Mon

te C

arlo S

imulat

ions

fo

r M

oder

n ga

mma-

trac

king

Arr

ays

E.Fa

rnea

INFN

Sez

ione

di P

adov

a, I

taly

Out

line

•Fr

om c

onve

ntio

nal t

o ga

mm

a-ra

y tr

acki

ng a

rray

s•

Resu

lts

from

Mon

te C

arlo

si

mul

atio

ns f

or A

GATA

•Po

lari

zati

on s

tudi

es w

ith

Gean

t4

Why

do

we n

eed

AGA

TA?

Our

goa

l is

to e

xtra

ct n

ew v

alua

ble

info

rmat

ion

on t

he n

ucle

ar s

truc

ture

th

roug

h th

e γ-

rays

em

itte

d fo

llowi

ng

nucl

ear

reac

tion

s

Prob

lem

s: c

ompl

ex

spec

tra!

Man

y lin

es li

e cl

ose

in

ener

gy a

nd t

he

“inte

rest

ing”

chan

nels

are

ty

pica

lly t

he w

eak

ones

...

Euro

pean

γ-r

ay d

etec

tion

sys

tems

TESS

AES

S30

EURO

GAM

GASP

EURO

BALL

III

EURO

BALL

IV

1980

1

986

199

2

1996

Neu

tron

rich

heav

y nu

clei

(N/Z

→2)

•Lar

ge n

eutro

n sk

ins

(rν-

r π→

1fm

)•N

ew c

oher

ent e

xcita

tion

mod

es•S

hell

quen

chin

g13

2+x S

n

Nuc

lei a

t the

neu

tron

drip

line

(Z→

25)

•V

ery

larg

e pr

oton

-neu

tron

asym

met

ries

•R

eson

ant e

xcita

tion

mod

es•

Neu

tron

Dec

ay

Nuc

lear

sha

pes

•Exo

tic s

hape

s an

d is

omer

s •C

oexi

sten

ce a

nd tr

ansi

tions

She

ll st

ruct

ure

in n

ucle

i•

Stru

ctur

e of

dou

bly

mag

ic n

ucle

i •

Cha

nges

in th

e (e

ffect

ive)

inte

ract

ions

48N

i10

0 Sn

78N

i

Pro

ton

drip

line

and

N=Z

nuc

lei

•S

pect

rosc

opy

beyo

nd th

e dr

ip li

ne•

Pro

ton-

neut

ron

pairi

ng•

Isos

pin

sym

met

ry

Tran

sfer

miu

m n

ucle

iSh

ape

coex

iste

nce

Challeng

es in

Nuc

lear

Str

uctu

re

Why

do

we n

eed

AGA

TA?

•Lo

w in

tens

ity

•H

igh

back

grou

nd•

Larg

e D

oppl

er b

road

enin

g•

Hig

h co

unti

ng r

ates

•H

igh

γ-ra

y m

ulti

plic

itie

s

Hig

h ef

fici

ency

Hig

h se

nsit

ivit

yH

igh

thro

ughp

utA

ncill

ary

dete

ctor

s

FAIR

SPIR

AL2

SPES

REX

-ISO

LDE

MA

FFEU

RISO

LH

I-St

able

Har

sh c

ondi

tion

s!N

eed

inst

rum

enta

tion

wit

h

Conv

enti

onal

arr

ays

will

not

suff

ice!

From

con

vent

iona

l Ge

to γ-r

ay t

rack

ing

ε ph

~ 10

%N

det

~ 10

0

Usi

ng o

nly

conv

enti

onal

Ge

dete

ctor

s, t

oo m

any

dete

ctor

sar

e ne

eded

to

avoi

dsu

mm

ing

effe

cts

and

keep

th

e re

solu

tion

to

good

va

lues

The

prop

osed

sol

utio

n:U

se t

he d

etec

tors

in a

non-

conv

enti

onal

way

!

Com

pton

Shi

elde

d G

e

Ge

Sphe

re

Ge

Tra

ckin

g A

rray

ε ph

~ 50

%N

det

~ 10

00

θ~

8º

θ~

3º

θ~

1º

Effi

cien

cy is

lost

due

to

the

solid

ang

le c

over

ed b

y th

e sh

ield

; poo

r en

ergy

re

solu

tion

at

high

rec

oil

velo

city

bec

ause

of

the

larg

e op

enin

g an

gle

Ω~4

0%

ε ph

~ 50

%N

det

~ 10

0

Ω~8

0%A

GATA

and

GRE

TA

AGA

TA•

Hig

h ef

fici

ency

and

P/T

ra

tio.

