Monte Carlo Simulation ofPrompt Neutron Emission During

Acceleration in Fission

T. Ohsawa Kinki University

Japanese Nuclear Data Committee

IAEA/CRP on PFNS, Vienna, Dec. 13-16, 2011

q

ε

Overall agreement betweenMadland-Nix (MN) model calculation and experiments is good.

Apparent discrepancy in the low-energy region (E<0.5 MeV).

Prompt Fission Neutron Spectrum

U-235(nth,f) U-235(nth,f)

Possibilities:

1. Uncertainties in the experimental data in the low-energy region.

2. Possible existence of scission neutrons.

3. Angular anisotropy in neutron emission in the CM-system of FF.

4. Possible effect of “yrast levels”.

5. Neutron emission during acceleration (NEDA), instead of after full acceleration.

What are the reasons for the discrepancy in the region En < 0.5 MeV?

We should examine the possibilities from physics point of view.

1. Uncertainties in experimental data in the low- energy region

(after F.-J.Hambsch)

Uncertainties coming from ◆ Scatted neutrons ◆ Low detection efficiency, …

2. Possible existence of scission neutrons.

[N. Cârjan, P. Talou and O. Serot, Nucl. Phys. 792, 102 (2007)]

R. W. Fuller (1962) ：　“ volcano erupting” in the Fermi sea

Recent work: N. Cârjan, P. Talou & O. Serot (2007) ：　 Time-dep. Potential + 2D-Time-dep. Schrödinger eq.

◆ The probability of occurrence and energy transfer in SCN emission should be treated on the physics ground, and not to be used as convenient tool for fitting to PFNS data.

3. Angular anisotropy of emitted neutrons in the CM-system of FF.

2( , , ) ( , )(1 cos ) /(1 / 3)c c b b q q

b=W(θ)/W(90º) – 1 >0

<J> = 7 - 8

[T. Ohsawa, INDC(NDS)-0541, p.71 (2009)]

More neutrons in the forward and backward directions ↓ 　　　　　　 　↓Enhancement of High-energy and Low-energy wings

Correlation between angle and energy

Experimental evidences:

5. Possible Effect of Yrast Level

Fragment angular momentum <J> = 7 - 8ħ

( 1)rotE I I

Yrast line: the lowest available states for given angular momenta I. (No internal excitation belowthe line. i.e. something like the “ground state” for the angular momentum.)

I

E

x

Bnγ(E2)

Initial excited states

n

n

n

n

n

High-energy neutron emission may be forbidden.

4. Possible effect of “yrast levels”

2 ( 1)*lim 2

I InE B

ILower limit of energyafter neutron evaporation

irrot rigid I I I

Soften the PFNS, the degree depending on

Transition to energy levelslower than yrast levels areprohibited.

Another effect of high angular momentum of FF:

5. Neutron Emission During Acceleration (NEDA)

Neutron emission after full acceleration

Neutron emission during acceleration

[B] Neutron emission [stochastic process]

• In order to examine the NEDA effect, we have to analyze the competition:

　 [A] Coulomb acceleration [deterministic process]

Scission

• Interest from Physics as well as Application point of view

[A] Coulomb acceleration

11 ln1 2 1final

ltv

χ = KE / KEfinal

vfinal =[2{(M-m)Mm} ・ 1.44(Z-z)z/l]1/2

Relation between relative acceleration χ and the time t after scission is described unambiguously by Eismont’s equation, once the FF charges and charge-center distance l are given.

l

By treating the charge-center distance as a random variable, we can simulate thevariance in TKE.

• Monte Carlo approach is a suitable and effective method to treat the stochastic processes. • In order to simulate the competition accurately, it is important to evaluate the neutron emission time τ exactly.• τ is not a constant; rather it varies over a wide range, as will be shown later, depending on the excitation energy, level density and inverse reaction cross section.

max

0

*

*3

162

dSE

Em

nCRC

CC

n

[T. Ericson, Adv. Phys. 9, 425 (1960)] Optical Model

Level Density Formula

[B] Neutron emission [stochastic process]

• τ were evaluated for four isobars with every mass number A of FF.

Initial Conditions for Monte Carlo Simulation (1) 1. Multimodal Random Neck-Rupture Model was used

to generate the mass , charge, TKE distributions of the primary fission fragments.

S1

S2SL

• Superposition of the modal distributions gives the total distribution.

• Scission shape parameters were taken from H.-H. Knitter et al.(1987) for U-235

[K. Nishio]

235U(n,f): 3 fission modes

120 140 160 180 200 2200.00

0.01

0.02

0.03

0.04

0.05TKE Distribution of Primary Fragments for U- 235(nth,f) (Based on the data of H.- H. Knitter et al. (1987))

157MeV 167MeV 187MeV

0.07%SL

81.6%

18.3%S1

S2

Prob

abilit

y

Total Kinetic Energy (MeV)

0 10 20 30 40 50 600.00

0.01

0.02

0.03

0.04

0.05

40.5 MeV

S1 0.07%

81.6%

14.0 MeV 24.4 MeV

TXE Distribution of Primary Fragments for U- 235(nth,f) (Based on the data of H.- H. Knitter et al. (1987))

SL

S2

Total Excitation Energy (MeV)

Prob

abilit

y

18.3%

TXE =ER(ZH,AH,ZL,AL) + Bn + En – TKE

20L HZ Z el

TKE

• Given the TKE distribution for a fission mode, the distribution of the charge-center distance is obtained.

