Simulating Gg Distributions
• What is Gg?
• How are Gg’s measured?
• What does the standard model
predict?
• Simulating Gg distributions.
• Constraining the Oslo method.
• Testing the Porter-Thomas
distribution
What is Gg?
• Gg is the total radiation
width.
Sum of partial radiation
widths, Ggi, for primary
transitions from the
capturing state
(resonance).
𝑁
Γ𝛾 =
Γ𝛾𝑖
𝑖=1
Neutron Capture Cross Sections:
Neutron hits target and sticks
•
AZ(n,g)A+1Z
Electron Beam
(n,g) Measurements at ORELA Employ C6D6 Detectors
CaptureFlux
Setup
at ORELA
monitor
Filters
Neutrons
Sampledetectors
g-ray
Deuterated Benzene
Detectors
Neutron Production
Target
Collimator
40 m
Sample
How is Gg Measured?
1
9
6
P
t
D
a
t
a
S
A
M
M
Y
F
i
t
D
a
t
a
S
A
M
M
Y
F
i
t
1
9
6
P
t
1
9
5
1
9
5
P
t
P
t
1
.
0
3
0
0
.
8
2
0
0
.
6
1
0
0
.
4
0
.
2
0
0
.
0
2
0
Transmion(n,g)(b)
• Gg determined from Rmatrix analysis of
neutron-resonance data.
• Typically need both
neutron total
(transmission) and capture
data.
• Capture area.
Ag=gJGnGg/(Gn+Gg).
• Depth of transmission dip
proportional to Gn.
• Total width.
Gt=Gn+Gg
1
0
1
.
0
0
.
8
0
.
6
5
0
.
4
0
.
2
0
0
.
0
4
0
1
9
4
P
t
1
.
0
1
5
0
.
8
1
0
0
.
6
5
0
.
4
1
9
4
0
0
.
2
P
t
1
5
0
.
0
1
9
2
P
t
1
0
1
.
0
5
0
.
8
0
0
.
6
1
9
2
0
4
2
.
7
2
.
7
2
.
8
2
.
9
E
(
k
e
V
)
n
2
.
8
2
.
9
E
(
k
e
V
)
n
P
t
3
.
0
3
.
0
What Does the Standard Model Predict?
• Strengths of primaries Ggi follow the Porter-Thomas distribution (PTD).
Same distribution as Gn0
Follows from assumption of compound nucleus model and central limit
theorem of statistics.
The PTD is a c2 distribution with 1 degree of freedom (n=1).
𝝆(𝝆𝒙)𝝆−𝟏 𝒆−𝝆𝒙
𝑷 𝒙; 𝝆 𝒅𝒙 =
𝒅𝒙
𝚪(𝝆)
𝚪
𝝂 = 𝟐𝝆, 𝒙 =
𝚪
• Sum of samples from N c2 distributions having n = 1 is a c2 distribution
with N degrees of freedom.
Expect Gg to follow a c2 distribution with n equal to the number of
independently-contributing channels, n≈100.
Comparison of Gn0 and Gg Distributions
103
Gn0.

Gn0
c DistributionsGg
196
Pt+n
Pt+n
1.0
Fraction Above G G
0.9
100
0.1
102 0.8
Fraction > Width
• Gammas, Gg.
n~100 channels.
Very narrow.
1.0
Width (meV)
• Neutrons,
Single channel, n=1.
PTD.
Very broad.
196
n = 0.5
n = 1 (PTD)
n = 20
n = 200
0.8
0.7
0.60.6
101
Gn0
Gg
Gn0
Gg
0.5
0.40.4
0.3
0.20.2
0.0
0.0
0
0
0 2000
4000100 6000
1
Pt196Gn0aGgDistributions Jan. 30, 2013 8:51:02 AM
PT196Gn0aGgVsE Jan. 29, 2013 1:34:17 PM
Chi2Dists Feb. 4, 2013 10:32:44 AM
200
8000
2
10000
GG
Width
(meV)
En (eV)
300
12000
3
14000 400
16000
4
1.0
196
Pt
Data
c2 dist.
0.5
• Example: 192,194,195,196Pt.
Often seems to be an
extra tail compared to
c2 distribution.