•Go

od p

osit

ion

reso

luti

on

on t

he in

divi

dual

γin

tera

ctio

ns in

ord

er t

o pe

rfor

m a

goo

d D

oppl

er

corr

ecti

on .

•Ca

pabi

lity

to s

tand

a

high

cou

ntin

g ra

te.

Puls

e sh

ape

anal

ysis

+γ-

ray

trac

king

Ingr

edient

s of

Gam

ma

Trac

king

Pulse

Shap

e Ana

lysis

to d

ecom

pose

reco

rded

wav

es

Highly

segm

ente

d HPG

e de

tect

ors

··

Iden

tified

inte

ract

ion

points

(x,y

,z,E

,t) i

Reco

nstr

uction

of

trac

ks

evalua

ting

per

mut

ations

of

int

erac

tion

point

s

Eγ

Eγ 1

Eγ 2

e2

e3

1

3

θ 1

θ 2

e1

02

Digital e

lect

ronics

to r

ecor

d an

d pr

oces

s se

gmen

t sign

als

1 2

3

4

Reco

nstr

ucte

dga

mma-

rays

Bene

fits

of

the

γ-ra

y tr

acking

scar

ce

good

Definition of the photon direction

Doppler correctioncapability

Det

ecto

r

Segm

ent

Puls

e sh

ape

anal

ysis

+

trac

king

γEn

ergy

(keV

)

v/c

= 20

%

Why

Mon

te C

arlo S

imulat

ions

?

•Ca

refu

l opt

imiz

atio

n of

the

geo

met

ry o

f th

e ar

ray

•Ev

alua

tion

of

the

expe

cted

per

form

ance

of

the

arr

ay in

a c

onsi

sten

t wa

y•

Prod

ucti

on o

f co

ntro

lled

data

sets

to

deve

lop

and

trai

n th

e re

quir

ed a

lgor

ithm

s

The

Mon

te C

arlo c

ode

for

AGA

TA

•Ba

sed

on G

eant

4 C+

+ cl

asse

s•

Even

t ge

nera

tion

sui

ted

for

in-b

eam

ex

peri

men

ts•

gam

ma-

ray

trac

king

is n

ot in

clud

ed d

irec

tly

in

the

code

(com

plic

ated

pro

cess

in it

self

!)•

“Raw

”dat

a pr

oduc

ed b

y th

e Ge

ant4

pro

gram

are

pr

oces

sed

with

a t

rack

ing

code

(in

this

wor

k,

mgt

) and

ana

lyze

d wi

th o

ther

pro

gram

s

Dat

a Ana

lysis

1.13

0.94

0.63

0.31

0.0

z [cm

]

0˚7.

5˚15

˚22

.5˚

27˚

ϕ

A0.

55B

1.0

r [c

m]

C1.

45D

1.9

E2.

35F

2.8

G3.

25H

3.7

-0.20

0.2

H

GF

E DC

BA

-0.20

0.2

100

200

300

rel. amplitude

100

200

300

t [n

s]

-1

-0.7

5

-0.5

-0.2

50

A

BC

DE

FG

H

-1

-0.7

5

-0.5

-0.2

50

100

200

300

rel. amplitude

100

200

300

t [n

s]

