦♥rt♦♥ Pr♠tr tt ♥ t

r♥♦r BVdss ❱ t Ids µ r♦t

r♦♥ ♦t(b) rrt t♦ ② st ①t ♦♥ tst♥

s ②♣ Pr♦r♠♥t ♣t♦♥s t ♦♦♠ ♠♣rtr♦ts(a) ♠♠r tt ts ♣r♠tr rs r♦♠ t r tr♥sst♦r trs♦ ♦t VT s ①♣♥ ♥ ♣tr Vth s t ♦ Vgs

tt s♣♣♦rt t ♦r r♦t rr♥t(b) ts ♥

tst

♣r♦r

P ❨ ❨P ❳ ❯ ❯

t ♠sr t t ❱ ♦♠♠♥ rq♥②

t♥ WVfb ♠❱ rs r♦♠ t ± ❱ µ ♦ t ♣t♥

♦t st ❯♥rrt r ③

r rt ♦♥rt♦♥ st ①t

♦t rr♥t Ids s♠♦♦t rt♦♥ µ ❯♥rrt ♥ ♦♥ ♣r♦stt♦♥

t rrt s

r rt ♦♥rt♦♥ st ①t

trs♦ ♠❱ t Ids ♦♥ ♣r♦stt♦♥

s♥ r♦♠ Id − Vgs ❯♥rrt

r rt ♦♥rt♦♥ ♠♣ r♥ t♦

♠♣rtr Tc < ♠❱ t Ids st ①t

♣♥♥ ❯♥rrt ♦♥ ♣r♦stt♦♥

❱ rt ♦♥rt♦♥ st ①t

① LIgbs ♥ t Vgs ❱ ♦♥ ♣r♦stt♦♥

rr♥t ❯♥rrt

s ②♣ ❯❨ Pr♦r♠♥t ♣t♦♥s t ♦♦♠ ♠♣rtr

st ♦ rs

②♦t ♦ t rt♦r t♦♥ s ♦♥ t r♥ t♦♥ ♥s ①♣r♠♥t t ♠ ♥t♦♥s ♦r ♥tr♦♥s ♣r♦t♦♥s ♣♦♥s ♥ tr♦♥s

♦♠ ♣ss ♦s♠trs s t ♣♥ ♣rt tt♦r ♦ strtr ♦r ♠sr♠♥ts rt♦♥ rs ♦r ♣♥ ♦s Pr♥♣ ♦ ♦s♠tr t♦♥♥ ♥s ♥ ♦s♠trs ♦♥③♥ ♥ s♦♥ ♦① ♠ ♦ ♦rr s ♣♥ ♦ ♣♥ s♦♥ ♦ ♦rr rr♥t r♦t ♣rt♥ ♣r♥♣ ♦ ♥ ♦s♠tr r♠ rtrst s♣tr ②♣ s♣ ♦ ♥ s♥ ♦s♠tr② s②st♠s s ♦♥

P st rrt♦♥ ts t② t t P st t② ♦♠♣♦st♦♥ t ♠ r rt♦r t ♠♥♥t ♦srt ♣r♦ ♥ t ♥♥ ♦ t r

rt♦r t rrt♦♥ ts t ❯ ♥ P rrt♦♥ s♦rs t t♣ ♦r ♥ ♣♥ ♦ rt♠ ♠sr♠♥ts ♠t r♣rs♥tt♦♥ ♦ t tr st♣ ♦ s ♥ ♣♥

♦s ♠sr♠♥ts t♣ s ♦r t rtr③t♦♥ ♦ t ♠trs

rt♦♥ rs ♦r ♠s ♥ rs♦t♦♥ ♠ ♣r♦s ♠sr ② ♦s ♠♣ rss tt♦♥ ♦ t♥q t♣ s ♦r t t♦♥ ♦ t ♥ t ♠

❯

P ♠sr♠♥ts ♦♠♣r t ♦tr ♠♣r♦ t♥qs Prt s♣tr ♥ t② t ♥t♠trs r♦♠ ♠ ①s ❱t♦♥ ♦ t rt♦♥ t ♦♥t r♦ s♠t♦♥s ♥ t② ♠sr ② r♥t ♦s♠tr ♠♥s tr♦♥s ♥ ♣♦t♦♥s ♦♥③♥ r♠ t♦rs ♦r ♥ P

t♦♥rtr③t♦♥ ♣r♦r ♣♣ t♦ ♦s♠trs s s♥stt② t♦ Ps ①♣r♠♥t st♣ s ♥st ♥ t ♠♥ s♣♦♥ss ♦ r s ①♣♦s t♦ t ❱ ❯ ♥tr♦♥

♠ ♦♠♣r t♦ t ♠♠ rs♣♦♥s s♣♦♥s ♦ s t♦ rrt♦♥ ♥ t ts ♦ t s♣♦♥ss ♦ t ♥ s ♦r t r♥t P ss ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r ②♣

s ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r P s ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r s ①♣r♠♥t s♦r♦♥ ♥♥♥ rs ♦r s t♦♥ rs♣♦♥s ♦ s ①♣r♠♥t s♦tr♠ ♥♥♥ rs ♦r s ♠sr

♦♦♥ rrt♦♥ ♥ t ♠①r♦♥ t r♥ rr♥t♦t rtrsts ♦ s ♠♣rtr s♥stt② ♦ t ②♣ t♦♥ rs♣♦♥s ♦ ②♣ s ①♣r♠♥t s♦tr♠ ♥♥♥ rs r♥t ♠rrs ♦r

②♣ tox µ♠ s ♠sr ♦♦♥ rrt♦♥♥ t ♠①r♦♥ t

r♥ rr♥t♦t rtrsts ♦ ②♣ s s ♣r♠tr

r♥ rr♥t♦t rtrsts ♦ ②♣ s s♣♠♥t ♠ s ♣r♠tr

♣ rrr r♦♠♠♥ ♦r t s t♦ s t t ①♣r♠♥ts

t ♦♥♥t♦♥ ②♦t ♦r t ♣ rrr r♦♠♠♥ ♦r t s t♦ s t t ①♣r♠♥ts

♠♥s♦♥ ♦ t ♠♦ ♦ t ♣ rrr ♦st♥ ts

r♦♥t ♦ t ♠♦ ♦ t ♣ rrr ♦st♥ t s ①♣r♠♥t t♦♥ ♦ t ♦♥t r♦ ♠♦ ② ♠♥s

♦ ♣r♦t♦♥ ♥ ♥tr♦♥ ①♣r♠♥t t ♥r② ♣♦st ♥ t s♥s♦rs s ♥t♦♥ ♦ t ♠♥ t♥ss ♥r② s♣tr ♦t♥ t ♠♦♥♦♥rt ♣r♦t♦♥s ❱ ♥

❱ t r♥t ♣♥ s ♦♥rt♦♥s

♣♥ ♦s P❲ ♥ ts ♥ ♣s P❲ ♦♥♥ s ♦♥ ♠sr♠♥ts t

❯

P❲ rt♦♥ rs♣♦♥s ♦r t ♦ Φeq P❲ rtrsts ♥ rrs s ♦rr ❱ rs tr ❱ ♣r♦t♦♥ rrt♦♥s ♥r s ♦rr ❱ rs tr ❱ ♣r♦t♦♥ rrt♦♥s ♥r s ❱ rs ♦r ♣r♦t♦♥rrt P❲ tr ♥♥♥ ♠♥ t r♦♥ s♥stt② ♦ P❲ s t r♥t ♥t♦♥ s ♥ r♦♠ rrt P❲ ♦s s t♠ tr ♥t♦♥ ♦ ♠ ♥ r♦♠ rrt P❲ ♦s s t♠ tr ♥t♦♥ ♦ ♠ t♦♥ rs♣♦♥s ♦ P❲ ♦s ♥♥♥ ♣r♦t♦♦ ♦r P❲ s ①♣r♠♥t t s ♦r t ♥♥♥ ♣r♠tr③t♦♥ ♦ t P❲

♦s ♣♥ ♦s t♠♣rtr ♦♥ts ❱t♦♥ ♦ t ♥♥♥ ♣r♠tr③t♦♥ ♦r t P❲ ♦s P ♦s ♦rt♠ ♥ ♥r rt♦♥ rs ♥♥♥ ♦ P ♥ ♣♥ ♦ s t♦♥ rs♣♦♥s ♦ ♦s

ttr♥s♠ss♦♥ s♣tr♠ ♦r µ♠ ♦ ♦ ♣t♦♥ ♠tr ♠tr s♥stt② t♦ ❱ ♣r♦t♦♥s ①♣r♠♥t st♣ ♦r t rrt♦♥ tst ♦ t ♦♥♥ s♥s♦r ♦r s♣

♣♣t♦♥s ♥trt s♥s♦r rs♣♦♥s ♥ ♠① r♦♥ ♦ ♥trt s♥s♦r rs♣♦♥s ♥ t ❱ ♣r♦t♦♥s ♦ ♣r♦t♦t②♣ ♦ ♥ ♥trt s♥s♦r t t tr ♠ ♦ t ♥trt s♥s♦r ♦♣ t P s♠t♦♥ ♦r t ♦t♣t ♦ t ♥trt s♥s♦r ♥stt② ♦ t ♥trt s♥s♦r ♣r♦t♦t②♣ t♦ ❱p tr