0.0
1.0
Fraction of Widths > GgGg
Comparison of
Measured Gg to c2
Distributions
195
Pt, 1-
0.5
0.0
1.0
195
0.5
Pt, 0-
0.0
1.0
194
0.5
Pt
0.0
1.0
192
0.5
0.0
0.5
1.0
GgGg
Pt
1.5
Simulating Gg Distributions: Step 1
Generating a Level Scheme
DICEBOX “Nuclear Realization”.
From r(Ex) to set of Exi’s.
100
104
𝑬𝒙
•
•
•
Pt
Oslo, E&B 2009, BSFG =2.4
Talys 2, BSFG (PSF's 1 and 3)
Talys 1, CT+FG (PSF 4)
Talys
4 5, Hilaire (PSF 5)
-1
10
103
10-2
Ex=Sn, r=D0
x
-1
1/2+ level density
P(E ) (MeV )
•
𝑵 𝑬𝒙 =
𝝆 𝑬𝒙 𝒅𝑬𝒙
𝑵 𝟎𝑬𝒙
𝑷 𝑬𝒙 =
𝑺𝒏 numbers to pick
Use N(Sn) 𝑵
random
Exi’s.
Throw away those below Ecut.
Add in known levels below Ecut.
Separate sets of Exi’s for each Jp
that can be reached by dipole
decay.
e.g. 197Pt decay from ½+
resonances; ½+, 3/2+, ½-, and 3/2-.
5
197
2
10
10-3
Ecut
10-4
101
Ex (MeV)
•
•
6
3
All models normalized to D0
10-5
2
100
10-6
0
0
1
1
2
2
1 29, 2013 3:15:34 PM
NcumNormVsExExample Jan.
Pt197LDOslo2p4VsTalys Jan. 28, 2013 2:53:41 PM
0
3
E3x (MeV) 4
Ex (MeV)
4
5
5
6
6
Simulating Gg Distributions: Step 2
Calculating the Ggi’s
• Egi = Sn – Exi.
• Calculate “PTD” factor ξi2.
ξi2 randomly chosen from
the PTD.
Generalize to allow n≠1.
• Ggi = D0 ξi2 fX1(Egi) Egi3.
Calculate Ggi ’s for each Jp
reached by dipole decay.
0.3
70
7
70
60
6
60
GG
(meV)
G
-7(meV) -3
gigi(meV)
fE1gi (10
MeV )
-7
fM1 (10 MeV -3)
• Calculate fX1(Egi)’s.
1.5
Oslo, E&B 2009 BSFG, =2.4, Gg=85.8 meV
Oslo, E&B 2009 BSFG, =2.4,
meV
197Gg=85.8
Talys model 1, Kopecky-Uhl,
Gg=79.5 meV
197Gg=79.5
Talys model 1, Kopecky-Uhl,
meV
Talys model 3, Hartree-Fock BCS, Gg=86.0 meV
Talys model 3, Hartree-Fock BCS, Gg=86.0
meV
197
Talys model 4, Hartree-Fock Bogolyubov, Gg=78.6 meV
Talys model 4, Hartree-Fock Bogolyubov, Gg=78.6
meV
Talys model 5, Goriely hybrid, Gg=84.4 meV
Talys model 5, Goriely hybrid, Gg=84.4
meV
+
Sn
Pt
Pt
Pt All levels
All levels
1.0 0.2
50
5
50
197
197
40
4
40
Sn
1/2
3/2+
1/2Models
3/2-
Pt M1 PSF
Pt E1 PSF Models
30
30
3
0.5 0.1
20
20
2
10
10
1
0.0 0.0
00
0
0 00 0
0
1
1
11
1
2
2
22
2
3 3
33
4
E
(MeV)
EEg3g(MeV)
(MeV)
g (MeV)
x
(MeV)
EE
g
Pt197M1PSFOslo2p4VsTalys4Models
Jan.
28, 2013
Pt197E1PSFOslo2p4VsTalys4Models
28,
2013
2:23:04
PM PM
Pt197CumGgiVsEgEB2009s2p4
Jan. 30,Jan.
2013
4:44:43
PM 2:31:33
Pt197CumGgiVsExEB2009s2p4 Jan. 30, 2013 4:45:42 PM
Pt197GgiVsEiEB2009s2p4 Jan. 30, 2013 11:52:54 AM
4 4
44
5
5 5
5
6
6 6
66
Simulating Gg Distributions: Steps 3 and 4
Calculating Total Widths and Iterating
• Sum Ggi’s to get total width.
𝚪𝜸 =
𝚪𝜸𝒊
170
𝒊,𝑿,𝑱
Pt
150
140
Gg (meV)
• Iterate.