∗

•

••

•

•

•

••

•• •••• •

••• • • •

• • •

••

Pulse

shap

ege

nera

tion

γ-ra

y tr

acking

Even

t ge

nera

tion

Det

ecto

r re

spon

se

Elec

tron

ics

Resp

onse

Fun

ction

Pulse

Shap

e Ana

lysis

to d

ecom

pose

reco

rded

wav

es

Pack

ing

and

smea

ring

of

simulat

ed d

ata

Clas

s st

ruct

ure

of t

he p

rogr

amA

gata

*Aga

taR

unA

ctio

n*A

gata

Even

tAct

ion

Aga

taPh

ysic

sLis

tA

gata

Vis

Man

ager

Aga

taSt

eppi

ngA

ctio

n

*Aga

taA

naly

sis

Aga

taG

ener

ator

Act

ion

CSp

ec1D

Aga

taG

ener

ator

Om

ega

Aga

taSt

eppi

ngO

meg

a

*Aga

taD

etec

tor

Con

stru

ctio

n

*Aga

taD

etec

tor

Shel

l

*Aga

taD

etec

tor

Sim

ple

*Aga

taSe

nsiti

veD

etec

tor

*Aga

taD

etec

torA

rray

Aga

taH

itDet

ecto

rC

Con

vex

Poly

hedr

onM

esse

nger

cla

sses

are

not

show

n!M

esse

nger

cla

sses

are

not

show

n!

*Po

ssib

ility

to

chan

ge p

aram

eter

s vi

a a

mes

seng

er c

lass

*Aga

taD

etec

torA

ncill

ary

CSp

ec2D

*Aga

taEm

itted

Aga

taEm

itter

*Aga

taEx

tern

alEm

issi

on

*Aga

taEx

tern

alEm

itter

*Aga

taIn

tern

alEm

issi

on

*Aga

taIn

tern

alEm

itter

Bui

ldin

g a

Geo

desi

c B

all (

1)B

uild

ing

a G

eode

sic

Bal

l (1)

Star

t with

apl

aton

ic so

lide.

g. a

n ic

osah

edro

nO

n its

face

s, dr

aw a

regu

lar

patte

rn o

f tria

ngle

s gro

uped

as

hex

agon

s and

pen

tago

ns.

E.g.

with

110

hex

agon

s and

(a

lway

s) 1

2 pe

ntag

ons

Proj

ect t

he fa

ces o

n th

e en

clos

ing

sphe

re;

flatte

n th

e he

xago

ns.

Bui

ldin

g a

Geo

desi

c B

all (

2)B

uild

ing

a G

eode

sic

Bal

l (2)

A ra

dial

pro

ject

ion

of th

esp

heric

al ti

ling

gene

rate

sth

e sh

apes

of t

he d

etec

tors

.B

all w

ith 1

80 h

exag

ons.

Spac

e fo

r enc

apsu

latio

n an

dca

nnin

g ob

tain

ed c

uttin

g th

ecr

ysta

ls. I

n th

e e

xam

ple

3 cr

ysta

ls fo

rm a

trip

le c

lust

erA

dd e

ncap

sula

tion

and

part

of th

e cr

yost

ats f

or

real

istic

MC

sim

ulat

ions

Al c

apsu

les

0.4

mm

spac

ing

0.8

mm

thic

kA

l can

ning

2

mm

spac

ing

2

mm

thic

k

Bui

ldin

g a

Geo

desi

c B

all (

3)B

uild

ing

a G

eode

sic

Bal

l (3)

6080

110

120

150

180

200

240

Geo

desi

c T

iling

of S

pher

e us

ing

60–2

40 h

exag

ons a

nd 1

2 pe

ntag

ons

The

code

: ge

omet

ry1.

Cand

idat

e co

nfig

urat

ions

for

AGA

TA w

hich

hav

e be

en

inve

stig

ated

hav

e 12

0 or

180

hex

agon

al c

ryst

als;

the

y ha

ve b

een

chos

en b

ecau

se o

f th

e po

ssib

ility

to

form

cl

uste

rs o

f de

tect

ors

with

few

ele

men

tary

sha

pes.

2.Th

e so

lid a

ngle

cov

erag

e is

max

imiz

ed o

nly

usin

g ir

regu

lar

hexa

gons

; wit

h re

gula

r he

xago

ns t

he

perf

orm

ance

of

the

arra

y is

lowe

r be

caus

e of

the

sp

aces

bet

ween

the

cry

stal

s.

3.Ge

odes

ic t

iling

pol

yhed

ra h

andl

ed v

ia a

spe

cial

ly w

ritt

en

C++

clas

s (D

.Baz

zacc

o)4.

