Monte Carlo Simulation for Statistical Decay of Compound Nucleus

Transcription

1 5th ASRC International Workshop Perspectives in Nuclear Fission JAEA Mar. 4 6, 22 Monte Carlo Simulation for Statistical Decay of Compound Nucleus T. Kawano, P. Talou, M.B. Chadwick, I. Stetcu Los Alamos National Laboratory B. Becker, Y. Danon Rensselaer Polytechnic Institute

2 Introduction Stochastic Aspects of Prompt Fission Neutrons and γ-rays Distributions of fission fragments Mass and charge distributions Y (Z, A) just after scission Spin and parity distribution R(J, π) in the initial fragments Kinetic energy T XE and excitation energy T KE distributions P (Ex ) and energy sharing between two fragments Distributions in evaporation process Level density of all nuclei appeared in the de-excitation process Neutron and γ-ray competition at each excited state Neuron emission angle to obtain the spectrum in the Lab-frame The microscopic calculation of prompt fission neutrons and γ-rays requires to integrate (sum) over these distributions.

3 Monte Carlo for Prompt Fission Neutrons and Gammas From Averaged Quantity to Distributions of These Quantities Neutron spectrum represented by a simple functional form Madland-Nix spectrum, modified MN by Ohsawa, P-by-P model by Tudora predominant pairs selected from Y (Z, A), or include all pairs a simple excitation energy distribution assumed (Terrell 958) Monte Carlo approaches to the fission spectra Lemaire et al., Randrup and Vogt, Litaize and Serot, Schmidt, Ohsawa Y (Z, A) and P (Ex ) sampled from distributions nuclear decay process calculated with an evaporation model Full Monte Carlo simulation Talou et al. Y (Z, A), P (Ex ), and R(J, π) sampled from distributions nuclear decay process calculated with the deterministic or Monte Carlo Hauser- Feshbach model

4 Neutron, Gamma ray Emission Probability E x Z, A Z, A- E S n E gamma-ray emission P (ɛ γ )de = T γ(e x E )ρ(z, A, E ) de N neutron emission P (ɛ n )de = T n(e x S n E )ρ(z, A, E ) de N where T n,γ are the transmission coefficients, ρ(z, A, E) is the level density, and the normalization N is given by N = Ex Ex S n T γ (E x E )ρ(z, A, E )de + T n (E x S n E )ρ(z, A, E )de integration performed only for spin and parity conserved states at low excitation energies, discrete level data are used (taken from RIPL-3)

5 Monte Carlo Hauser Feshbach Method Total Excitation Energy Z, A Z, A- (d) (c) (a) (b) S (A) n Z, A-2 S (A-) n Algorithm in CGM starting at (Z, A, E ), P (ɛ n ) and P (ɛ γ ) are calculated choose a next state (Z, A, E ) by a random sampling method repeat this until the state reaches at a discrete level each time P s are re-calculated it is faster if all the P s are calculated at the beginning, but the memory size can be GByte at a discrete level, do Monte Carlo gamma-ray cascade based on branching ratios in RIPL-3

6 Sequential Neutron Emission Simulation Neutron and gamma-ray emission spectra from excited 4 Xe initial spin distribution by the level density, events 2 hours on a laptop computer MeV first neutron second neutron gamma-ray 5 MeV first neutron second neutron gamma-ray 2 MeV first neutron second neutron third neutron gamma-ray Spectrum [/MeV].. Spectrum [/MeV].. Spectrum [/MeV] Secondary Energy [MeV] Secondary Energy [MeV] Secondary Energy [MeV] MeV 5 MeV 2 MeV ɛ γ =.87 MeV.89 MeV.6 MeV ɛ n =.37 MeV.44 MeV.48 MeV

7 Initial Spin/Parity Changes Energy Spectra neutron and gamma-rays from 38 Xe at 5 MeV J = J = Neutron Spectrum [x/mev]... Gamma Spectrum [x/mev] Secondary Neutron Energy [MeV] Secondary Gamma Energy [MeV] The initial spin (distribution) also has a large impact on the neutron/gamma-ray competition above neutron separation energies.

