Monte Carlo Simulation for Statistical Decay of Compound Nucleus

Transcription

1 CNR20, Prague, Czech Republic, Sep. 9 23, 20 Monte Carlo Simulation for Statistical Decay of Compound Nucleus T. Kawano, P. Talou, M.B Chadwick Los Alamos National Laboratory

2 Compound Nuclear Reaction, and Related Models Resonance and Hauser-Feshbach Theoris are Central Nuclear Database mass, structure, discrete levels, ground state deformation, fission barrier Models optical model, level density, photo strength function, fission Non-CN Contributions direct reaction, DSD capture, pre-equilibrium emission Statistical Hauser-Feshbach Width Fluctuation Correction GOE, Moldauer, HRTW, KKM Off-Diagonal Matrix Elements KKM, NWY, generalized transmission, EW transformation, detailed barance All physical quantities can be evaluated by microscopic, phenomenological, or experimental approache However, accurate knowledge about nucleus is crucial.

3 HF Theory: Significance in Nuclear Data World Neutron capture on 89 Y Calculated cross sections often reasonable from kev to 50 MeV ENDF/B-VII.0 70group Boldeman ENDF/B-VII. 70group Capture Cross Section [b] Neutron Incident Energy [MeV] Nowadays, the HF codes play a central role in the nuclear data evaluation above the resonance regions.

4 Inferred Cross Section Explore Unknown C.S. By Combining Theory and Experiments prompt γ-rays from a decay of compound nucleus this is partial information requires supplemental theoretical calculations 9/2+ 7/2+ 5/ /2+ 5/2+ 3/ keV keV 483keV 5/2-3/2-9/2-7/2-29keV Production Cross Section [b] GEANIE 4 Gammas sum Bayhurst (975) CN spin-dist. (4 Gammas) CN spin-dist. (Total) FKK spin-dist. (4 Gammas) FKK spin-dist. (Total) 3/2+ 0 / /2[400] / /2[505] IT 00% 0.53 d 3/2[402] 93 Ir Neutron Energy [MeV] Isomeric state production cross section for 93 Ir.

5 Many aspects involved in Compound Reactions foramlism of compound nuclear reactions experimental technique, including direct / indirect methods surrogate reaction technique microscopic descriptions of nuclear properties time-dependent simulations for dynamical compound nuclear reaction process non-equilibrium process strong connection with applications and more... CNR* 2007(+2n): an ideal place for exchanging our expertise

6 HF Theory: Challenges for Future Development Digging into better modeling / parameters in Hauser-Feshbach Model microscopic descriptions neutron capture off-stability, fission, reactions on excited state improved systematics reduce uncertainties better prediction for unknown reaction cross section Beyond Cross Sections application to other nuclear processes new approach Monte Carlo (this talk) more sensitive to nuclear structure coincidence, correlation new applications gamma-ray strength function level density fission neutron event generator in transport simulations

7 Two Implementations for MCHF at LANL Computer Programs CoH 3 and CGM CoH 3 + ECLIPSE (talks at CNR2009 and SNA&MC 200) general Hauser-Feshbach and pre-equilibrium calculation code generate decay probabilities P for all reaction channels first, P (c n, k n, c m, k m ) = T (c m k m c n k n ) c m k m T (c m k m c n k n ) then, Monte Carlo calculations are done with another code, ECLIPSE calculation fast, but angular momenta conserved only in an average sense TK, P. Talou, et al. J. Nucl. Sci. Technol. 47, 462 (200) CGM (present work) calculate compound nucleus decay by using both deterministic and stochastic (MC) methods, with very fine energy grid include neutron and γ-ray channels only, but conserve spin and parity multi-neutron emission, with non-constant energy grid (just technical, but will be important)

8 CGM Cascading Gamma ray and Multiplicity Nuclear Masses AW & FRDM RIPL-3 Discrete Levels Level Density Gilbert-Cameron parameters QRPA Gamow-Teller Strength CGM Gamma-ray cascade simulation Beta-decay calculation Statistical Decay Particle Transmission Gamma-ray Transmission ENSDF beta-decay to low-lying states Entrance Channel Optical Model (transmission generator) Spectra of gamma-ray, neutron, electron, and neutrino for beta-decay Spectra of gamma-ray and neutron, and multiplicities from a given state deterministic, or Monte Carlo CGM (about 70% of the code are from CoH 3 ) was developed (a) for studying β-delayed neutron and γ emission, (b) as an event generator in a transport code (MCNP6), and (c) a Monte Carlo approach to the prompt fission neutron spectrum (talk by P. Talou).

9 Neutron, Gamma ray Emission Probability E x Z, A Z, A- E 0 S n E gamma-ray emission P (ɛ γ )de 0 = T γ(e x E 0 )ρ(z, A, E 0 ) de 0 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 0 Ex S n T γ (E x E 0 )ρ(z, A, E 0 )de 0 + T n (E x S n E )ρ(z, A, E )de 0 integration performed only for spin and parity conserved states at low excitation energies, discrete level data are used (taken from RIPL-3)

10 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, E0 ), 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

11 Gamma Ray Energy and Multiplicity 238 U + n (E th ), γ-ray production probabilities E, M, and E2 are included m = 4.77 ɛγ =.0 MeV M added Eγ = 2 MeV, Γ γ = 0.6, σ 0 =.2 mb (assumed) m = 4.52 ɛγ =.06 MeV

12 Gamma Ray Energy Spectra for n+u238 Looking for pygmy resonance / scissors mode 00 without scissors mode with scissors mode without scissors mode with scissors mode 0 Gamma-Ray Spectra [/MeV] Gamma-Ray Spectra [/MeV] Gamma-Ray Energy [MeV] Gamma-Ray Energy [MeV] Total Energy Spectra Spectra for m = 2 4π-calorimeter experiments like DANCE, and high-intensity γ-ray source like HIγS at TUNL are able to identify these dipole resonances (priv. comm. M. Krtička, J. Ullmann, A. Tonchev).