Rele

vant

geo

met

ry p

aram

eter

s re

ad f

rom

file

(gen

erat

ed w

ith

an e

xter

nal p

rogr

am)

GRET

A v

s. A

GATA

120

hexa

gona

l cry

stal

s2

shap

es30

qua

drup

le-c

lust

ers

all e

qual

Inne

r rad

ius

(Ge)

18.5

cm

Am

ount

of g

erm

aniu

m23

7 kg

Sol

id a

ngle

cov

erag

e81

%

4320

seg

men

tsE

ffici

ency

: 41

% (M

γ=1)

25

% (M

γ=30

)P

eak/

Tota

l:57

% (M

γ=1)

47

% (M

γ=30

)

Ge

crys

tals

siz

e:Le

ngth

90

mm

Dia

met

er80

mm

180

hexa

gona

l cry

stal

s3

shap

es60

trip

le-c

lust

ers

all e

qual

Inne

r rad

ius

(Ge)

23.5

cm

Am

ount

of g

erm

aniu

m36

2 kg

Sol

id a

ngle

cov

erag

e82

%64

80 s

egm

ents

Effi

cien

cy:

43%

(Mγ=

1)

28%

(Mγ=

30)

Pea

k/To

tal:

58%

(Mγ=

1)

49%

(Mγ=

30)

Expe

cted

Per

form

ance

Resp

onse

fun

ction

Abs

olut

e ef

fici

ency

val

ue in

clud

es t

he

effe

cts

of t

he t

rack

ing

algo

rith

ms!

Valu

es c

alcu

late

d fo

r a

sour

ce a

t re

st.

Effe

ct o

f an

cilla

ry d

evices

Abs

olut

e ph

otop

eak

efficien

cy (tr

acking

inc

lude

d)Pe

ak-t

o-to

tal ra

tio

(res

pons

e fu

nction

)

Anc

illar

y de

vice

s ha

ve a

n im

pact

com

para

ble

to

the

case

of

conv

enti

onal

arr

ays

(tra

ckin

g is

“rob

ust”

!)

Anc

illar

y de

vice

s ha

ve a

n im

pact

com

para

ble

to

the

case

of

conv

enti

onal

arr

ays

(tra

ckin

g is

“rob

ust”

!)

The

code

: ph

ysics

1.Sc

hem

atic

bui

lt-in

eve

nt g

ener

ator

2.Po

ssib

ility

to

deco

de “r

ealis

tic”

even

t st

ruct

ure

and

sequ

ence

fro

m a

for

mat

ted

text

file

3.Po

ssib

ility

to

coup

le t

he c

ode

to g

ener

ic G

eant

4 ev

ent

gene

rato

rs

Effe

ct o

f th

e re

coil

velocity

β=20

%Th

e co

mpa

riso

n be

twee

n sp

ectr

a ob

tain

ed k

nowi

ngor

not

kno

wing

the

even

t-by

-eve

nt v

eloc

ity

vect

or s

hows

tha

t ad

diti

onal

in

form

atio

n wi

ll be

ess

enti

al t

o fu

lly e

xplo

it t

he c

once

pt o

f tr

acki

ng

0.3

0.7

2.4

∆β

(%)

0.3

0.6

2σ di

r(deg

rees

)

0.3

0.5

1.5

δ s(cm

)

5020

5

β (%

)

Unc

erta

inty

on

the

reco

il di

rect

ion

(deg

rees

)

The

Firs

t St

ep:

The

AGA

TA D

emon

stra

tor

Obj

ective

of

the

fina

l R&

D p

hase

200

3-20

081

sym

met

ric

tri

ple-

clus

ter

5 as

ymmet

ric

triple-c

lust

ers

36-f

old

segm

ente

d cr

ysta

ls54

0 se

gmen

ts55

5 di

gita

l-cha

nnel

sEf

f. 3

–8

% @

Mγ=

1Ef

f. 2

–4

% @

Mγ=

30Fu

ll ACQ

with

on

line

PSA

and

γ-ra

y tr

acki

ngTe

st S

ites

:GA

NIL

, GSI

, Jyv

äsky

lä,K

öln,

LN

LCo

st ~

7 M

€M

ain

issu

e is

Dop

pler

co

rrec

tion

cap

abili

ty→

coup

ling

to b

eam

and

re

coil

trac

king

dev

ices

AGA

TA D

emon

stra

tor

+ PR

ISM

A

E. F

iore

tto

INFN

-LN

LE.