❳r②s t♦♥ r♥ss tsts ♦ ♣♦t♦♦s s ♦r t s♥s♦rs t♦♥ r♥ss tsts ♦ s s ♦r t s♥s♦rs t♦♥ r♥ss tsts ♦r t ♣t① P♦r ♥

sP ♥ rs ♦r t ♥♥♥ ♠♣♦② t ♥stt② t♦ ❯❱ t ♦ t s♥st s ♦♥ ♣♦

t♦♦s Pr♦t♦t②♣ ♦ t♠ s②st♠ s♥ ♦r t ♠♦♥t♦r♥ ♥ P

ts t♦♥♥ tt♥t♦♥ ♥ t ♦♣t r s ♦r t rt♠

t♠ ♠sr♠♥ts ♥ t rt♦r P♦ts ♦ t ♥tr♦♥ r♦ssst♦♥ ♦ ♥trst ♦r ♠trs ♠♣s ♦ ♠trs ①♣r♠♥t t② ♦r ♥tr♦♥ rrt♦♥ ♦ ♠trs rst rrt♦♥ ♦r ♥tr♦♥s♥st s ♠♠ s s♠♣s rrt ♥ t ♥ rt♦r

❯

♦♠♣♠♥tr② rrt♦♥s ♦r ♥tr♦♥s♥st s s♠♣s ♣r♣r ♦♥ t ♥ ♠tr

②♦t ♦ t ♥ ts t t P rt♦r ♥t♥st② ♦ t ❱ ♣r♦t♦♥ ♠ r t♦ ♦r t rr

t♦♥ tst t♦♥ ♠sr♠♥ts r♥ t rst rrt♦♥ r♥ ♦♥t r♦ s♠t♦♥s ♦r ♦♣rt t Pr♠r② ♠ t♦♥ ♠sr♠♥ts r♥ t s♦♥ rrt♦♥ r♥ ♥stt② rt♦ ♦r s ♥ r♥ t s♦♥

rrt♦♥ r♥

♥trt s♥s♦r rrr ♦r t ①♣r♠♥ts Pr♦t♦t②♣s ♦ t rt♦♥ ♠♦♥t♦r ♦r s ♥ t t♥♥ t ♥rr♦♥ rs

♥ ♦♥ t r♥ s

s ②♦t ♦r s ♥ t st♦♥ ♥ ♣r♦r

st ♦ s

①♠♠ ♦ss ♥ ♥s ♥s ♥♥ ♦ss ♥ ♥s ♥s ♦s ♥ ♥ st♠t♦♥s ♥ t stt♦rs ♦ ♥

rtrsts ♦ t r♦♠ ♠s ♥ ♥r rt♦♥s s ♦r ♥tr♦♥♥ ♠sr♠♥ts ♠♠r② ♦ t ♣r♦♣rts ♦ ♣ss ♦s♠trs s ♦r ♠sr♠♥ts s ♣r♦♣rts ♦ 2 ♥ r

s♦r ♦s t♦rs ♥ t r♦♠ t ♣rt s♣tr

♦s♠trs ♥stt ♦r ts tss ♦r tr♦♥ s♥stts ♦ r s tr♦♥ s♥stts ♦ r s ♥♥s ♦ t ♣rt ①♣t ♥tr♦♥s ♥ ♦rr rt♦♥ r♦♠

♠♠r② ♦ t s♦r♦♥ ♥♥♥ tst ♦♥ t ♥t s Pr♠trs ♦ t rt♦♥♥ ts ♥ ①trt r♦♠ t

s♦r♦♥ ♥♥♥ tst ♥②t t♦♥s ♦ t rt♦♥ tr♥s♣♦rt rtrsts ♦r t

♣♥

P❲ ♦s ♦r t sts rr ♦t t P❲ s♥stts ♥ ②♥♠ r♥s t r♥t ♥t♦♥ s ♥ ♣r♠trs ♦ ♥ ♦s ♠♠r② ♦ t ♣r♦r♠♥s ♦ s♥stt② ♦rrs s♦♥

♦s

t s♥stt② ♦ s t♦ ♥tr♦♥s ♣tr ♦♠♣♦st♦♥ ♥ t ♥ ♥ ♥tr♦♥ ts

♦t♦♥ ♦ tst s ♥ t♦r r♥s ♦r t rt♦♥ t②♣s ♥ ♥rs ♦ t

t② t P

s ②♣ Pr♦r♠♥t ♣t♦♥st ♦♦♠ ♠♣rtr

s ②♣ ❯❨ Pr♦r♠♥t ♣t♦♥s t♦♦♠ ♠♣rtr

st ♦ ♣t♦♥s

st ♥ rrs r♦♥♦♦ ♦rr

♦tt sr ♦s♥ r ♦♠s ♥ rr②r♦st♦♥ ♦♥t♦r♥ ♥ ① ♥r♦♥♠♥ts t r♦♠ t t② t♦ t ①♣r♠♥ts P♣r P t♦ ♣rs♥t t t t♦♥ts ♦♥ ♦♠♣♦♥♥ts ♥ ②st♠ ❲♦rs♦♣ t♥s r♣t♠r s♦ ♥ Pr♣r♥t ♦t♦♥s PP st

t sr s♥♦ ♦ P ♦tt♣t♠③t♦♥ ♦ t♦♥ ♦♥t♦r♥ ♥s♦rs ♦r t ①♣r♠♥ts ♠t♦♥ ♥ ①♣r♠♥t ❱t♦♥ P♣r P t♦ ♣rs♥t t t t♦♥ ts ♦♥ ♦♠♣♦♥♥ts ♥ ②st♠ ❲♦rs♦♣ t♥s r ♣t♠r

r♥♥③r♥♥③ rr r♠♥s t③♣tr s ❱é ss s♦♥ ♦tt ♥ srt♠ r ♦♣t rt♦♥ ♦s♠trs ♦r ♥r ♥r♦♥♠♥t ♠♦♥t♦r♥r♦♥ tr♠♦♥r rt♦rs P♣r s♠tt ♦r ♣t♦♥ ♥ s♦♥ ♥♥r♥ ♥ s♥

♦tt sr ♥é ss rr②r♦sPrt♦♥ ♦ t r♠ ♥♥♥ ♦ ① t①♠♦♥t♦r♦s♠trs rrt ♥ rs t♦♥ ♥r♦♥♠♥t ♣♣ P②ss ttrs ♦ st

sr ♦tt ♥ ♦♦s♠tr② ssss♠♥ts ♥ t rrt♦♥ ts t t P rt♦rP♣r ♣rs♥t t t th r♦♣♥ ♦♥r♥ ♦♥ t♦♥ ♥ ts ts ♦♥♦♠♣♦♥♥ts ♥ ②st♠s ♣ r♥ ♣t♠r r♥s ♦ ♣♣

❱é ♦tt P r sr ts r ♦ ♦rèr P t② ♥é ♥ ss♥♥ ♦s♠tr② s ♦♥ ♣t② t♠t ♠♥s♥ trs P♣r

P❯

♣rs♥t t t r ♥ ♣ t♦♥ ts ♦♥r♥ tt ❯ ② r♥s ♦ ♣♣

♦tt sr ♦ ♥r ♠♥③ ♥ ♦♠ss♣♦♥s ♦ ♦s♠trs t♦ ♥s ♦ st tr♦♥s ♥ r♥ ②♠♣♦s♠ ♦♥r♥ ♦r t♦ ❱♦♠ ♦♠ t② t♦r ♣♣ r♥s ♦ ♣♣

♦tt sr r ❱é Pr♦st ♥ ss♣t② t♠t ♠♥s♥ trs ♦r ❲s♣tr♠ tr♦♥ sr♠♥t t ♥ Pr♦ ❲♦rs♦♣ r ♣♥ ♣t♠r ♣♣ r♥s ♦ ♣♣

♦tt sr ♦ r ❱é Pr♦st ♥ ss♦♥♣t♦♥ ♦ ♥ ♥trt s♥s♦r ♦r t rt♦♥ ♠♦♥t♦r♥ ♦ t ①♣r♠♥t t t r r♦♥ ♦r P♣r ♣rs♥t t t r ♥♣ t♦♥ ts ♦♥r♥ t♥t ❯ ② r♥s ♦ ♣♣

r♥♥③r♥♥♦ sr ♥r ♣rs♦♥ Prtr ♦tt t♦♥ ss♠s ❲♦r♠ t♦♥ ♦♥t♦r♥ ②st♠ ♦r t ①♣r♠♥ts ♥ ①♣r♠♥t rs ♥ Pr♦ ❲♦rs♦♣ r♠♣s r♥ ② ♦ ♦t

♦tt sr ♥ ♦♥s♦r t♦ t ♦♠♣t♦♥ ♦ ♦stt ♥s♦rs ♦r t♦♥ ♦♥t♦r♥ ♦t ② ♦ ❬♥♥❪ r♥①♣tr♠♦♥

tr ♦♥trt♦♥s t♦ ♦♥r♥s ♥ ♦rs♦♣s

♦ ♦tt P ♣r s♥♦ sr♠t♦♥ ♦r rt♦♥ r♦♥ ♦♣t♠③t♦♥ ♦ ♠♦♥t♦r♥ tt♦rs♥ ①♣r♠♥t t♦♥ P♣r ♣rs♥t t t ♦♠♣t♥ ♥ ♥r②♥ r P②ss ♦♥r♥ P ♠ ♥ rr②

