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Hydrogen Burning in StarsHydrogen Burning in StarsHydrogen in induced reaction have lowest Coulomb barrier ⇒ highest reaction rate
Hydrogen burning provides energy production in “Main Sequence Stars” in the HR Diagram (sun)until hydrogen fuel is depleted ⇒ the life time of
main sequence star depends on the reaction rates
The stellar evolution, or subsequent evolutionary stages depend on the
subsequent nucleosynthesis mechanisms or their nuclear fuel processing!
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Topics in Nuclear Astrophysics IIITopics in Nuclear Astrophysics IIIStellar Hydrogen burning
nuclear reactions in the pp-chains pp-nucleosynthesis and energy productionneutrino origin & neutrino signals pp-experiments underground
nuclear reactions in the CNO cyclesthe CNO cyclesCNO nucleosynthesis and energy productionCNO experimental questions
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Nucleosynthesis Sites and ConditionsNucleosynthesis Sites and Conditions
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Temperature and Density Temperature and Density Evolution in Stellar CoreEvolution in Stellar Core
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Hydrogen Burning Stage of Hydrogen Burning Stage of Stellar EvolutionStellar EvolutionStars with M>1.5Mo
Stars with M<1.5Mo
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The ppThe pp--chainschains
pp-1: 1H(p,e+ν)2H2H(p,γ)3He3He(3He,2p)4He 84.7%
pp-2: 3He(α,γ)7Be 13.8%7Be(e-,ν)7Li 13.78%7Li(p,α)4He
pp-3: 7Be(p,γ)8B 0.02%8B(β+ν)24He
fusion of 4 1H → 4He + 2e+ + 2νe + 26.7 MeV energy release
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neutrinoneutrinoproductionproduction
contributions from different reactions in the pp-chains. The branching point of3He(3He,2p)4He/3He(α,γ)7Beis extremely important forgeneration of high energyneutrinos (accessible toHomestake Chlorine detector)
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Impact of pp-chain reaction rates on ν production
High precision (<5%)measurements for theinterpretation of solarν flux at ν detectors &ν oscillation analysis!
For summary and details: Adelberger et al. Rev.Mod.Phys. 70, 1265 (1998)
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Network for the pp-chain I
)2,(
4
),()2,(
3
),(),(
2
)2,(),(
1
3333
2123333
111212
3333111
21
212
21
212
212
pHeHeAHeHe
pHAHHpHeHeAHeHe
epHAHHpHAHH
pHeHeAHeHeepHAHH
NYYdtHed
NYYNYYdtHed
NYYNYYdtHd
NYYNYYdtHd
συρ
συρσυρ
συρσυρ
συρσυρ
γ
νγ
ν
⋅⋅⋅=
⋅⋅⋅+⋅⋅⋅⋅−=
⋅⋅⋅⋅+⋅⋅⋅−=
⋅⋅⋅⋅⋅+⋅⋅⋅⋅⋅−=
−
−
Hydrogen is depleted under release of neutrinos!Helium is being produced + energy release 4H⇒14He!
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pp-chains in the sun
H
He
Li
Be
B
C
pp-1
pp-3
pp-2
activation
Impact on neutrino detectionBorexino
SNO & Superkamiokande
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life time characteristicsEnormous differences in S-factors due to nuclear interaction
Sp+p = 5 10-25 MeV-barn weak interactionS7Be(p,γ) = 2 10-5 MeV-barn electromagnetic interactionS3He(α,γ) = 5 10-4 MeV-barn electromagnetic interactionS2H(p,γ) = 2 10-4 MeV-barn electromagnetic interactionS3He(3He,2p) = 5 MeV-barn strong interaction
Differences translate into differences in reaction rate and life times some nuclei will be processed extremely fast, others will be processed extremely slow.
Slowest process in the fusion sequencedetermines life time of burning phase andenergy production in the sun!!!