Fio

rett

oIN

FN -

LNL

195

MeV

19

5 M

eV 3

636S

+ S

+ 20

820

8 Pb,

Pb

, θθ l

ablab

= 80

= 80

oo

E (

E ( a

.ua.u .

).)

∆∆E ( E (a.u a.u.).)Z=1

6Z=1

6

Z=2

8Z=2

8

XY

X p

osition

X p

osition

Y po

sition

Y po

sition

∆∆E/E

< 2%

E/E <

2%

Z/Z/∆∆Z

~ 60

for Z

=20

Z ~ 6

0 for

Z=20

∆∆tt< 5

00

< 500

psps

∆∆X =

1 mm

X = 1

mm

∆∆Y =

2 mm

Y = 2

mm

∆∆tt~ 3

50

~ 350

psps, ,

∆∆X =

1 mm

X = 1

mm

∆∆Y =

1 mm

Y = 1

mm

Firs

t in

stal

lati

on s

ite

for

the

Dem

onst

rato

r:

the

PRIS

MA

sp

ectr

omet

er a

t LN

L

AGA

TAD

emon

stra

tor

MCP

Qua

drup

ole

Dip

ole

MW

PPA

C

Ion

Cham

ber

Effe

ct o

f th

e re

coil

velocity

90Zr

rec

oils

wit

h E~

350

MeV

(wit

h 10

% d

ispe

rsio

n) a

ssum

ed.

βfr

om r

econ

stru

cted

tra

ject

ory

leng

th a

nd T

OF.

Dir

ecti

on f

rom

sta

rt d

etec

tor.

AGA

TA

Dem

onst

rato

r +

PRIS

MA

Aga

taGe

ant4

cod

e (E

F)

+PR

ISM

A s

imul

atio

n (A

.Lat

ina)

Perf

orman

ce

Phot

opea

k ef

fici

ency

P/T

Rati

o

1 M

eV p

hoto

ns, p

oint

sou

rce

at r

est.

Tra

ckin

g is

perf

orm

ed.

~14c

m: P

ossi

ble

targ

et-d

etec

tor

dist

ance

for

the

Dem

onst

rato

r on

PRI

SMA

Effe

ct o

f th

e re

coil

velocity

Peak

FW

HM

Phot

opea

k ef

fici

ency

1 M

eV p

hoto

ns, M

γ=

1. Tr

acki

ng is

perf

orm

ed.

Typi

cal v

alue

s fo

r re

acti

on

prod

ucts

at

PRIS

MA

AGA

TA v

s. C

onve

ntiona

l ar

rays

AG

ATA

1A

GA

TA 1

ππG

ASP

Con

f. II

GA

SP C

onf.

II

45 H

PGe

dete

ctor

s(1

5 tr

iple

clu

ster

s)40

HPG

e de

tect

ors

with

ant

i Com

pton

“Rea

listic”

Simulat

ions

28Si

+ 28

Si@

125

MeV

. Par

ticl

e de

tect

ion

with

EU

CLID

ES. K

inem

atic

al r

ecal

ibra

tion

.

AGA

TA1π

arra

y

GASP

Conf

.II

γFo

ld 1

γFo

ld 3

E.Fa

rnea

, F.

Recc

hia

E.Fa

rnea

, F.

Recc

hia

The

code

: ph

ysics

1.Po

ssib

ility

to

choo

se s

et o

f Ge

ant4

inte

ract

ions

for

ph

oton

s (s

tand

ard

trea

tmen

t or

low-

ener

gy t

reat

men

t)2.

Com

pton

pro

file

opt

iona

lly c

onsi

dere

d3.

Line

ar p

olar

izat

ion

of t

he p

hoto

ns o

ptio

nally

con

side

red

Star

ting

con

side

rati

ons:

in p

rinc

iple

, lin

ear

pola

riza

tion

of

phot

ons

is in

clud

ed in

to t

he G

eant

4 st

anda

rd li

brar

ies.

A n

on-

stan

dard

app

roac

h is

use

d, d

efin

ing

a “p

olar

izat

ion

vect

or”

spec

ifyi

ng t

he d

irec

tion

of

the

elec

tric

fie

ld v

ecto

r. D

oes

this

prod

uce

the

corr

ect

resu

lts?

