Post on 27-Mar-2015
1Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Olivier SEROT
Commissariat à l’Energie Atomique – Centre de Cadarache
Direction pour l’Energie Nucléaire / Département d’Etudes des Réacteurs /
Service de Physique des Réacteurs et du Cycle / Laboratoire d’Etudes Physiques
Prompt neutron emission from Monte Carlo simulation
2Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Prompt neutron emission from Monte Carlo simulation
Introduction
Initial input data needed
Calculation procedure
Preliminary results
Olivier LITAIZE + Olivier SEROT / CEA-Cadarache / DENCollaborations
252Cf(SF)
3Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Context
• Prompt neutron and prompt gamma spectra and their multiplicities are very important data for nuclear applications
• The evaluation files (JEFF,…) are not satisfactory (lack of data, same data for various fissioning nuclei…)
Our aim is to develop a Monte Carlo code able to simulate statistical decay of the fission fragments:• Look at the physical quantities which can be assessed: (A,TKE), P(), E(A), N(,A)….
• Test models related to the emission process
Introduction
4Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
S. Lemaire et al., [Phys. Rev. C, 72(2), 024601 (2005)];
hypothesis H1: RT=TL/TH=1: doesn’t work hypothesis H2: partitioning the excitation energy between the two fragments from experimenatl data: <>(A), <>(A) and <E>(A): less predictive
• P. Talou et al., [CNR 2009]RT values for each fission mode
Randrup and Vogt, [Phys. Rev. C80, 044611, 2009 + Phys. Rev. C80, 024601, (2009)]
Similar codes already exist:
Introduction
5Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
80 100 120 140 160 180
2345678
[M
eV]
Pre-Neutron Mass, amu
40
60
80
100
KE
[M
eV]
80 100 120 140 160 1800
1
2
3
4
5
6
7
Yie
lds
[%]
Thèse N. Varapai, Université Bordeaux 2006
Ionisation chamber
NE213
Y(A,KE,Z)=Y(A) × Y(<KE>, KE) × Y(Z)
Initial input data / 252Cf(SF)
Allow to sample the mass, charge and KE of the fission
frament
Mass and KE distributions from Varapai’s thesis
work
6Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Allow to sample the mass, charge and KE of the fission
frament
Mass and KE distributions from Varapai’s thesis
work
Nuclear charge distribution
Most probable charge taken from Walh evaluation: ZP
Charge dispersion:z assumed independent of the mass
/c)Z(Z 2pe
cπ
1Y(Z)
1/12)2(σc 2Z
Y(A,KE,Z)=Y(A) × Y(<KE>, KE) × Y(Z)
From Wahl, Phys. Rev. 126 (1962) 1112
Initial input data / 252Cf(SF)
7Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Sampling of the light fragment: AL , ZL , KEL
Total Kinetic Energy
Total energy
Total Excitation Energy
HL KEKETKE
*H
*L EETKEQTXE
)Z,B(A)Z,B(A)Z,B(AQ CNCNHHLL
1 Then, the mass and charge of the heavy fragment are deduced:AH=252-AL
ZH=98-ZL
Its kinetic energy (KEH) is sampled on the experimental kinetic energy distribution AH , ZH , KEH
2
3 The Total Excitation Energy (TXE) available at scission can be deduced:
Calculation procedure
8Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
** EU
W
a
a Level density parameterAsymptotic level density parameterEffective excitation energyShell corrections (Myers-Swiatecki, …)
*γU
*e1
U
δW1 aa
Ignatyuk’s model
4 Partitioning of the excitation energy between the two fragments
Calculation procedure
At scission: TXE=Eint+EdefThe main part of the deformation energy is assumed to be converted into intrinsic excitation energy (Ohsawa, INDS 251(1991)):
2HL,HL,
HL,def2
HL,0HL,HL,exc
Ta
ETaE
n
n
n
~10-20s~10-17s
~10-14s
scission
fully acc. FFNeutronemission
gammaemission
9Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Weisskopf spectrum