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lifetime of sun!slowest reaction rate: 1H(p,e+ν)2H
−
−
−
−
⋅−⋅⋅⋅⋅⋅=
⋅−⋅
⋅⋅⋅⋅=
=⋅⋅=
3/19
3/1
9
22
37.33/2
99
248.43/2
9
3/19
][1093.4
][109.32
2
TH
TZZ
HH
H
H
ppAH
Hpp
eBarnMeVSTX
eBarnMeVSTZZAX
NAX
HH
ρ
µρ
συρλ
µ
with ρ=10 g/cm3; XH=0.5; T9=0.015; S=5 10-25 MeV barn
⇒ λpp=2.34·10-19 [1/s]; ⇒ τpp=1/λpp=4.5·1018 [s]
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The p+p reactionThe p+p reaction1H(p,e+ν)2H is a reaction based on weak interaction mechanism
the S-factor is calculated: S=5 10-25 MeV-barn
1.E+12
1.E+14
1.E+16
1.E+18
1.E+20
0.01 0.1 1 10
temperature [GK]
life
time
[s
]1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
0.01 0.1 1 10
temperature [GK]
NA< σ
v>
cm3 /g
/s sun
What would be the life time of hydrogen with strong interaction S=5 10-5 MeV-barn?
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Speculation in hydrogen burningSpeculation in hydrogen burning
Sweak=5·10-25 MeV-barn ⇒ Sstrong=5·10-5 MeV-barn
τ ≈ 4·1018 s ≈ 1.3·1011 y⇒ τstrong ≈ 4·10-2 s ≈ 1.3·10-9 y
The nature of the nuclear reaction mechanism controls the lifetime of stars in general and our sun specifically.
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energy production
−
− ⋅−⋅⋅⋅⋅⋅⋅=
⋅⋅⋅=⋅=
3/19
37.3
63/2
9272
617
][1076.4
1065.9
T
ppH
Hpppp
eBarnMeVSQTX
sgergQ
AXr
Q
Hρ
λρ
ε
[ ]
⋅=
⋅=
=
Θ
Θ
serg
gM
sgerg
33
33
1092.5
102
96.2
ε
ε with Q6=26 MeV
⋅=
serg
obs33104ε
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Experimental difficulties!
Background level from cosmic ray &natural activities
Extrapolation(something missing?)
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Reaction Yield as function of Reaction Yield as function of energyenergy
dxdE
nE
dEEEEY
E
EE
⋅=
⋅= ∫∆−
1)(
)()()(
ε
εσ Yield is experimental observable
product between actual reactionprobability (cross section) and the atomic interaction between beam particles & target material.
Two energy dependentfunctions σ(E) and ε(E)
∆E ≡ energy loss in targetE ≡ beam energyn ≡ number density of active target atoms
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reminder ….
LnA
Nn A
ν
ρν
=
= solid: NA=6.022·1023 atoms/mole
gas: L=2.69·1019 atoms/cm3
ν : number of atoms/molecule
example: N2 gas ν=2 ⇒ n=5.48·1019 atoms/cm3
Al solid ν=1, ρ=2.69g/cm3, A=27 ⇒ n=6·1019 atoms/cm3
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energy loss dE/dxenergy loss dE/dx
significant changes in ε over the critical energy range of astrophysical measurements
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Thin Target Yieldno significant change in σ or ε over energy loss range ∆E
xn
dxndE
EEdEdEdEEEY
E
EE
E
EE
∆⋅⋅≈
⋅
∆⋅=
∆⋅=⋅=⋅≈= ∫∫
∆−∆−
σσε
σε
σεσ
εσ
)()(
if molecular target with Na=na∆x active atoms/cm2
and several Ni=ni∆x inactive atoms/cm2
ia
ii
aii
iaa N
NNNE εεεεε ⋅+=⋅+⋅=∆
∑∑ ;
TaOOTa εεε ⋅+=52
52Ta2O5
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Example: 3He+4He
0.00000010.0000010.000010.00010.0010.010.1
110
1001000
10000
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
energy [keV]
cros
sse
ctio
n[n
barn
]
cross section in nano-barn (10-33 cm2)
and stopping power in MeV/mg cm2
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Detection count rate
yield Y is number of reactions/incoming particleto determine count rate you need to correct for detection efficiency η and number of incomingbeam projectiles Np.