Star

ting

con

side

rati

ons:

in p

rinc

iple

, lin

ear

pola

riza

tion

of

phot

ons

is in

clud

ed in

to t

he G

eant

4 st

anda

rd li

brar

ies.

A n

on-

stan

dard

app

roac

h is

use

d, d

efin

ing

a “p

olar

izat

ion

vect

or”

spec

ifyi

ng t

he d

irec

tion

of

the

elec

tric

fie

ld v

ecto

r. D

oes

this

prod

uce

the

corr

ect

resu

lts?

Unp

olar

ized

Com

pton

sca

tter

ing

The

angu

lar

dist

ribu

tion

of

the

scat

tere

d ph

oton

is a

fun

ctio

n of

the

ph

oton

ene

rgy

and

of t

he s

catt

erin

g an

gle:

()

()

()

()

cosθ

1c

mE1

EE

θsi

nγ

2αθ

Wθ

sin

EEEE

EE2r

θ,E

W

200

01

22

2

10

01

2

012 0

0

−+

=

−=

→

−

+

=

1 ke

V

255

keV

511

keV

10

22 k

eV

2

044

keV

Polarize

d Co

mpt

on s

catt

ering

In t

his

case

the

ang

ular

dis

tibu

tion

dep

ends

als

o on

the

dir

ecti

on o

f th

e po

lari

zati

on (i

n th

e pi

ctur

es t

he d

irec

tion

e0

is a

long

the

x a

xis)

. In

case

of

a fu

lly p

olar

ized

pho

ton

beam

:

()

()

10

22

22

2

01

01

2

012 0

de

cosδ

cos

sinθ

cos

θsi

n2

γ2α

cos

θsi

n2

EEEE

EE2r

θ,W

rr

⋅=

=

−=

−+

= ϕ

ϕϕ

ϕ

1 ke

V

255

keV

511

keV

10

22 k

eV

2

044

keV

The

form

alism

A c

onve

nien

t fo

rmal

ism

to

trea

t po

lari

zati

on (l

inea

r an

d ci

rcul

ar) i

s th

at o

f th

e St

okes

par

amet

ers

and

of t

he s

catt

erin

g m

atri

x de

velo

ped

by F

ano

et a

l.

Ord

er z

ero

appr

oxim

atio

n: d

efin

e po

lari

zati

on t

hrou

gh

the

Stok

es p

aram

eter

s an

d co

nver

t in

tern

ally

to

the

nati

ve G

eant

4 fo

rmal

ism

. Che

ck w

ith

sim

ple

idea

l cas

es

that

the

res

ults

are

con

sist

ent

with

the

ory.

Ord

er z

ero

appr

oxim

atio

n: d

efin

e po

lari

zati

on t

hrou

gh

the

Stok

es p

aram

eter

s an

d co

nver

t in

tern

ally

to

the

nati

ve G

eant

4 fo

rmal

ism

. Che

ck w

ith

sim

ple

idea

l cas

es

that

the

res

ults

are

con

sist

ent

with

the

ory.

Our

tes

t be

nch

•O

ur t

est

benc

h wa

s an

“ide

al”8

-ele

men

ts p

olar

imet

er (p

lus

a ce

ntra

l sc

atte

rer

and

an a

ddit

iona

l ext

erna

l sca

tter

er t

o st

udy

doub

le

scat

teri

ng)

•Th

e “r

ed”d

etec

tor

lies

in t

he s

catt

erin

g pl

ane

•Th

e as

ymm

etry

rat

io is

use

d to

ben

chm

ark

sym

met

ric

pola

rim

eter

s:

•U

sing

a b

eam

of

know

n po

lari

zati

on o

ne c

an d

eter

min

e th

e po

lari

zati

on s

ensi

tivi

ty:

•Th

e ex

peri

men

tal a

sym

met

ry (t

o be

com

pare

d to

the

the

oret

ical

va

lue)

sho

uld

be c

orre

cted

by

the

pola

riza

tion

sen

siti

vity

:

Asy

mmet

ry

()

()

()

()

()

90θ,

Wθ,

W90

θ,W

θ,W

θ,A

++

+−

=ϕ

ϕϕ

ϕϕ

()