Use same level schemes, etc.
New Ggi’s by varying ξi2 only.
Yields distribution of Gg’s.
• Shape of Gg distribution due to:
Shapes of LD and PSF models.
“PTD” fluctuations.
197
160
130
120
110
100
90
80
70
60
50
0
100
200
300
400
500
600
Iteration
PT197GgTotVsIterationBSFG2009s2p4 Jan. 30, 2013 1:12:42 PM
700
800
900
1000
Examples: LD and PSF Models in Talys
*Didn’t
use. Couldn’t normalize.
0.9
104
0.8
-3
0.7
103
0.6
-7
fE1 (10
) -1)
MeV
1/2+ level
density
(MeV
• Five LD models.
1 – Const. T + Fermi Gas.
2 – Back-shifted Fermi Gas.
3 – Generalized Superfluid.*
4 – Goriely.
5 – Hilaire.
• Five PSF models.
1 – Kopecky-Uhl Lorentzian.
2 – Brink-Axel Lorentzian.
3 – Hartree-Fock BCS.
4 – Hartree-Fock Bogolyubov.
5 – Goriely’s Hybrid.
0.5
102
0.4
Talys model 1, Kopecky-Uhl, Gg=79.5 meV
197 model 3, Hartree-Fock BCS, Gg=86.0 meV
Talys
Talys model 4, Hartree-Fock Bogolyubov, Gg=78.6 meV
Talys
Goriely
1, model
Const. 5,
T+
F.G. hybrid, Gg=84.4 meV
2, BSFG
4, Goriely
5, Hilaire
Pt
197
Ex=Sn, r=D0
Pt E1 PSF Models
0.31
10
All models normalized to D0
0.2
Sn
0.1
100
0.0
0
0
1
1
2
2
Pt196LDD0Eq153JPi0p5p Nov. 28,
2012
Pt197E1PSFTalys4Models
Jan.
30,1:42:56
2013 PM
2:37:39 PM
3
3
E (MeV)
Exg (MeV)
4
4
5
5
6
6
Talys Results for ‹Gg›
value, ‹Gg› = 85.9±1.8 meV, for
simulations.
400
Talys Predicted Gg (meV)
• Talys calculation with 4 LD and
5 PSF models.
• Normalized LD models to
ORELA D0 = 153 eV.
LD models 1 and 2 normalized
using “a”, models 4 and 5 using
“c” and “d”.
• PSF models un-normalized.
• Chose LD/PSF combinations
which gave closest to ORELA
196
Pt (n target)
LD models normalized to D0
Level density model 1
Level density model 2
Level density model 4
Level density model 5
300
200
ORELA
100
0
1
2
3
4
E1 g-ray Strength Function Model
Pt196GgAvevsLDandPSF Nov. 28, 2012 1:46:18 PM
5
Simulation Results with Talys Models
Agrees with nuclear physics
lore.
• Decreasing n results in much
better agreement between
simulation and data.
1.0
0.8
E1 + M1 simulation, n = 0.5
0.8
E1 + M1
simulation,
n = 1.0eV.
LD model
norm.
to D0=153
Measured
= 85 meV,
g model
TalysG
LD
1, n = 1.0
0.6
0.6
norm. to D0=153 eV.
PSF model 4, no norm.
0.4
0.4
196
Pt+n
0.2
0.2
0.0
0.0
0.6
0.6
Another sign of violation of
the PTD?
Firm s wave
Talys LD 2, PSF 1, Gg=75.0 meV
Talys
196 LD 2, PSF 3, Gg=79.8 meV
Pt+n
Talys LD 1, PSF 4, Gg=73.5 meV
Talys
5, PSF 5, Gg=77.8 meV
FirmLD
s wave
1.0
Fraction
Above>Threshold
Fraction
GgGg
• All simulations using Talys
models yielded Gg distributions
significantly narrower than
measured.
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0
1.1
1.1
1.2
1.2
Threshold GgGg
Pt196GgDistVsSimNu1a0p5 Jan. 30, 2013 3:26:50 PM
Pt197GgDistTalys4Cases Jan. 24, 2013 4:20:03 PM
GgGg
1.3
1.3
1.4
1.4
1.5
1.5
1.6
1.6
Simulation Results with LD and PSF from the Oslo
Method
0.3
1.5
4
101.0
-1
-7
-3
1/2+ flevel
density
(10
)-3  )
MeV(MeV
E1Fraction
-7 > GgG
g
fM1 (10 MeV )
• What was the experimental
spin distribution?
