prompt fission neutron and gamma-ray properties in a monte...

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U N C L A S S I F I E D

Prompt fission neutron and gamma-ray properties in a Monte-Carlo Hauser-Feshbach framework

Ionel Stetcu

Theoretical Division

Los Alamos National Laboratory

Slide 1

Main collaborators: T. Kawano, P. Talou, M. Jandel

LA-UR-14-26942

PRC 87 (2013) 014617

PRC 88 (2013) 044603

PRC 90 (2014) 024617



Outline

Slide 2

Ø  Motivation

Ø  The Monte-Carlo Hauser-Feshbach method

Ø  Results for prompt particles, discussion select parameters:

u  Initial spin distribution

u  Excitation energy sharing between fragments

u  Sensitivities to other parameters

Ø  Summary and outlook



Motivation

Slide 3

v  Basic science:

u  Understand the pre- and post-scission physics

u  Interpret experimental data

u  Provide guidance on detector design

v  Applications:

u  Nuclear energy: future reactors (new fuel compositions, new geometries, etc.)

u  Existing fuel cycle (safety, waste management, etc.)

u  Nuclear forensics

u  Astrophysics (reaction networks)



Experiment

Slide 4

u  Specroscopy: GAMMASPHERE (binary/ternary fission) – ANL, BNL

u  Calorimetry:

v  DANCE – n-induced fission

v  fusion-fission reactions (Dubna)

v  Crystal ball 162xNaI(TI) 4π array (Darmstadt)

u  See talks in FIESTA2014: R.C.Haight, N.Colonna, A.Tsinganis, F.Tovesson, M.Jandel, A.Oberstedt, J. Ullmann etc.



Fission simulation

Slide 5

q  Assumptions:

u  Prompt fission products emitted from the fully accelerated fragments

u  No emission occurs during the evolution from saddle to scission

u  No emission at the neck rupture

u  No time information (stop at the ground/isomeric state)

u  Fission fragments are compound nuclei

q  C++ code (MPI implementation) CGMF=CGM+FFD

u  deterministic and Monte-Carlo modes

u  similar to DICEBOX at low energies

u  other similar implementations: FREYA (LLNL), FIFRELIN (CEA), GEF (Schmidt)



Hauser-Feshbach for fission fragments

Slide 6

Treat fission fragments as compound nuclei

Description of:

§  average prompt fission neutron spectrum

§  average prompt fission neutron multiplicity

Ø  P(ν), ν(A)

Ø  prompt gamma observables

Ø  correlations between particles

Ø  Same approach applicable to describe beta-delayed neutrons/gammas

Madland-Nix / Los Alamos model

Complication: more parameters, some not well known



Hauser-Feshbach formalism for n-induced reactions

Slide 7

§  Neutron emission probability:

ü  Transmission coefficients computed using an optical model

ü  Density of states

§  Gamma emission probability:

ü  Transmission coefficients calculated from the gamma strength function

ü  E1, M1 and E2 transitions only

ü  Density of states

ü  Discrete levels

P (�n)dE ∝ Tn(�n)ρ(Z,A− 1, E − �n − Sn)

P (�γ)dE ∝ Tγ(�γ)ρ(Z,A,E − �γ)

102

104

106

108

1010

1012

1014

1016

5 10 15 20 25 30

Leve

l Den

sity

[MeV

-1]

U [MeV]

140Xe

ρ(U)− 1

12√2σ

exp(a√aU)

a1/4U5/4

ρ(U) =1

Texp(U/T )



Input into the fission simulations

Slide 8

§  Experimental Information: u  Primary fission fragment yields u  Internal excitation energy

u  Ingredients used in HF calculations (gamma strength functions, discrete levels)

TXE = Qf (Al, Zl;Ah, Zh;Ac, Zc)− TKE

= Ml +Mh −Mc + Einc +Bn(Ac, Zc)− TKE

§  Theory/Model: Ø  Charge distribution: from Wahl systematics Ø  Parity distribution: assumed equiprobable Ø  Excitation energy sharing: Ø  Initial spin distribution:

Ø  Ingredients used in HF calculations (optical model parameters)

Zp = AhZc

Ac+∆Z

RT =Tl

Th

NO DIRECT MEASUREMENTS

§ de-excitation feeding patterns of the ground-state bands

§  angular anisotropy of prompt fission gamma rays

§  isomeric ratios

P (J) ∝ (2J + 1) exp�−J(J + 1)/(2B2)

�



Energy sharing

Slide 9

RT =Tl

Th

RT=1: thermal equilibrium (like in the Los Alamos model)

RT=constant

RT(A)

v  symmetric fission: RT=1

v  ~130: maximum (closed shell)

v  >130 RT decreases to below one (deformation)



Sensitivity to the initial angular momentum

Slide 10

Fragment mass

P (J) ∝ (2J + 1) exp�−J(J + 1)/(2B2)

�

B2 =IT�2

I = α I0rig(Z,A,β)

Experimental evidence*: Jrms=5-8 for LF and 7-10 for HF



Sensitivity to the initial angular momentum (cont)

Slide 11



Isomeric ratios and the angular momentum

Slide 12

thermal neutron capture on stable nuclei: better handle on initial spin and excitation energy

0.1

1

10

Rat

io e

xper

imen

t to

calc

ulat

ion

high spin g.s.high spin isomer

69Zn

71Zn

71Ge

73Ge75Ge

77Ge

77Se

79Se

81Se

83Se

85Sr

80Br

109Pd

115Cd

121Sn

123Sn

125Sn

127Sn

127Te

131Te

133Xe

135Xe

137Ce

139Ce

138Cs

197Hg

PRC 88 (2013) 044603



Sensitivity to the optical potential

Slide 13

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 2 4 6 8 10 12

Rat

io to

Max

wel

lian

Energy [MeV]

nth+235U

Kornilov,2010ENDF/B-VII.0

Koning-DelarocheBeccheti-Greenlees

Wilmore



Selected results for n+235U – neutron observables

Slide 14

Becker et. al., Phys Rev C 87 (2013) 014617

α ν

1.0 2.598

1.2 2.557

1.3 2.539

1.4 2.524

1.5 2.507

1.7 1.462

2.0 2.435

3.0 2.326

4.0 2.254 α=2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2 4 6 8 10 12

Spec

trum

(Rat

io to

Max

wel

lian)

[1/M

eV]

Neutron Energy [MeV]

T=1.32 MeV

nth+235U

Kornilov,2010CGMF

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4 5 6 7 8

Prob

abilit

y

Neutron Multiplicity

nth+235U

Holden, 1988Franklyn, 1978

CGMF =2

0

1

2

3

4

5

80 90 100 110 120 130 140 150 160 170

Prom

pt N

eutro

n M

ultip

licity

(n/fi

ssio

n)

Fission Fragment Mass (u)

nth+235U

Vorobyev, 2009Batenkov, 2004

Nishio, 1998Maslin, 1967CGMF =2.0



Cutoff γ energy

Slide 15



nth+235U: gamma observables

Slide 16 Data from M. Jandel et. al.



nth+239Pu

Slide 17



252Cf (sf)

Slide 18



Isomeric states in CGMF

Slide 19

0.01

0.1

1

10

0 1 2 3 4 5 6

Photo

ns/M

eV/F

ission

[MeV]

252Cf(sf)

Billnert, 2013T =

T = 6ns

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Photo

ns/M

eV/F

ission

[MeV]

252Cf(sf)

Billnert, 2013T =

T = 6ns

134Te, 135Xe

135I, 139Cs, 137Xe



Summary and outlook

Slide 20

²  De-excitation of fission fragments described within the MCHF formalism

Ø  Gamma-ray strength

Ø  OMP for neutron emission

Ø  Neutron-gamma competition

²  MC histories recorded and used to produce average quantities and for post processing

²  Good quantitative agreement with experimental data

u  Some discrepancies still exist (neutron/gamma spectra too soft)

²  Requires some fine tuning (many parameters)

²  Future work: extension other actinides and extend the range of incident enegies

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