1γ1

90,9

0A

AAQ

thth

−=

=fo

r ful

ly p

olar

ized

bea

ms

QAA

exp

=

Non

-sym

met

rica

l po

larimet

er, or

polariza

tion

non-

orth

ogon

alto

the

scat

tering

plane

Dat

a ar

e fi

tted

wit

h th

e fo

llowi

ng e

xpre

ssio

n:

()

()

()

ψco

s2P

1θ

sin

γI

)I(

20

−+

−=

ϕϕ

From

P a

ndψ

the

max

imum

asym

met

ry is

fou

nd,

Am

ax=

A(θ

,ψ),

whic

h sh

ould

be

com

pare

d to

the

th

eore

tica

l val

ue:

E0

= 4

50.6

keV

θ=

90°

χ2

= 1

.13

I 0

=

504

.8(3

)P

= 0

.76(

1)ψ

= -6

4.4°

(4)

Am

ax=

0.5

4(2)

511

keV

at(

30°,

60°)

mod

ified

Sta

ndar

d P

olar

ized

Com

pton

Sca

tterin

g

()

θsi

nγ

θsi

nP

Pθ,

A22

max

−=

Chec

k wi

thG4

LowE

nerg

y inte

ract

ion

0.85

7100

0.70

2(1)

0.60

14(7

)

3483

92

1399

25

3489

54

5602

22

3484

93

1387

82

3488

33

5596

40

[1 1

0]

Cal

. 255

81(4

)90

90ψ

exp(d

eg)

9090

90ψ

th(d

eg)

0.68

57

0.35

(3)

0.24

6(20

)

562

454

588

744

566

444

581

739

[1 1

0]

(90,

90)

0.42

96

0.22

(4)

0.15

2(30

)

267

227

249

328

281

239

251

297

[1 1

0]

(90,

30)

412

180

333

225

311

270

349

315

0.19

(4)

Aex

p=

Aex

p/Q

0.57

14

0.13

6(26

)

358

316

355

413

[1 0

0]

(90,

90)

Q=

Aex

p/Ath

Ath

Aex

p

13590450

Stok

esA

ngle

Give

n th

esy

mm

etry

,opp

osit

ede

tect

ors

can

be s

umm

ed.

Indi

vidu

al a

naly

sis

can

put

inev

iden

cean

omal

ies.

ψ=

angl

e wh

ere

the

min

imum

of

the

angu

lar

dist

ribu

tion

lies

A =

(Im

ax-I m

in)/(

I max

+Im

in)

511

keV

a

t90°

(E1

= 25

5.5

keV

)

Roug

hly

a fa

ctor

2 d

iffe

renc

e!

Prob

lems

with

G4

inte

ract

ions

•Ca

refu

l ins

pect

ion

of t

he c

ode

show

tha

t th

e lo

w en

ergy

inte

ract

ion

sets

pro

vide

d wi

th t

he G

eant

4 pa

ckag

e tr

eats

pol

ariz

atio

n in

a c

once

ptua

lly w

rong

wa

y, r

esul

ting

in a

fac

tor

2 at

tenu

atio

n of

the

an

isot

ropy

•Th

e “s

tand

ard”

inte

ract

ion

set

trea

ts p

olar

izat

ion

prop

erly

fro

m t

he c

once

ptua

l poi

nt o

f vi

ew, b

ut

the

impl

emen

tati

on f

ails

•Bo

th o

f th

em w

ere

rewr

itte

n in

a m

ore

sati

sfac

tory

way

(D.B

azza

cco)

.

Gene

ral co

mpa

riso

n

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

[10

0]

90-9

0 [

110]

90

-90

[10

0]

30-0

0 [

110]

30

-00

[11

0]

30-6

0

Low

ESt

dSt

okes

new

Std

new

Low

E

Summar

y•

The

perf

orm

ance

of

AGA

TA (a

nd G

RETA

) un

der

a wi

de r

ange

of

cond

itio

ns h

as b

een

eval

uate

d in

a r

ealis

tic

way

usin

g a

spec

ially

wr

itte

n, G

eant

4-ba

sed

C++

code

•Th

e tr

eatm

ent

of li

near

pol

ariz

atio

n pr

ovid

ed b

y Ge

ant4

has

bee

n re

vise

d in

or

der

to o

btai

n re

sult

s co

mpa

tibl

e wi

th t

he

theo

reti

cal e

xpec

tati

ons