♣r sr ♦ P ♦tt ♠t♦♥ ♦ P♥ ♦r ♦tt t♦♥ ♦♥t♦r♥ ♥s♦rs ♥ Pr♦ ♦ t P❱ ❲♦rs♦♣ ♥ ♠ t♦r

♥♦♠♥ts

rst ♦ t♦ ①♣rss ♠② t♥s t♦ Pr♦ r♥t ss ❯♥rst② ♦♥t♣r ♥ t♦ r ♦ ♦r s♣rs♥ ts tss ♦r ♥ tr♦♥t♥♦s s♣♣♦rt ♥ ♥♦r♠♥t

r② s♣ t♥ ♦s t♦ ♠② ♦ss ♦ t rst ♦ r♥ rsr t♦ t ♣r t♦ ♦r t r♥ t st ♦r ②rs s♣♥t t ♥ ♣s♥t ♦r♥ t♠♦s♣r s tss ♦r s ♦r♥ s ♦♦r ②②② ♦♦rt♦♥ ♥ t ♦rt♦r② ♦ ♥ ❲t s ♦♥t♦s ♥tss♠ s ♥ ♠② tr ♥ sr ♦♠♥s ♦ t ♣♣ s♥s s s ♥t r②② ❲t ♠ t ♣sr t♦ sr ♦♦ ♠♦♠♥ts s s t t ♦♥s ♥ s ♥ ②s ♦ ♦♦ t♦ ♠ r ♦♣ r

♠ rt t♦ t r♦♣s ♥ P ♥ t ♣rs♦♥s ♦ t t♦r♦♣ rs ♠♠♥ ss♠s ♥ rst♥ ♦r♠ ② r ②s ♦♥♥t ♥♠② tss ♣r♦t ♥ ♦st ♠ t♥ tr t♠s r ♦♥ r♥② ♥♦♦♣rt♥ t♠♦s♣r ♥ ♣rtr ♦ t♦ t♥ rst♦♣ ♥r ♥♠♦s ♥♥r Prr♦t ♦ t r♦♣ ♥ ♥ ♥t♦♥♥ r♥♦s r♦♠ t P ♦♥♥ ♦r tr s♣♣♦rt ♥ ♣r♣r♥ t ♥trt rrrs

r r ♠♥② ♣♦♣ t♦t ♦♠ ts ♦r ♦ ♥♦t ♥ ♣♦ss t♦ t♥ t ♣♦♣ tt ♣r♦ rrt♦♥ ts tst s♠♣s ♦r rrtt♠ ♠♦♥ t♠ ♠② s♣ t♥s ♦ t♦ ♦r ♥ r♦ ❱♦ ♥r♦♥ r ♦rt♦♥ ❯ ❲♦t s ♥ ♦r r♥ P r♦ ♦♥ r s t♦ t♥ s♦ t ♦s ♦ Pr t♥s P♦s♣P❯ r♥♦ ♦♣♦ ♥ ♦r ❯ ♦r♦r t♦ t♥ t♥♥ ♦r t sss♦♥s ♦t ♣rts ♥r② ♣♦st♦♥ ♥ s♦♥ ♥s♦♥ ♦①

♠ rt t♦ ♣r♦rs ♥ s♣② t♦ ♥t♦② ♦s♥ ♥ r ❯♥rst② ♦ ❲♦♦♥♦♥ érr rr②r♦s ♦rt ♦♥t♥♦s sss♦♥s ♦♥ t ♣②ss ♥ ♦♥ t ♣r♦t♦♥ ♣r♦ss ♦ s♦♠ ♦t ♣♥ ♦s ♥ t ♦s♠trs ♠♣♦② ♥ ts st② ♠ s♣②rt t♦ ♥r ♦♠s ♦r s ♦♥t♥♦s ♣ ♥ t s ♦ trt♦♥ ts ♥ tr♦♥s ♥ s♦ ♦r t ♣t♥ ♠♦♥strt ♥ ♦rrt♥

❲

♠② ♥s ♠♥sr♣ts

♠ ♥t t♦ ♠♥② r♥s ♥ ♦s ♦ t éq♣ tr♦♥q t ②♦♥♥♠♥ts ♦ t 2 ❯♥rst② ♦♥t♣r r t ♠trs tst♥ ts tss ♦r ♥ ♠♥tr t ♥♦ ♠ r♦♠ ♥♥t♦♥ ♥ r ♥② t♥s ♦ s♦ t♦ rr ♥é ♦r s ♣ t t♥tr♣rtt♦♥ ♦ t s♦r♦♥ ♥♥♥ t ♦r t s

♠ s♦ rt t♦ Pr♦ Pr♦ rt r♥ P♦②t♥ tt ♥ tr t♥ ♦ ♠② ♣r♦t t ♦♥t♥♦s② ♦♦ ♠ r♥ t ②rs ♦ P♥ ②s ♥ ♦ ♦♦ t♦ ♠

s♣ t♥ ♦s t♦ t ♥♦♥♠ r♥s tt ♠t r♥ ♠②st② ♥ ♥ t♣♥ P♣♣ ❱♥♥③♦ ♠♥ ❱tt♦r♦ rt ♦rtstr ♦♥ ① t♦ t P r♥s s♣♣ ♦rs r♥♥ srt♥♦ rt♦ ♥ t♦ ♠② ♥r ♦r♥♦s r♥s ss♥r♦ ♥r ♥♥t♦♥♦ s♣t t st♥ s♣rt s t② st r♣rs♥t ♠② st r♥s❲t♦t t ♦♥t♥♦s s♣♣♦rt ♥ ♥♦r♠♥t ♦ ♠② ♠② ♦ ♥♦trr r rt t♦t ♦s t♦ ❱♠ tt s r② ♦s t♦ ♠ ♥ t rst②rs ♦ ♠② st② ♥ ♥ ♥ ♥♦ ♠ sr s s ♦♥t♥♥ t♦ ♦♦ ♠ r♦♠ t s②

♦ t♦ ♦♥ ts tss ② ①♣rss♥ ♠② rtt t♦ ♦r♦t ♥tr♥ ♠② ♦♥② ♠♦♥ts ♦ t s ♠♠t② ♠ t ♣♦r t♦ s♦♠♠♣♦rt♥t s♦♥s ♥ s♦ t ♥r② t♦ r♥ ts ♦r t♦ t ♥ ♥ t st ♣♦ss② r③♦ ♦t

♦r♣②

❬♦❪ ♦st♦ tr ♦♥s t t② ♦r tst ♦ rr ♠♦♥ ♠rs t rts ♥str t ♥ P②ss sr

❬❪ s ts② r♠♣ r♦♥ ♦srtrsts ♦ ♥r② ♥tr♦♥s ♦r rt♦♥ ♠ t♦♥ ♦s♦♥ s♠♦♥t♦r s t P②ss ♥ t♦♥ tsPr♣r♥t P

❬❪ ♥ Pr♦♣♦s P

❬❪ s♦♥ ♣♦st♦s t ♥t ♦♣♠♥ts ♥ ♣♣t♦♥s r♥st♦♥s ♦♥ r ♥

❬♥t❪ ❲ ♥tr♣ ❨♦♥♦♦ t ♥ ♠sr s♣♠♥t ♠♥ s♦♥ ♦r ♠♦♥♦♥rt ♥tr♦♥s r♥st♦♥s ♦♥ r ♥

❬s❪ s♦♠ ♦r♥ tr tr♦♥ ♦s♠tr② P ♦rr r♠ t♦♥ rt♦r ♦rt♦r②

❬❪ ♦♠♠tt t♥r ♣rt ♦r rtr③♥ ♥tr♦♥ ♥ s♣tr ♥ tr♠s ♦ ♥ q♥t ♠♦♥♦♥rt ♥tr♦♥ ♥ ♦r rt♦♥r♥ss tst♥ ♦ tr♦♥s rs♦♥

❬❪ ♥ s♥ ♣♦rt ♥

❬❪ ♦♥ ♥ rs Pr♦r♠♥ ♦ r♥ ♣ s♥ sr ♥tr♦♥ ♥r♦♥♠♥ts r♥st♦♥s ♦♥ r ♥

❬❪ st st♠t♥ ♥ r♥ rr♦rs ♥ ♦s♠trs s② ①♣♦sr t♦ r♥t rt♦♥s r♥st♦♥s ♦♥ r ♥

❬❪ rt♦rr♦♥s ① ♠sr♠♥t ♦ r♦♥s s♥ tt♦♥ ♠t♦st trt r ♥ t rrt♦♥ t② ♣♦♠ tss ❯♥rstt P♦t♥ t♥② r♦♥ ♣♥

P❨

❬❪ s Pr♦t♦♥ ♦sss ♥ t s♣rs♦♥ s♣♣rss♦rs ♦ ♥ ♦ Pr♦t♦t

❬❪ s♥s ♥ P ♦♥③♥ rt♦♥ ♠ ♥r tr♥sst♦r♥♥ s r♥st♦♥s ♦♥ r ♥

❬r❪ r♥♦ ♦s♠♥ s♦♥ ❱ r st ♥ ♣st♠t♦♥ ♦ t♦♥ r♦♥ ♠♣t ♦♥ tt♦rs tt♦♥ ♥♥ ♣t♠③t♦♥ ♥

❬r❪ r♥r r♦ t③♥ r♦♥♥ ❱ P♥♦ t♥s♦♥ r ♥ ss♠s rt♦♥ ♦ ♦♥r②♠ss♦♥ ♦♥t♦rs ♦ s♦t Pr♦t♦♥ ♠ ♥t♥st② ♥ t P♦rt r ❨♦ ♣♦rt