]/1[106.1
][]/1[ 19 sAIYsNYI p ⋅⋅⋅=⋅⋅= ηη
detection efficiency η depends on interaction probability between radiation and detector material
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Yield and event rate
1E-23
1E-18
1E-13
1E-08
0.001
100
0 200 400 600 800 1000 1200
energy [keV]
yiel
d/pr
ojec
tile
Y
ield
/s
yield/projectile for a 10 µg/cm2 target
yield/s (event rate) for a beam of I=100 µA at η=10%BG
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example: 12C(α,γ)16O
low energy measurementslimited by background rate
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Background: Cosmic RaysBackground: Cosmic Rays
10-6
10-3
10-1
MuonsNeutronsPhotons
LNGS/surfaceRadiation
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Underground Laboratory
significant CR reduction>1000 m.w.e.
physics underground: http://www.sns.ias.edu/~jnb/
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LUNA @ Gran SassoRock as passive shieldingcosmic ray background Reduction ≈ 10-4
4-50 keV Accelerator p-, α-beams ≤ 1 mA
Study of pp-chainse.g. 3He+3He
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Passive Background Reduction
Ge-detector background spectrum
15 m.w.e.unshielded
3400 m.w.e.40cm Pb shield
Significant background reduction but …!
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LUNA-II upgrade
50-400 keV VdG
Accelerator Laboratory
p-, α-beams ≤ 0.5 mA
Study of p-capture on CNO nuclei (CNO-cycles) and α capture on light nuclei
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Branching and Neutrino Flux
H
He
Li
Be
B
C
pp-1
pp-3
pp-2
increase in the 3He+3He reaction rate by factor X would reducethe neutrino flux from the 7Be(e-,ν), 8B(β+ν) significantly!The resonance possibility appeared at its time as potential solution for solar neutrino problem! ⇒ Search for resonance!
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Example: Example: 33He+He+33He He for ppfor pp--I/ppI/pp--II branchingII branching
W.A. Fowler: Is there a broad resonance in the 3He+3He system????
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Background ReductionBackground Reductionbackground reduction by underground locationevent identification by p-p coincidence requirement
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Present status on Present status on 33He(He(33He,2p)He,2p)44HeHe
extensive search towards low energies but no evidence was found
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77Be(p,Be(p,γγ))88BB
impact on ν detectors and interpretation of ν flux measurements
reaction determines the branch between pp-II and pp-III:
pp-II feeds the 7Be(e-,ν)7Li neutrino sourcepp-III feeds the 8B(β+ν)24He neutrino source
impacts Chlorine, SuperK and SNO experiments
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Coulomb breakCoulomb break--up techniquesup techniquese.g. e.g. 77Be(p,Be(p,γγ))88BB
7Be(p,γ)8B
through capturereaction techniques
8B(γ,8B)p
reaction with realor virtual photonsCoulomb break-up
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Coulomb dissociation methodCoulomb dissociation method
8B+208Pb −> 7Be+p+208Pb
virtual photon theory8B(γ,p)7Be (abs.)
detailed balance7Be(p,γ)8B (capt.)
virtual photon number:
σ( γ , p) =(2 j7 +1)(2 j1 +1)
2(2 j8 +1)k17
2
kγ2 σ(p,γ )
dσdEγ
C.D.
=nEγ
σ (γ ,p ) E2>>E1>>M1
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Coulomb Dissociation ExperimentCoulomb Dissociation Experiment
production target
primary beam (cyclotron)
D1
D2
F1
F2 target
plastic scintillatorhodoscopes
RIPS (RIken Projectile fragment Separator)
radioactive beam
56 NaI(Tl)
8B beam
p
7Be
PPAC
Riken, GSI, NSCL/MSU
RIB experiments
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GSI versionGSI version
7Bep
8B
target208Pb
4×Si
2×MWPC30×plastic
Q-pole
Dipole
ReturnYoke
KaoS spectrometer
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Experimental Results (NSCL/MSU)Experimental Results (NSCL/MSU)
E2 terms are the main observables!
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Results and comparisonResults and comparison
useful method if conditions (E2 transitions, ground state transitions) are guaranteed!
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Network simulations at low temperature conditions of 107 K
time [s]
mas
s fra
ctio
n X