Affects slopes of LD and
PSF.
• What is the true spin
distribution?
Affects normalization of PSF
and shape of simulated
distribution.
• Would be better to know
more about low-lying levels
in 197Pt.
Ecut = 0.269 MeV.
Only 2 ½- and 2 3/2- levels.
Firm sGwave
Oslo, E&B 2009 BSFG, =2.4,
g=85.8 meV
BSFG
=2.7, n=1, GgNI=89.1 meV
Sn
Oslo,
E&B
20091,BSFG,
=2.4,
G
=85.8
meV
197
Talys
model
Kopecky-Uhl,
GgEB2005.
=79.5
meV
Sn
g
BSFG
EB2009.
Talys
model
1, 3,
Kopecky-Uhl,
GBCS,
meV=2.4,
Talys
model
Hartree-Fock
Gg=86.0
meV n=1, GgNI=85.8 meV
g=79.5
Oslo,
E&B
2009,
BSFG =2.4
Talys
model
3,
Hartree-Fock
BCS,
Gg=86.0 G
meV
Talys
model
4,
Hartree-Fock
Bogolyubov,
g=78.6 meV
Talys
2, BSFG
(PSF's 1 and
3)
Talys
model
4, 5,
Hartree-Fock
Bogolyubov,
Gg=78.6 meV
Talys
model
Goriely hybrid,
Gg=84.4 meV
Talys
1, CT+FG
(PSFhybrid,
4)
Talys
model
5, Goriely
Gg=84.4 meV
Talys 5, Hilaire (PSF 5)
Pt
0.8
103
0.2
1.0
0.6
102
0.4
10.1
0.5
10
LD model norm. to D0=153 eV.
197
r=D0
Pt M1 PSF Models
Measured Gg = 85 meV,Exn=Sn,
= 1.0
197
Pt E1 PSF Models
Ecut
196
Pt+n
All models normalized to D0
0.2
100
0.0
0.6
0.00.0
00 0
0.7
0.8
11 1
0.9
1.0
1.1
1.2
1.3
33 
44
2 22
4
G3gG
g
(MeV)
E
EEgxg(MeV)
(MeV)
Pt197GgDistOsloBSFG2005vs2009c Jan. 28, 2013 1:42:06 PM
Pt197M1PSFOslo2p4VsTalys4Models
Jan.
2013
2:31:33
Pt197E1PSFOslo2p4VsTalys4Models
Jan.
28,28,
2013
2:23:04
PMPM
Pt197LDOslo2p4VsTalys Jan. 28, 2013 2:53:41 PM
1.4
1.5
1.6
5 55
6 66
Problems, Improvements, and Future Plans
•
•
•
n=9.8, <Gg>=556 meV
1.0
n=21, <Gg>=289 meV
Data
c2 fit
0.5
6
1-
2-
95
Mo(n,g)
Coincidences/Singles
•
How to decompose PSF data into E1
and M1?
Fit E1 and M1 is everything else?
Vice versa?
How to normalize slopes of LD and
PSF?
 is correct when simulated Gg
distribution matches data?
Ohio U. method?
Simulating 194Pt+n Gg distribution
might be even more interesting.
More widths/better statistics.
Tail is more pronounced.
Simulate 95Mo+n Gg distributions.
Have 6 Jp’s.
Sensitivity to upbend?
Simulate 88Sr, 116,120Sn, 134,136,137Ba,…
Fraction of Widths > Gg
•
0.0
50
500
1000
0
200
n=22, <Gg>=344 meV
1.0
4
400
600
800
n=28, <Gg>=252 meV
3
0.5
4-
32
0.0
0
200
400
600
0
200
400
600
All 314 Resonanes
Firm p = + by trans. shape
Firm p =3- +by trans. shape
1
1.0
0
2+
n=183,
1 <Gg>=1862 meV
0
3
n=184,
4 <Gg>=178 meV
5
(Soft Singles)/(Hard Singles)
0.5
J1VsJ3AllResCwoBoxes Feb. 8, 2013 11:45:08 AM
0.0
0
200
400
600
800
0
Gg (meV)
Mo95GgDistWFitAll6JpisNew Feb. 5, 2013 10:57:01 AM
200 400 600 800 1000
6