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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
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