2. TKE distribution was converted into the TXE distribution

Initial Conditions for Monte Carlo Simulation (2)

• The TXE distribution is calculated from energy-conservation relation.

HL

LL AA

ATXEE

*

**

**

,,,

HHLL

LLL EAaEAa

EAaTXEE

HL

LL AA

ATXEE

*

3. Partition of the TXE between the two fragments Three working hypotheses in accordance with P. Talou et al. (2007)

Initial Conditions for Monte Carlo Simulation (3)

H0 　 Equipartition of Energy

H1 　 Equitemperature assumption

H2 　 Partition according to ν(AL,H)

Monte Carlo Code “NEDAEMON”

• Select fission mode (S1, S2, SL, …)

• Sampling of (AL , ZL , TKE, I )

• Calculation of ER, TXE, etc.

• Cascade Process

• Accumulation of calculated data (Total of 109 events)

nSE*

TTk C

exp

2 cosf fE E E q

nR SEE **

• Condition for Neutron Emission

• Transformation into L-system

• Excitation Energy of the Residual Nucleus

Random sampling

• Neutron Spectrum in the CM-system

q

• Mass formula• TEX Partition (H0, H1, H2)

• Neutron Emission Time τ• FF Acceleration Time t• NEDA Probability P(X), …

• PFNS calc. [NEDAPEK]

ε

l

Results (1)

• The agreement with measured data as well as with other MC calculations is rather good, irrespective of the hypothesis H0, H1, H2. → Estimation of TXE in the present analysis is adequate.

Frequency Distribution of the Number of Emitted Neutrons

Results (2)The Average Number of Neutrons Emitted from FF of Mass A

• The saw-tooth structure is reproduced, without ad hoc adjustment.• Among the 3 hypotheses, H2 gives the best representation. → The following calculations were done with H2.

Results (3)The Neutron Emission Time as a Function of Mass for 235U

Our findings are: • The neutron emission time τ varies over a wide range from fragment to fragment. • The gross structure is caused by the shell effects on the LDP and Sn. • Fluctuations between neighboring FF is due to even-odd effect.

H2

Under different hypothesis For different fission modes

S1 HF S1 LF S2 HF S2 LF SL~ 90% 8.6% 2.2% 10.0% 11.9% 18.1%~ 95% 14.9% 3.9% 16.7% 19.1% 27.5%~ 99% 42.6% 13.4% 42.9% 43.6% 53.2%

235U(nth,f) Integral NEDA probability

NEDA probability as a function of χ

χ

NEDA probability is high at the final stage of accele-ration.

The average value for 252Cf(sf) is ~16%,due to higher Q- value.

Results (4)

A certain fraction of neutronsare certainly emitted before full acceleration.

235U(nth,f)

1

, ,0, ,j j f j m jN E N E E T P d

PFNS with Consideration of NEDA Effect (Code NEDAPEK)

HLj

ijmijfjijiHiL

i TEENEN,

,,,,,,,

,,1

iii

iiii

vw

ENvwEN

◆Modal neutron spectrum for mode i

◆Total neutron spectrum (summed over possible modes)

Results (5)

◆Single-fragment neutron spectrum

PFNS with and without consideration of NEDA

NEDA enhances the low-energy wing

Results (6)

Angular anisotropy of emitted neutrons in the CM-system of FF

2

2

2( )

( )

( , )[1 ( ) / 4 ]1( , , )4 (1 / 3)

f

f

E E c f ff c E E

f

b E E EN E E d

E b

[T. Ohsawa, INDC(NDS)-0541, p.71 (2009)]

Two possibilities:

b=0.05 C. Budtz-Jørgensen et al., INDC(NDS)-220, 181 (1989)

b=0.1 V.F. Gerasimenko et al., INDC(NDS)-220, 283 (1989)

Results (7)

Result： → Next page

NEDA + Anisotropy

Taking into account the CM-anisotropy of neutron emission, in addition to NEDA-effect, in the multimodal Madland-Nix model, significantly enhances the low-energy component and improves the agreement with experimental data in the region less than 0.5 MeV.

Conclusions1. Monte Carlo simulation of competition of Coulomb

acceleration and neutron emission was made to examine the possibility of NEDA.

2. The initial condition for starting the Monte Carlo calculation was sampled from Multimodal Random Neck-Rupture model.

3. The simulation showed that ~10% of neutrons were emitted before 90%-acceleration for 235U(nth,f); and ~16% for 252Cf(sf).

4. Existence of NEDA-neutrons enhances the low-energy wing of the PFNS. Consideration of CM-angular anisotropy of neutron emission, in addition to NEDA, further increases the low-energy component of the spectra and improves the agreement with experimental data in the region <0.5 MeV..

That’s it. Thanks!