❬r❪ r♥r ♦ ♥s r♦♥ ré♦r ré♦r❱ r♥ ♥ ♥t♥s st ♥tr♦♥ ♠ ♥ ♦♥ tt♣②♥t♠s♠s

❬♦❪ ❱ ♦rsr ♣r♦♣rts ♦♦♥ ❱ ② ♦♥ tr♦♥ ♥♥tr♦♥ rrt♦♥s ♥ Pr♦ ♣♣t♦♥ ♦ rt♦rs ♥ rsr ♥♥str② P ♣rss ❨♦r ♣s

❬❪ ♠rs ♦ttr ♦♠s ♠s ♣ ♦s♠trs ♦♥tr♠ ♥♥♥ ♥ ♥tr♦♥ rs♣♦♥s r♥st♦♥s ♦♥ r ♥

❬♦♦❪ ♦♦♥ P ♥ ♣♣rs rt♥s ♥s ♥ rs st ♣♥t♦♠ ♦s♠tr② ♦r s♥♥♥ ♣r♦t♦♥ ♠s P②ss

❬♣❪ P❲ s♦♥ ♣♥ ♣♦t♦♦ tst ♦♥♥ r♦♠ ♣t♦♠♦♥t♦rs tt♣♦sr♠♦s♦♠

❬r❪ rr r♦♥♥r ♥ ♥t♥r ts ♦ ♣ ♦♠tr②♠trs ♥ s♥ ♦♥ ♥r② ♣♥♥ ♦ ♣ ♦s♠trs r♥st♦♥s ♦♥ r ♥

❬❪ r s ♦ ♥ r♦ ♥♣ ♣♦s♠tr② r♥st♦♥s ♦♥ r ♥

❬♠❪ ♠♥③ ♦♠s ♥ ♠② ♦s ♠♣♣♥s②st♠ ♦r t tr♦♠♥t ♦r♠tr ♦ t r ①♣r♠♥t t ♥str t ♥ P②ss sr

❬♠❪ ♠♥③ sr ss♠s ♠s st② ♦♥ t ♣♣t②♦ s♦ stt rt♠ ♦s♠trs t♦ t ①♣r♠♥t t t r r♦♥♦r ♥str t ♥ P②ss sr

P❨

❬♣❪ ♣r t ♦ sr P ♦tt ♠t♦♥♦r t♦♥ r♦♥ ♣t♠③t♦♥ ♦ ♠♦♥t♦r♥ tt♦rs ♥①♣r♠♥t t♦♥ ♥ Pr♦ ♦♠♣t♥ ♥ ♥r② ♥ rP②ss P ♠ ♥ rr②

❬r❪ r♦♥ ♠♦♥t♦r ♦s♠tr② ♦ ♣tr♠ ♥tr♦♥ ♠ ♦r ♦r♦♥♥tr♦♥ ♣tr tr♣② P tss ❯♥rst② ♦ ❲♦♦♥♦♥ str

❬❪ ♥ s♥ ♣♦rt ❱♦

❬❪ r♠s tr♥♥♦s ♦ Prt ① ♠sr♠♥t ttt♦♥ tt♦rs P t P②ss ②

❬❪ rs t ♦♥sst♥t st ♦ ♥tr♦♥ r♠♦♥ts r♦♠ tr♠ t♦ ❱ ♦r ♦♦② ♠♣♦rt♥t ♠trs P②ss

❬❪ ♥ ♥ ❲ r ♦r② ♦ tr♠♦♠♥s♥ ♥ rt♣♥♦♠♥ ❲♦r ♥t Ps♥ ♦

❬❪ ♥ Pr♦♣♦s

❬♦❪ ♦♦rt♦♥ ♠t♦♥ ♦♦t ♥str t ♥ P②ss sr

❬♦♥❪ ♦♥♥① ♦♥r t P ③♠ ♦♠♣rs♦♥ ♦♦s ♦s♠tr② s②st♠s ♦r rt♦♥ ♠ sts ♥ ♦r tt♦rs♥ rt♦rs ♥str t ♥ P②ss sr

❬♦♥❪ ♦♥♥ r ❲ ♥ ♠s t s ♦r ♥rs rt♦♥ s♥stt② r♥st♦♥s ♦♥ r ♥

❬♦♥❪ ♦♥♥② ♦♥♥ P r② ❲ ♥ ♠s trts ♦r♠r s♥stt② ♥ P ♦s♠trs r♥st♦♥s ♦♥ r♥

❬♦♥❪ ♦♥♥ ♦♥♥② rt② ♦② ❲ ♥ ♥ ♠str ♣r♦r♠♥s ♥ rt♦♥ s♥stt② ♦ st P ♦s♠trs♥r s ♦♥tr♦ r♥st♦♥s ♦♥ r ♥

❬♦♥❪ ♦♥♥ rt② ♥ ♦♠♠③ ♣t♠③st s ♦r ♠r ♦s ♠sr♠♥t ♥ Pr♦ t♦♥ ts ♥ ♦♠♣♦♥♥ts ♥ ②st♠s ♦♥r♥ t♦ ♦♥tr r♥ ♣t♠r ♣s

P❨

❬♦r❪ ♦rtt ♥ ♦r♦♥ t rt♦♥ ♥ s♠♦♥t♦rs ♥ P♦♥t ts♥ s♦s ❱♦ ♠♦♥t♦rs ♥ ♠♦r r②sts r♦r ♥ ♥ P♥♠ Prss ❨♦r rst t♦♥

❬♦r❪ ♦rt ♥ t♠♥ t♦♥ r♦♥ ♥ t ①♣r♠♥t♦t

❬♦r❪ ♦r♥s ♥ ♦s♥ ❱rt♦♥ ♦ ♦♥t r♦ t♦♥s ♥st♥tr♦♥ tr♣② s♥ s♦♥ ♠r♦♦s♠tr② r♥st♦♥s ♦♥r ♥

❬♥❪ ♥♥♠ r ♦r ♥ts t s♦t ♣t♦♥s ♥ r ss♥r♥srs ♦♠♥t♠ ♥ ♣ ♦s♦♥s t P tss ❯♥rst② ♦♠r ❨

❬❪ s♦♥ ♥ ttr rt♦♥ ♥r♦♥♠♥t ♥ t ♥♥rtt♦r ♥str t ♥ P②ss sr

❬❪ ♥♦ ♥ rrr ♥rs ♥ ♠ts♦♥♦①s♦♥ strtrs P②s ♠ ♦s

❬♠❪ ♠♦s ♦t ♦s sts ♦ ♥ q♣♠♥t ♦r t Prs♥tt♦♥ ♥ t t t ❲P ♦♠r ♦♥♥ tt♣r♥r

❬r❪ P rss♥♦rr ♥ P ♦♥③♥ rt♦♥ ts ♥ s ♥rts ❲② ♥trs♥ ❳

❬♠❪ ♠♥♦ r♥ ❯ ♥ ②♥ P r♥ st ♥②s ②s ♦ ♦♥② P r♦ ♦ ❨ ♥ ♥♥t P♦t♦③ ♠t r♥ ♥ ❩②r t♦♥r♥ss sts ♦ − ♦♥t♥t qrt③ rs rrt t tr♦♥s ♥str t ♥ P②ss sr

❬s❪ ss t s ♣♦t♥ttés s ♣é♥♦♠è♥s ♠♥s♥ ♣rst♠t♦♥ ♦♣tq ♥s s srs ♥♦trr① ♣♣t♦♥ à rést♦♥ ♥ tr ♣♦rt ♦s♠ètrs P tss ❯♥rst②♦♥t♣r r♥

❬s❪ ss ♥♦♣ r♠♣ ♦② ♥é sqt s♦t ♦t Prt♦♥ ♦ ♦ ♦srt ts ♥ ♣♦r ♠t ♦①s♠♦♥t♦r t tr♥sst♦rs s ♦♥ s♦r♦♥ ♥♥♥ ♠sr♠♥ts ♣♣ P②s

❬s❪ ss P♦ ts ❱é r♠♥s r♦ ♠♥③ sr ♥é sqt s♦t ♥r② ♣rtrrt♦♥ ♦ ♦♣t② st♠t ♠♥s♥t ♠s t r♥st♦♥s ♦♥ r ♥

P❨

❬s❪ ss s ♥s♠s ♥ ♣ ♥♦♦② ♦rs ♦♦s ♥

❬s❪ ss s♦t ♥♥ ♥ rt♠ ♦s♠tr② s♥ ♦♣t② st♠t ♠♥s♥ ♥t ♦ ♣ t ♥ ②st

❬❪ ♥ ♥ ❲t♥s ts ♥ rrt s♦♥ tr♦♥ ♣r♠♥t rs♦♥♥ ♥ tr♦♥♥r ♦ rs♦♥♥ ♦ t rs♥ ♥♥t♠♦♥②♥② ♣rs P②s

❬♣❪ P♦r ♥sP tst ♦♥♥ r♦♠♣t① ♥ tt♣♣t①♦♠

❬①❪ ❳ rr② ♦ ①♣r♠♥t ♥r rt♦♥ t s r t r tt♣♥s♦r

❬❪ ♦ r t♦♥♥ ts ♥ ♣ s♠r♦♥ tr♥sst♦rs r♥st♦♥s ♦♥ r ♥

❬s❪ ssó rrr ♥t P ❯ tts ♥ Pr♦s♣t ♦rr♦♥ ♣♣t♦♥s ♥ Pr♦ ♦ t ♦♥t r♦ ♦♥r♥ s♦♥t♦r ♣r♥r❱r r♥ ♣s

❬❪ t♦♦ P ❲♥♦r r s♥♠r ♥ ♥②t ts ♦ ♦① tr♣s ♥tr tr♣s♥ ♦rr tr♣s ♦♥ ♠t♦① s♠♦♥t♦r s ♣♣ P②s