Z)1,a(A
SZ)(A,E)EZ,1,T(A n
**
2ε/T
2e
T
εφ(ε)
where T is the temperature of the residual nucleus:
5 Neutron evaporation
Energy limit for the neutron emission:
rotnn* ES(J)SE
J2
1)J(J EE
2
Yrastrot
0.31β1 MR5
2 2rigid J
22Fluide βMR
8π
9J
)/B1/2)((J 22
1)e(2JP(J)
: Myers-Swiatecki
Spin distributions
Inertia momentum• Appoximation of the rotational energy• Erot allows to simulate competition neutron-gamma
(Vandenbosch – Huizenga)B= 8 forl LF B=9 for HF
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
Yie
ld (
arbi
trar
y un
it)
Spin
Distribution initial spins Light Heavy
JES(J)SE rotnnlim
Calculation procedure
10Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Modèle RTLH E*lim inertie <>L <>H <>tot <E*>L <E*>H
A 1.00 Sn - 1.82 2.44 4.26 15.79 18.11
B 1.25 Sn - 2.28 1.93 4.21 19.64 14.23
Vorobyev et al. (2004) 2.05 1.70 3.76 - -
80 100 120 140 160 1800
1
2
3
4
5
Pro
mp
t n
eutr
on
mu
ltip
licit
y
Mass
Model A Budtz_Jorgensen
With model A: saw-tooth not reproduced and more neutrons from heavy fragment
With model B: ratio L:H in better agreement with experiment
Preliminary results
11Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Modèle RTLH E*lim inertie <>L <>H <>tot <E*>L <E*>H
C 1.25 Sn+EYrast Jrigid 2.16 1.85 4.01 19.65 14.24
D 1.25 Sn+EYrast Jfluid 1.06 0.46 1.52 19.66 14.24
E 1.25 Sn+EYrast 0.4 Jrigid 1.98 1.71 3.69 19.64 14.22
Vorobyev et al. (2004) 2.05 1.70 3.76 - -
Strong impact of the rotational energy:
With rigid model: overestimation of the total neutron multilplicity With fluid model: completely wrong! Intermediate: satisfactory
Preliminary results
12Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Preliminary results
Modèle RTLH E*lim inertie <>L <>H <>tot <E*>L <E*>H
F RT(A)=0.0116A Sn+EYrast 0.4 Jrigid 2.08 1.70 3.78 19.66 14.28
G RT(A) Sn+EYrast 0.4 Jrigid 2.06 1.70 3.76 19.89 14.27
Vorobyev et al. (2004) 2.05 1.70 3.76 - -
120A si 13.60.10A
120A si 1.830.029A )(AR
LL
LLLT
Model G:
RT=TL/TH
LLT 0.0116A)(AR
Model F (test)
13Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Preliminary results
(A,TKE) (model G)
80 90 100 110 120 130 140 150 160 170
140
160
180
200
220
240
140
160
180
200
220
240 Qmax TKE
Mass Number
TK
E [
Me
V]
0.10000.50000.90001.3001.7002.1002.5002.9003.3003.7004.1004.5004.9005.3005.7006.100
14Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
80 100 120 140 160 1800
1
2
3
4
P
rmo
pt
ne
utr
on
mu
ltip
lic
ity
Mass
Model G Budtz
Preliminary results
(A) (model G)
Reasonable agreement
except in the [155-170] mass
region
15Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Preliminary results
(TKE) (model G)
140 150 160 170 180 190 200 210 2200
1
2
3
4
5
6
7
8
9
10
Pro
mp
t n
eu
tro
n m
ult
iplic
ity
TKE [MeV]
-light -Heavy -Total
Contributions of the light and heavy fragment needed to
understand the (TKE) behaviour
Reasonable agreement except in the very high
TKE energy
16Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
(A) (modèle G)
80 100 120 140 160 1800.0
0.4
0.8
1.2
1.6
2.0
2.4
ModelG Budtz
Mass
Me
an
Ne
utr
on
En
erg
y [
Me
V]
Preliminary results
17Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Preliminary results
P () model G
Léger Lourd Total
Modèle G: Vorobiev:
Reasonable agreement
Modèle RTLH E*lim inertie <>L <>H <>tot <E*>L <E*>H
G RT(A) Sn+EYrast 0.4 Jrigid 2.06 1.70 3.76 19.89 14.27
Vorobyev et al. (2004) 2.05 1.70 3.76 - -
18Workshop Espace de Structure Nucléaire Théorique / 12-16 April, 2010
Energy spectrum in the lab. (modèle G)
<E> = 2.13 MeV (Budtz)<E> = 2.20 MeV (modèle G)
Maxwellienne (T=1.42 MeV):Modèle G:
Preliminary results