8 Application to Fission Fragment Decay Initial Conditions U-235 thermal neutron fission Y (A, T KE) evaluated from experimental data P (Z A) from Wahl systematics R(J, π) from level density J distribution, with scaled σ(u) R(J, π) = J + /2 2σ 2 exp T XE given by the distributions above and energy conservation { } (J + /2)2 2σ 2 Parameters in the Hauser-Feshbach Model Neutron optical potential by Koning-Delaroche Kopecky s γ-ray strength function Level density systematics based on KTUY5 mass model Nuclear Excitation Energy [MeV] Fragment Mass Y (A, U ex ) for R T =

9 Anisothermal Parameter Excitation Energy Sharing Between Fragments 2 Excitation Energy Ratio (light/heavy) Excitation Energy Ratio (light/heavy) RT=. RT=.5 RT from Litaize and Serot (2) Heavy Fragment Mass RT=. RT=.5 RT from Litaize and Serot (2) Heavy Fragment Mass Ratio of the temperatures in two fragments: R T = T l = U l a h (U h ) T h U h a l (U l ) Many different estimates for RT Ohsawa, Talou, Litaize and Serot, Shu Neng-Chuan et al. Schmidt et al., Manailescu et al., Becker et al., Vogt and Randrup (different parametrization) RT =. still gives more excitation energy to the light fragment near A = 3 due to the level density Actual excitation energy sharing depends on the level density model adopted

10 Prompt Neutron Multiplicity and Probability Probabilities for Each Multiplicity, and ν for Each Fragment.5.4 RT=.2 RT from Litaize and Serot Franklyn 978 Boldeman 967 Diven 956 Holden RT=.2 RT from Litaize and Serot Maslin 967 Nishio 998 Batenkov 24 Probability.3.2 Number of Neutrons Number of Neutrons Mass Number Note that R T by Litaize and Serot is for 252 Cf Deterministic HF calculations for CN Decay process for better statistics RT is sensitive to ν(a), but not so sensitive to P (ν)

11 Average CMS and LAB Neutron Spectra Kinematic Boost for the Light Fragment in the LAB Spectrum CMS Spectrum [/MeV].. LAB Spectrum [/MeV].. RT=.2 L H RT=.2 L H RT Litaize and Serot L H Madland-Nix L H.. Fission Neutron Energy [MeV] RT Litaize and Serot L H Madland-Nix L H.. Fission Neutron Energy [MeV] The CMS-LAB conversion by Terrell s method The Madland-Nix spectrum represents the fission spectrum in ENDF

12 Full Monte Carlo Calculation, Ratio to Maxwellian Detailed Comparison with MN Model Calculation.2.2 Ratio to Maxwellian (T=.42 MeV) Ratio to Maxwellian (T=.42 MeV) Litaize and Serot (Determinisit) RT=.2 (Monte Carlo) Madland-Nix.. Secondary Neutron Energy [MeV].2 Johansson 977 Hambsch 29 RT=.2 (Monte Carlo) Madland-Nix.. Secondary Neutron Energy [MeV] Our LAB-spectrum gives higher than ENDF below 2 MeV and above MeV Need more statistics to obtain higher energy tail Optimization of RT is required too (Becker et al. PRC paper prepared)

13 Evaporation (Weisskopf) or Maxwellian? Asymptotic form at very low energies Evaporation: fe (ɛ) = Aɛ exp( ɛ/t ) f E (ɛ ) = fe (ɛ) ɛ for ɛ Maxwellian: fm (ɛ) = A ɛ exp( ɛ/t ) f M (ɛ ) = 2 ɛ fm (ɛ) ɛ/2 for ɛ Watt: fw (ɛ) = A sinh(. Bɛ) exp( ɛ/t ) f W (ɛ ) = B 2 ɛ fw (ɛ) ɛ/2 for ɛ. from Hauser-Feshbach s-wave neutron transmission coefficient T = 2πS ɛ level density is assumed to be constant within a small energy width fhf (ɛ) T ρ(e x ) = C ɛ for ɛ Spectra [arb. unit]. Maxwellian Evaporation Watt.. Emission Energy [arb. unit]

14 Concluding Remarks Hauser-Feshbach Method for Fission Fragment Decay CGM: Monte Carlo Hauser-Feshbach code developed at LANL In this study we performed Monte Carlo simulations for prompt fission neutron and γ-ray emissions. Sampled fission fragments from Z, A, Ex distributions Neutron and γ-ray emission with the Hauser-Feshbach method, both deterministic and Monte Carlo Several models for anisothermal parameter RT tested. We applied our model to the fission of 235 U at the thermal energy, and calculated P (ν), ν(a), and total neutron emission spectra. The γ-ray results (not shown in this talk) similar to ENDF evaluation. This work was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-6NA25396.