❬❪ t♦♦ ❲ ❲rr♥ P ❲♥♦r s♥♠r ♥ ♥②t ts ♦ ♥tr tr♣s ♥ ♦rrtr♣s ♦♥ ♣♦strrt♦♥ ♥♥♥ rs♣♦♥s r♥st♦♥s ♦♥r ♥

❬❪ rst♥r P ♥ ♥♥ ♦s♠trs Prs♥tt♦♥ ♥ tt t ❲P ♠r ♦♥♥ tt♣r♥r

❬r❪ rtt ♥♦♦ ♦ r♠♦♠♥s♥ ❲♦r ♥t Ps♥♦ rst t♦♥

❬②♥❪ ②♥♦ ♥ t♥s♦♥ t♦♥ ♥r♦♥♠♥t ♥ t s♣rs♦♥ ♣♣rss♦r r♦♥s ♦ ♥ ♦ t Pr♦t♦t

❬❪ r♦♠ ♦r♦♠ ♦s♠tr ♠s ② P ♥♦♦② ❲②♥ ❯ ♦♥♥ tt♣s♣♦r♣♦♠

P❨

❬❪ ♥ ❲ ♠ Pr♦♣rts ♦ ② rrt s r♥st♦♥s ♦♥ r ♥

❬③❪ ③ r sr♦ sr♦ ❨♦r ♥rs♥ ③♥r r♠♥♥ ♥ ø♦ttr♥s♥ r♦s♠tr② ♠t♦s ♦♥ r♦♠ 2O3 ♦r r♦tr♣② ♣♣t♦♥s t♦♥ sr♠♥ts

❬s❪ ss♥ ♥ rr②r♦s tr♥sst♦rs t > µ♠ t t ♦① ♦r ♦♥③♥ rt♦♥ ♦s♠tr② ♥ Pr♦ t s ♦ ②♠♣

❬❪ rt♦♥ r♥ss sss ♦r t ♥①t ♥rt♦♥ ♦ rt♦rs ♥ ①♣r♠♥ts ♥ s♦rt ♦rs ♥♦t♦♦ ♥s ♦r rt♦♥ t♦r♥ ssss♠♥ts

❬❪ sr r ♠r t r♦② P ♦② rrt♦♥ ③♦♥s t t P ♥str t ♥ P②ss sr

❬❪ sr ♠r t t♦♥ st ts ♥ t P st t r♥st♦♥s ♦♥ r ♥

❬♦❪ ♦ts ♦♣♠♥ts ♥ ♦♥ tt♦rs ♥ tr ♠♣t♦♥ P②ss sr♠♥ts P tss ❯♥rst② ♦ s♦

❬r❪ P r♥ t t♦♥ ♦rt♦rs ♦ ♥tr♦♥ r♦ss st♦♥s t♥ r♦♠ ❱ s♦tt♣ss♠s②♠♠rs♥♥r♥st♠

❬r♦❪ r♦♦♠ t Prt t r♦♣ ♦ Prt P②ss PPr P②s

❬❪ ❲ s rr r♦♦r♥s♥ ♥ r♥♦ t♦♥ ts st♥ ts ♥ P r♥ ♠♣♠♥tt♦♥ ♦ t Pr♦s♥Pr♦t ♥ Pr♦ t♦♥ ts t ❲♦rs♦♣ ♣s

❬♠❪ P♦t♦tt♦rs tsts ♦♥♥ r♦♠ ❯ ♣♦t♦♥s♣r♦ts ♣ tt♣ss♠♠ts♦♠♥♣r♦ts♣♣

❬r❪ r♥ s ② ♥ r ♠♣rtr ts ♥ ♦♥ tr♠ ♥ ♦ ♠♣♥t ♥ ♥♠♣♥t t ♦①s r♥st♦♥s ♦♥ r ♥

❬❪ ♥ ♥stt♦♥ ♦♥ ♣♦t♦♦s ♦r st ♣rt ♦s♠tr② ♠♠r t♥t Pr♦t P

P❨

❬r❪ r♥♥③ r♥♥♦ ♦♣♠♥t ♦ ♠ ♦♥t♦♥ ♦♥t♦r s②st♠♦r t ①♣r♠♥t rs ♦ t s♥ ❱ ♠♦♥ P tss ♦P♦②t♥q r s♥♥ t③r♥ s

❬♦❪ ♦♠s s♣r ♦s♠tr ♥r ♣r♥♣s ♦ ♥ ♠t♦ ♦ rt♦♥ tt♦♥ ♥str t ♥ P②ss sr

❬♦❪ ♦♠s ♥ ♠s ♠♥s♠ ♦ s♠ ♥stts♥ rrt r♥sst♦rs r♥st♦♥s ♦♥ r ♥

❬♦❪ ♦♠s ♠s P② ♥ rs♥ ♥rt② ♦ ♣rt♦♥ ♦s♠trs ♦♣rt t ③r♦ s t tt

❬♦❪ ♦♠s ♥ ♠s r ♦ t s ♦ ♠t♦①s♦♥s s ♥trt♥ ♦s♠trs t P②s ♠

❬♦❪ ♦♠s ♠s ♥ ♥s ♦s♠trs ♠♣r♦♠♥t♦ rs♣♦♥st② ♦s♠étrs ♠é♦rt♦♥ r♣♦♥st ♥ Pr♦ t♦♥ ts ♥ ♦♠♣♦♥♥ts ♥ ②st♠s ♦♥r♥ t♦ ♦♥t♣r r♥ ♣t♠r ♣s

❬♦❪ ♦♠s ♥ ♠s ♥♦♦ ♦ t♦♥ ts ①♦r ❯♥rst② Prss s♦♥ t♦♥ ❳

❬❪ P♦t♦♥ ♠ss tt♥t♦♥ ♥ ♥r② s♦r♣t♦♥ ♦♥tsr♦♠ ❱ t♦ ❱ ♥t ♣♣ t s♦t

❬❪ s P r♥ss ♥ t♥ ♦ tr♥s♣♦rt ♥ ♦①s r♥st♦♥s ♦♥ r ♥

❬❪ s ♦r② ♦ rs♣♦♥s ♦ rt♦♥ s♥s♥ t r♥sst♦rs ♣♣ P②s

❬❪ s ♦r② ♦ rs♣♦♥s ♦ rt♦♥ s♥s♥ t r♥sst♦rs♥ ③r♦ s ♦♣rt♦♥ ♣♣ P②s

❬❪ t♥♥ ♥ P r♥♦ st♠t♦♥ ♦ ♣♦♥ ♥ s♣♠♥t ♠♥ s♦♥ ❯

❬❪ t♥♥ ♥ Pr♥♦ P♦♥ ♥ s♣♠♥t ♠ ♥ s♦♥s ♥str t ♥ P②ss sr

❬❪ t♥♥ t♦♥ ♥r♦♥♠♥t ♠t♦♥s ♦r t tt♦r ♦t

❬❪ t♥♥ ♥ ♦ ♦♠♣tt♦♥ ♠t♦ t♦ st♠t ♥ ♥t❯♣st rts ♥ ♥ rt♦r ♥r♦♥♠♥t ♥str t ♥ P②sssr

P❨

❬❪ t♥♥ t♦♥ ♥r♦♥♠♥t ♥ ①♣r♠♥t r Prs♥tt♦♥ ♥ t t t♦♥ ts ♦rs ♣r

❬r❪ r é♦♣♣♠♥t ♥ s②stè♠ rt♦r♣ ♣r ♠♥s♥ st♠é ♦♣tq♠♥t ♣♣t♦♥s ① ♦♥trôs s trt♠♥ts ♥ r♦tér♣ ♠♦t♦♥ ♥t♥sté t ① ♦♥trôs s s① ♣r♦t♦♥s té♥r P tss ❯♥rst② ♦♦s r♥

❬❪ s st P♦ ♦♠♠③ ♦r ❲ ♥♠♠r② rrt♦♥ ♥ ♣♦strrt♦♥ rs♣♦♥ss ♦ ♦s r♥ s r♥st♦♥s ♦♥ r ♥

❬t❪ ❨ ts♠r ❨ t ♦rst ♦♠ st ♥tr♦♥rrt♦♥ ts ♥stt② ♦ ♥♥ s②st♠s ♦r st ♥tr♦♥ ♥♥ ♥r② ♦ ❱ t P②s ♠

❬❪ r ♥ ②♥ ❲ ♥ ♦♣♠♥t ♦ trt♦♥ s♥stt② ♦ P ♦s♠trs ♥ Pr♦ t♦♥ ts ♥ ♦♠♣♦♥♥ts ♥ ②st♠s ♦♥r♥ t♦ ♦♥t♣r r♥ ♣t♠r ♣s

❬❪ r ♦♥♥ ❲ ♥ t ♦ t♦①♣r♦ss rt♦♥s ♦♥ t ♦♥tr♠ ♥ ♦ ♣ ♦s♠trs ♥s♦rs ♥tt♦rs

❬❪ r ❲ ♥ ♥ ♠s ♥stt♦♥ ♦ ♦♥♣ t♠♣rtr ♥♥♥ ♦ ♣ ♦s♠trs r♥st♦♥s ♦♥ r ♥

❬♠❪ ❨ ♠♦t♦ ♦ss ts♠♦t♦ ♥ ♦ ♦t ♦s rtt ② ♦s♠tr ♦♥♦r ss tt r♥st♦♥s♦♥ r ♥

❬❪ ❱ ss♥ t r♦♠ ♥stt s ♣rs♦♥ ♦s♠tr P②ss

❬♦♥❪ ❨ ♦♥♦② t tr♦♥ s♣♠♥t r♦ssst♦♥s ♦r strtr♠trs ♦ ❱ tr

❬r❪ r♠r s♠♦♥t♦r sttr♦♥ ♦s♠tr ts rtrsts♥ ♣♣t♦♥s r♥st♦♥s ♦♥ r ♥

❬r❪ r♠rr ♦♣♠♥t ♦ t♦♥ ♦♥t♦r Prs♥tt♦♥ ♥ t t ♠t♥ ♦♠r ♦♥♥ tt♣r♥①♣tr♠♦♥

❬r❪ r♠rr ❱ ♥r♦ ♥ ❩rt♥ ♦♥♣ts♥ ♥ ♥t♦♥ ♣t♦♥ ♦ t♦♥ ♦♥t♦r

P❨

❬r❪ rt♦ rtr③t♦♥ ♦ ♥tr♦♥ ① ♥ t ①♣♦sr ♥♥ ♦ t rt♦r ♥ ♥ ♥ Pr♦ r ♥r② ♥ ♥trr♦♣ ♦♥r♥ r♠ t ♦♥ ♣t♠r ♣s

❬r♦❪ r♦♥♥r ♥ rr s ♦ ②r♦♥♦s ♠tr ♦r s♥st③♥ ♣ ♦s♠trs t♦ ♥tr♦♥s r♥st♦♥s ♦♥ r ♥

❬♠❪ ♠r♥ ♥ rr②r♦s ❯♥s ♠t ♦① s♠♦♥t♦r♦♥③♥ rt♦♥ ♦s♠trs t Pr♦t ♦s

❬♦❪ ♦♥♦rá♥ ö♥r ♥ t t ♦♠♣t♦♥ ♦♦s♠tr② ♠t♦s ♥ rt♦♥ s♦rs ♦r ♠tr tst♥

❬♦❪ ♦♥♦rá♥ r♦② ♥ rtt Prt ♥ sr♠♥ts② tt♦♥ ♥q ♦r t♦♥ ♠ ts s♦♥♣♦rt P

❬r❪ r♦② P ♦② t♦♥ ♦ ♣rt ①s ♥ t P s♦♥ ♣r♦t♦♥rrt♦♥ ③♦♥ ❯PP❳P ♥ ♦♦♥ ♣ts

❬❪ ♥ Pr♦♣♦s P

❬♥❪ ❱ ♥ ♥t ♥♥ ♦♥ r ❱♦rs ♥s♠s ♦ t♦♥ ts ♥ tr♦♥ trs ♦♥ ❲② ♦♥s

❬♥❪ ♥strö♠ ♦ rtrst t♦♥ r♥ss ♦ s♦♥ tt♦rs ♥ r♦♠ ♥r② ♣②ss ♥str t ♥ P②sssr

❬s❪ s ♥s ♦♥ ❲ ♥♥rt③ ♥ ❯ ♠t t♦♥ts ♥ t ♠tt♥ ♦s sr ♦s ♣♦t♦♦s ♥ ♦♣t♦♦♣rs♥ Pr♦ ♦♥ r♦♣♥ ♦♥r♥ ♦♥ t♦♥ ♥ ts ts ♦♥ ♦♠♣♦♥♥ts ♥ ②st♠s ♥t♦ r♥ ♣t♠r ♣s

❬❪ ② ♦♠♣s♦♥ ♥ t♥ ♣♣t♦♥s ♦ ♦s♠trs ♦♥ ♥ tts r♥st♦♥s ♦♥ r♥

❬❪ ♥t ❯tst♦♥ ♦s♠ètrs s♠♦♥trs s♠ t♦rs éértrs ♣rts t é♥r

❬♥❪ ♥ ❱ ♥r♦ r♠rr rst♦ ③ ❱rt♥ ❯♥ ♥ ♥♥♦ ♠ ♥ ♥♣♥ ♣♦r r♥sst♦rss ② r♠ tr♦♥s rss Pr♦t♦♥s ♥ st tr♦♥s r♥st♦♥s ♦♥ r ♥

P❨

❬❪ ❲ ♥ t ♦ r♦r♦♠ ♠s ♦r ♥ ♦s♠tr② t Pr♦t ♦s

❬❲❪ P ❲♦rtr ♥ P ❲♥♦r ♠♣ t♥q ♦r s♣rt♥ t ts ♦ ♥tr tr♣s ♥ tr♣♦① r ♥ ♠t♦①s♠♦♥t♦rtr♥sst♦rs ♣♣ P②s tt

❬r❪ r♦ ♥ ♥♦ç t♦♥r♥ss sts ♦ − ♦♥t♥tqrt③ rs rrt t ❱ ♣r♦t♦♥s ♥ Pr♦ th PP ♦♥ ♦♥str♦♣rt ♣rt s♣ tt♦rs ♥ ♠ ♣②ss ♣♣t♦♥s

❬t❪ ③ tr♦♦② ♥sttt ♥s♣t♦rt ♦r ♦♥③♥ t♦♥s t♦♦ ♦t t♥rs s♦ tt♣r♦st♥r③

❬❪ P rs P ① P q Prt st ♥tr♦♥ ②s ♥ s♣trr♦♠ trts ♦ r②♥ t♦♠ ♥♠r ♦♠r t tr♦♥s r♦♠ t♦ ❱ P②s ♦

❬s❪ ss♦s ♦♣ sqt Pr♦st s♦t ♣t② t♠t♠♥s♥ ♦ rrt ♦♣ P♦s♣♦rs r ♦ tt ♥♦r♠ s

❬s❪ ss♦s ♦♥trt♦♥ à ét ♣é♥♦♠♥è ♠♥s♥ ♣r st♠t♦♥ ♦♣tq ♥s sr ♠♥és♠ ♦♣é ér♠ s♠r♠ ♥ ♥ tst♦♥ ♥ ♦s♠étr P tss ❯♥rst② ♦♥t♣r r♥

❬♦❪ ♦ t♦♥ ♠ ♥ s♦♥ ♣rt tt♦rs r♦s♦♣ ts♥ r♦s♦♣ ♣r♦♣rts P tss ❯♥rst② ♦ ♠r r♠♥② ❨

❬♦❪ ♦ rtrst ♥strö♠ rr♥t ♦ r♦♥ rrts♦♥ tt♦rs ♠tr ♣♥♥ ♥str t ♥ P②ss sr

❬♦❪ ♦ rtrst ♥ ♥strö♠ t♦♥ t♥ ♠r♦s♦♣ ts ♥ ♠r♦s♦♣ ♥s ♥ s♦♥ tt♦r ♣r♦♣rts trr♦♥ rrt♦♥ ♥str t ♥ P②ss sr

❬♦r❪ ♦r♥ r♥♦ ♥ P ❩②r♦♠s ❲♥♥ t ♥ ♥sr♥ tr♦♥ ♥s t P ♦♥ ♦s ♥ Pr♦ r r♦♣♥ ♦♥r♥ ♦♥ t♦♥ ♥ ts ts ♦♥ ♦♠♣♦♥♥ts ♥ ②st♠s r♦♥ r♥ ♣t♠r ♣s

❬❪ ❱ rr ♥t♥ t♦♣♣ r♥♥♦ P ♥rt ♦ tttr♦♥ ♦s♠tr ♦r ♣ ♣♣t♦♥s r♥st♦♥s ♦♥ r♥

P❨

❬❪ ♠ ♦♠♥t♦♥ ♦♥ t trs ♦ ② r ♣rts ♥2 ♠s ♣♣ P②s

❬❪ ♠ ♦♥③♥ rt♦♥ ts ♥ ♦①s ❲♦r ♥tPs♥ ♦

❬❪ r P ♦ ♥ ♥tr♦♥ s♣tr♠ ♠sr♠♥ts t t r♠② ♣srt♦♥ t② r♥st♦♥s ♦♥ r ♥

❬sr❪ ♥rr ♠ttrs tsts ♦♥♥ r♦♠ ♣t♦♠♦♥t♦rs tt♣♦sr♠♦s♦♠

❬P❪ Pt ♥ P ❳r② r ♣r♦ ♦r t♦t ♦s tst♥ r♥st♦♥s ♦♥ r ♥

❬Ps❪ Pstr↔á t♦♥ s ♥ Prs♥tt♦♥ ♥ t t ♦r♠ r

❬P❪ Ps ♠♦♥s P rs ♦♠♣rs♦♥ ♦ ♣ t♦t ♦s rs♣♦♥s♦r ♦ ♠♠s ♥ ♥r② ♣r♦t♦♥s r♥st♦♥s ♦♥ r♥

❬P❪ Pttr ♥♦① ss P♦ ❱é s♦t sqt ♦t ♦rrrssrt rtr③t♦♥ ♦ ♥ ♥trt♥s♦r ❯s♥ ♣t② t♠t ♠♥s♥ ♦r ♥t ♦s♠tr② r♥st♦♥s ♦♥ r ♥

❬P♦❪ P♦ ss ts ♥s♥♥ Pttr sqt s♦t t ♣♣t♦♥s t♦ r♦tr♣② ♦ ♦s♠♣♣♥ s②st♠ s♦♥ t ♦♣t② st♠t ♠♥s♥ ♥ Pr♦ ♠♥♦♥r♥ ②♦♥ r♥ t

❬P♦❪ P♦ ❨r sr♦ ♥ r t♠ ♠♥s♥r♦♠ 2O3 r ♦s♠trs t♦♥ sr♠♥ts

❬P♦s❪ P♦s♣s st t ❱ ❱r ♦♠♣rs♦♥ ♦ ♥s ♦ ♥tr♦♥ss ♦♥t♥♥ ♦r♦♥ ♥ t♠ ♥tr♥ ♦t ♦

❬P♦s❪ P♦s♣s t s♦♥ ♦♥ ❱ ♥rt ♥♦r r♦② t ①♣r♠♥t tsts ♦ ♥tr♦♥ s♥ ♥ t ♦rr r♦♥ ♥tr♥ ♦t ♦

❬P♦t❪ P♦ttr ört ♥ t♥s♦♥ ♥ ♠♦♥t♦r♥ ♥ ♥r②str② rt♦♥ s P

❬Pr♦❪ ❩ Pr♦③ ♦ ♥ r♦s ♥tr♣rtt♦♥ ♦ t rs♣♦♥s♦ ♦s♠tr ♦ ♥r

P❨

❬Pr♦❪ ❩ Pr♦③ rt③ ♦♣♦ ♣r♥② ts ♥ t♦s♠tr ♣r♠trs ♦ ♥ ③♦s♦ ♥tr♦♥ s ♦ t Pr♦t♦s

❬P❪ ❱ Pt ♥♦♣ ❨ ❱ss② ♠ Pr♦ ♠♥ rtr P②ss

❬❪ ♦tt st② ♦♥ t rs♣♦♥s ♦ s♦stt ♦s♠trs t♦ s ♦r t♠sr♠♥t ♦ t rt♦♥ ♥r♦♥♠♥t ♦ t ①♣r♠♥t t ♣♦♠ tss r♥ P♦②t♥ ♦r♥♦ t② ♥ t♥

❬❪ ♥ r sr t♦r ♥♠rs ♥

❬❪ ♦tt ♥ sr st② ♦ t rs♣♦♥s ♦ s♦stt ♦s♠trst♦ s ♦r t ♠sr♠♥ts ♦ t rt♦♥ ♥r♦♥♠♥t ♦ t ①♣r♠♥t t t ♦t ②

❬❪ ♦tt t ♦s♠trs Prs♥tt♦♥ ♥ t t t ❲P ♠r ♦♥♥tt♣r♥r

❬❪ ♦tt sr ♦ r ❱é Pr♦st ♥ ss ♦♥♣t♦♥ ♦ ♥ ♥trt ♥s♦r ♦r t t♦♥ ♦♥t♦r♥ ♦t ①♣r♠♥t t t r r♦♥ ♦r r♥st♦♥s ♦♥r ♥

❬❪ ♦tt sr ♥ ♦ ❯ t ♦♠♣t♦♥ ♦ s♦stt s♥s♦rs ♦r rt♦♥ ♠♦♥t♦r♥ ♦t ♦ ②

❬❪ ♦tt sr ♦ ♥r ♠♥③ ♥ ♦♠s s♣♦♥s ♦ ♦s♠trs t♦ ♥s ♦ st tr♦♥s r♥st♦♥s ♦♥ r ♥

❬❪ ♥r t♦♥ r♥ss st② ♦ ♣rt② s♦♥ ♥ t ♦♣♠♥t ♦ rt♦♥ ♠ ♠♦♥t♦r♥ s②st♠ ♦r s♦♥ s ♥ ♠①rt♦♥ P tss ❯♥rst② ♦ ❲♦♦♥♦♥ str

❬♦s❪ ♦s♥ t ♣♥ ♦s t ♠sr♠♥ts r♥ ♦ st♥tr♦♥ ♦s t Pr♦t ♦s

❬♦s❪ ♦s♥ ❱ r ❱ ts t ♥t ♥♦③rr ❯s ♦ ❯r♥♥ s♠♦♥t♦r ♦s♠trs ♥ ♣rtrt♦r r♥st♦♥s ♦♥ r ♥

P❨

❬♦s❪ ♦s♥ r♦♥ ♣♥ ♥ ❱ r ♦s♠trs t r♦ ♦ ♥♣st♦♥ ♦♥ ♦s♠tr rtrst ♥♠①♠♠ ♥tr♦♥ ♥ ♠♦t ①r② r♥st♦♥s ♦♥r ♥

❬♦s❪ ♦s♥ ❨ r ♦r♥s P r♥ ❱ Prrt♦ ♥♦♥ ❩♥ts ❱ r P♥♦s② ① ♥r tr♦♥ ♦s♠tr② t ♣♥r s♦♥ ♣♥ ♦s r♥st♦♥s♦♥ r ♥

❬♦s❪ ♦s♥ Prt ♦♠♠♥t♦♥ t ♦s♥ ❯♥rst② ♦❲♦♦♥♦♥ str

❬❪ ♥é ss sqt s♦t ♦t P r♠♣ ♦② ①♣r♠♥t t♦♥ ♦ ♥ rt ♠t♦♦ ♦①tr♣ rtr③t♦♥ ♦r ♣rt♥ ♦♥ tr♠ tr♠ ts ♥♠t ♦① s♠♦♥t♦r s r♥st♦♥s ♦♥ r ♥

❬❪ ♥é ❯♥ ♥♦ ♣♣r♦ sét♦♥ s ♦♠♣♦s♥ts t②♣ ♣♦r ♥r♦♥♥♠♥t rt s♣t P tss ❯♥rst② ♦♥t♣r r♥

❬❪ ♥é ss sqt s♦t ♦t r♠♣ Prt♦♥ ♦ t ♦♥ ②r tr♠ ♥♥♥ ♦ rrt ♦♠♠r ss ♦♥ ①♣r♠♥t s♦r♦♥ rs r♥st♦♥s ♦♥ r ♥

❬❪ ♥é ss sqt s♦t ♦t r♠♣ ♦② t♦♥ ♦ s t♦t ♦s rs♣♦♥s s♥ t s♦r♦♥♥♥♥ ♠t♦ r♥st♦♥s ♦♥ r ♥

❬r❪ rr②r♦s ♥ ss♥♥ ♦① tr♥sst♦rs ♦r ♦♥③♥rt♦♥ ♦s ♠sr♠♥ts ♦♣r♦tt♦♥

❬r❪ rr②r♦s ♥ s♦s t♦♥ ♦s ♠sr♠♥ts s♥ s ♥st s ♣s

❬r❪ rr②r♦s ♥ ❱ P♦s ♦♥③♥ rt♦♥ ♦s♠trs r♦♠♦ t♦ ♦s ♠sr♠♥t t P②s ♠

❬❪ ❩ ♥♦ P♦ t♦♥♦ ♦♥trt♦♥ ♦♦rr r♣s t♦ t rs♦ ❱♦t t ♥ ♣ ♦s♠tr r♥sst♦rs r♥st♦♥s ♦♥ r ♥

❬❪ r ❲t③♥r ❲sr st ♥tr♦♥ rs♣♦♥s ♦ ♥♥ ♣r♦s ♣♣ t s♦t

P❨

❬❪ ❨ ♥ ❲ ♥ ♠ ♠ Pr ♥ ♥ ♦ ♥②ss ♦ ♥♦♠♦s t ♦♥♦r t r♥st♦♥s ♦♥ r ♥

❬❪ ♥ t ♥♦♦ ♦ t ♣②ss ♥ r♦♦ t ♣♣♥♦tt❲♠s ❲♥s 2nd t♦♥

❬❪ r Pss ♦s♠trs ♥ t Prs♥tt♦♥ ♥ t tt ❲P ♦♠r ♦♥♥ tt♣r♥r

❬♠❪ ♠♦♥ ♥ r ♦♥r② ♠s ♦r tsts ♥ t P st ①♣r♠♥t r PP ♦t st

❬♦♣❪ ♦♣♦ P ❩ Pr♦③ ♣r♥② ts ♥ t♦s♠tr ♣r♠trs ♥ ♣♣t♦♥ ♦ ③♦s♦ ♦♥ s ♦♥♦ ♥ Pr♦ t♦♥ ts ♥ ♦♠♣♦♥♥ts ♥ ②st♠s ♦♥r♥ t♦ ♦♥t♣r r♥ ♣t♠r ♣s

❬♦❪ ♦r ②r ♥ ② t♦♥ ♦ s ♠t♦①s♦♥ s♠♦♥t♦r t tr♥sst♦r tt♦r s rt♦♥ ♦s♠tr P②ss

❬♣❪ ♣rs tr♦♥ ♥r② ♣♥♥ ♦ ①ss r rrr t♠rt♦♥ ♥ s♦♥ r♥st♦♥s ♦♥ r ♥

❬❪ t♦♣♣♥ ♥ r♥ ♦ ♦♥s ♥ ♠ttr s tt♣sr♠♦r

❬❪ ♥ r ②♥ ♥ ♠♣rtr♦♠♣♥st♦♥ ♦ P ♦s♠trs ♥ Pr♦ tr♦♥ ♦♠♣♦♥♥ts♦♥r♥ ♦♦r tr♥s ♣s

❬❪ ♥ t♦ t♦♥ ♥ ♦tt② s r ♥r② Prt rt♦rs r ♥♦♦② Ps♥ ♦♥♦♥ ❯

❬♠❪ P ♠♠rs t ♠ ♦rrt♦♥s ♥ s♠♦♥t♦rs ①♣♦s t♦♠♠ tr♦♥ ♥ ♣r♦t♦♥ rt♦♥s r♥st♦♥s ♦♥ r ♥

❬❪ rt③ ♥ r♦♥ ①♣r♠♥t rt♦♥s ♦ s♦♥ rtr♦♣ s st ♥tr♦♥ s♠♥tr ♦s♠tr r♥st♦♥s ♦♥r ♥

❬❪ rt③ rst♦♥ ♥②ss ♦ t ♦ st♥tr♦♥ ♦♠r♠♥t♦♥ t rr♥t♦t rtrst ♦ ♦♥tt② ♠♦t ♣♥ ♦s ♣♣ P②s

P❨

❬③❪ ③ P②ss ♦ s♠♦♥t♦r s ♦♥ ❲② ♦♥s 2nd t♦♥

❬③❪ ③ ♠♦♥t♦r s P②ss ♥ ♥♦♦② ♦♥ ❲② ♦♥s

❬❪ t ♦♥♦rá♥ P P rrt♦♥ t② t ♥ Pr♦ rst r♦♣♥ ♦♥r♥ ♦♥ t♦♥ ♥ ts ts ♦♥♦♠♣♦♥♥ts ♥ ②st♠s r♥♦tt r♥ ♣t♠r ♣s

❬❪ t Prs♥tt♦♥ ♥ t t ♠t♥ r ♦♥♥ tt♣r♥①♣tr♠♦♥

❬❪ ♥♥ ♠♦♥t♦rs ♥rr ♠ttrs ♥ tt♦rs t ♦♦

❬♠❪ ♠♠♥ t♦♥ ♠♦♥t♦r♥ t ♦♠♠r ♣♥ ♦s ♠♠r t♥t Pr♦t P

❬♦❪ ♦♠♣s♦♥ rts♦r♥ r♦♥ ♠s s♦♥ ♦s♥s ♥ ♦♥s ♦s♣t ♥ ❯ ♦♥t♦rs ♦r t ❱tt r♥st♦♥s ♦♥ r ♥

❬❪ ♦t r♦ss t♦♥ st ttr♥ ♥ rt ss♦t♦♥t t

❬❪ P ♥♥ P t♦ rt ♠t♦♥ ♥ ♥②ss ❯s♥P♣ Pr♥t ❯♣♣r r 3rd t♦♥

❬❱❪ ❱é é♦♣♣♠♥t rtrst♦♥ t rss♠♥t ♥ ♦s♠ètrsé sr ♠♥s♥ st♠é ♦♣tq♠♥t st♥é ① ♣♣t♦♥s s♣ts P tss ❯♥rst② ♦♥t♣r r♥

❬❱❪ ❱é rt r ♥é ts ♦rr r♠♥s ♦t ss r♥♥ ♦ rt♦♥ s♥s♦r s ♦♥ ♦♣t②st♠t ♠♥s♥ r♥st♦♥s ♦♥ r ♥

❬❱❪ ❱é ♦tt P r sr ♦ r ♥é ts ss t ♥♥ ♦s♠tr② s ♦♥ ♦♣t② st♠t♠♥s♥ ♠trs r♥st♦♥s ♦♥ r ♥

❬❱♥❪ ❱♥ ❱♦♦r ts ♦ rt♦♥ ♦♥ ♠trs ♥ ♦♠♣♦♥♥ts r ♦s♠tr② ❨♦ ♣♦rt

❬❱t❪ ❱tts ♦♥ P ♦rt ♥ rr②r♦s ssss♠♥t ♦ ♥ ♣ s s ♦srt ♥s♥st ♠♠ ♦s s♥s♦r r♥st♦♥s ♦♥ r ♥

P❨

❬❱♥❪ ❱♥ r♥♥r t♥♥ Pr♦t♦♥ ♦ r♦t s♦t♦♣s ♥ s♠♣s ② str② rt♦♥ s t ♣r♦t♦♥ rt♦r P

❬❱♥❪ ❱♥ Prt ♦♠♠♥t♦♥ t ❱♥ P

❬❲❪ P ❲♦rs ♥② ♦ ♥ t③ rs♣♦♥s ♦ t♥♥ tt♦r tr r♣rt ♥ ♥tr♦♥ rrt♦♥s ♣♣ ts♦t

❬❲❪ ❲tr P rt♦r ts srs P ♥tr♥ ♣♦rt

❬❲❪ ❲r③ ❲②s③ r③♠♥s r♦s③③ P s♦♥ strtrs♣r♦ss t ♥ Pr♦ t ❲♦rs♦♣ ♦♥ t♦♥ r♥♥ ♦♦♥ tt♦rs ♠r

❬❲❪ ❲♥♥s ♥ ♥ ♦♥ ♦s♠tr ♦r t ♥ tr♦♥s Prs♥tt♦♥ ♥ t t r ❲P ♠r ♦♥♥ tt♣r♥r

❬❲❪ ❲♥♥s ♦r t ❲ ♦r♥ r♦♣ tr♦♥s ♥ trrt♦♥ t♦r♥ ♦r t ♦♥tr♦ ♦ t ♠♥ ♥ Pr♦ ❲♦rs♦♣♦♥ tr♦♥s ♦r ①♣r♠♥ts ♣s

❬❲❪ ❲♥♥s P♥r s♦♦ Prs♥ ♥rs♥ rt♦♥ s♥ t ♥ Pr♦ ❲♦rs♦♣ ♠♦♥① ❳ ♣s

❬❲❪ ❲♥♥s ♥tr♥ t t rt♦r r♥ ♣②ss ♦♣rt♦♥ ♥ Pr♦ t ❲♦rs♦♣ ♦♥ tr♦♥s ♦r ①♣r♠♥ts r r♠♥② ♦t

❬❲❪ ❲♥♥s t♦♥ ♠♦♥t♦r♥ ♦r q♣♠♥t ♥ t t♥♥ ♥t♦♥ ♣t♦♥ P

❬❩♣❪ ❩♣ ♦② r♠♣ P r ts ♦ rt♦♥♥ ♦①tr♣♣ r ♦♥ ♥rs♦♥②r ♦ ♠♦t② t ♥ ♣♣ P②s tt

❯ ♥ r♥çs

éértr t s ①♣ér♥s ss♦és ♥ ♣②sq s tsé♥rs ♣r♦s♥t ♥ ♥r♦♥♥♠♥t rt ♦♥t ♠étr♦♦ r♣rés♥t ♥ ét♥♦♦q ♠♣ r②♦♥♥♠♥t ♣r♦t ♣r s ♦s♦♥s ♣r♦t♦♥s ééréssr très ♦♠♣① t ♦♠♥t très ♥t♥s ♠sr s é♣ôts é♥r t ♥s s ♠tér① s♠♦♥trs ♦♥trr á ssrr té ss②stè♠s étr♦♥qs ♣♥♥t ♦♥t♦♥♥♥t

s ♦s♠ètrs s t s ♣♥ ♦s ♣tés ① ♠♣s r②♦♥♥♠♥t ♦♥t été rtérsés s♦s ér♥ts t②♣s rrt♦♥s ss ttqt♦♥ ① s t ① ♣♥ ♦s ♦♥t été sét♦♥♥és ♥tért♦♥ s s♣♦sts été été s♣♣♦rt s s♠t♦♥s ♦♥t r♦ ♥♣rè ér♥ts ♠tér① s②♥tétsés ♣♦r ♦s♠étr ♥ ♠♣ ♠①t ♦♥tété rtérsés ♥ ♥ tr tst♦♥

♥ ♥s

♦♣♠♥t ♥ rtrst♦♥ ♦ t♦♥ ♦♥t♦r♥ ♥s♦rs ♦r t ♥r②P②ss ①♣r♠♥ts ♦ t rt♦r

❯ ♥ ♥s

t♦♥ ♠♦♥t♦r♥ t t ♥r② P②s ①♣r♠♥ts ♦ t t ♥①t ♣rt rt♦r ♥ ♦r t ①st♥ ♦s♠tr② t♥♦♦s rt♦♥ ♥r♦♥♠♥t ♥rt ② t ♥r② ♣r♦t♦♥ ♦s♦♥s ♦♠♣① r♥ ♦② r② s ♠sr♠♥t ♦ t ♥r② ♣♦st♦♥ ♥ t ♥ ♥♥s ♦r s♠♦♥t♦r ♠trs tr♦r ♣ t♦ ♥sr trt② ♦ t tr♦♥ s②st♠s r♥ t ♦♣rt♦♥

♥ ts ♦r t qt♦♥ ♦ ♥ ♣♥ ♦ ♦s♠trs st ♦rt ♠sr♠♥ts ♥ t rt♦♥ s ♣rs♥t srs ♦ t♦ s♥ t♦ ♣♥ ♦s ♥ t♥ st ♥ rtr③ ♥ t ♥ ♦ tr♥stt♦♥ t t ♥s♦rs ♥trt♦♥ sss s♣♣♦rt ② t ♦♥t r♦s♠t♦♥s sts r s♦ ♣rs♥t ♥② t ♣♣t② ♦ ♠trs ♦rt ♦s♠tr② ♦ t ♠① s t t s ♥ s♦ sss r

P

♦s♠étr ♦♠♣♦s♥ts t ②stè♠s

♦s♠étr éértrs ♣rts s ♦s ♣♥ ♠♥s♥ t♠é ♣tq♠♥t

♥tté t rss ♦rt♦r

♥sttt tr♦♥q ❯ ❯ ♥♥ ♥tr tr♦♥q t r♦♣t♦étr♦♥q ♦♥t♣r 2❯♥rsté ♦♥t♣r P è♥ t♦♥ ♦♥t♣r ❳