13 Gamma Ray Spectra w/o Neutron Competition 54 Gd below and above S n J π =, 2 J π = 5, kev above Sn below Sn kev above Sn below Sn Gamma-Ray Spectra [/MeV decay] 0 Gamma-Ray Spectra [/MeV decay] Gamma-Ray Energy [MeV] Gamma-Ray Energy [MeV]

14 Gamma Ray Spectra Depends on Parity Distribution Gamma-Ray Spectra [/MeV decay] kev above Sn even parity 80% even parity 20% 54 Gd above S n parity distribution important odd (negative) parity at neutron capture state parity flips by E transition γ-ray multiplicity = 2 3 fewer even parity states suppress γ branching an exact parity distribution in the continuum unknown Gamma-Ray Energy [MeV]

15 Variable Bin Width Calculation Behavior of low energy neutrons constant energy-bin calculations faster no information on neutrons when energies are Z, A Z, A- Z, A-2 Z, A-3 less than E variable energy-bin slower, algorithm becomes complicated gives correct spectrum shape at low energies neutron and gamma-rays from 37 Xe at 0 MeV 0 gamma-ray (x000) neutron 0 gamma-ray (x000) neutron Total Excitation Energy S (A-) n S (A-2) n Spectrum [/MeV] Secondary Energy [MeV] Spectrum [/MeV] Secondary Energy [MeV] S (A) n low energy neutrons come from all the every compound decay stages

16 Evaporation (Weisskopf) or Maxwellian? Asymptotic form at very low energies Evaporation: fe (ɛ) = Aɛ exp( ɛ/t ) f E (ɛ 0) = fe (ɛ) ɛ for ɛ 0 Maxwellian: fm (ɛ) = A ɛ exp( ɛ/t ) f M (ɛ 0) = 2 ɛ fm (ɛ) ɛ/2 for ɛ 0 Watt: fw (ɛ) = A sinh( Bɛ) exp( ɛ/t ) f W (ɛ 0) = B 2 ɛ fw (ɛ) ɛ/2 for ɛ 0 from Hauser-Feshbach s-wave neutron transmission coefficient T0 = 2πS 0 ɛ level density is assumed to be constant within a small energy width fhf (ɛ) T 0 ρ(e x ) = C ɛ for ɛ 0 Spectra [arb. unit] Maxwellian Evaporation Watt 0 Emission Energy [arb. unit]

17 Comparison with CGM No Cascade Mode Neutron Spectrum [/MeV] 0 0 MeV CGM Maxwellian Evaporation Watt Neutron Spectrum [/MeV] 0 5 MeV CGM Maxwellian Evaporation Watt Neutron Spectrum [/MeV] 0 20 MeV CGM Maxwellian Evaporation Watt Secondary Neutron Energy [MeV] Secondary Neutron Energy [MeV] Secondary Neutron Energy [MeV] Neutron Spectrum [/MeV] 0 0 MeV CGM Maxwellian Evaporation Watt Neutron Spectrum [/MeV] 0 5 MeV CGM Maxwellian Evaporation Watt Neutron Spectrum [/MeV] 0 20 MeV CGM Maxwellian Evaporation Watt Secondary Neutron Energy [MeV] Secondary Neutron Energy [MeV] Secondary Neutron Energy [MeV] The evaporation spectrum does not give a correct spectrum shape in the low energy region. The Watt spectrum better describes the Hauser-Feshbach spectrum (but in CMS).

18 Watt Spectrum?

19 Asymptotic Gamma Ray Energy Spectra from Hauser-Feshbach transmission coefficient E assumed T (ɛ) = Cɛ 3 level density constant temperature ρ(e x ) = ( Ex T exp T spectrum will be f(ɛ) = T (ɛ)ρ(e x ) = C ɛ 3 exp Lemaire et al. (Phys. Rev. C 73, (2006)) f(ɛ) = ɛ2 ( 2T 2 exp ɛ ) T ) ( ɛ ) T Gamma-Ray Spectra [arb. unit] 0 E 2 exp(-e/t) E 3 exp(-e/t) CGM Gamma-Ray Energy [MeV]

20 Sequential Neutron Emission Neutron and gamma-ray emission spectra from excited 40 Xe initial spin distribution by the level density 00,000 events 2 hours on a laptop computer 0 0 MeV first neutron second neutron gamma-ray 0 5 MeV first neutron second neutron gamma-ray 0 20 MeV first neutron second neutron third neutron gamma-ray Spectrum [/MeV] Spectrum [/MeV] Spectrum [/MeV] Secondary Energy [MeV] Secondary Energy [MeV] Secondary Energy [MeV] 0 MeV 5 MeV 20 MeV ɛ γ = 0.87 MeV 0.89 MeV.06 MeV ɛ n =.37 MeV.44 MeV.48 MeV

21 Correlation Between First and Second Neutrons Energy correlation in the emitted neutrons from excited 40 Xe 0 MeV 5 MeV 20 MeV the joint probability normalized to [decay, n-mev, γ-mev] patterns shown are due to discrete levels in the residual nucleus

22 Correlation Between Gamma Energy and Neutrons Energy correlation between total γ-ray energy and neutrons from excited 40 Xe 0 MeV 5 MeV 20 MeV the joint probability normalized to [decay, n-mev, γ-mev]

23 Neutrons and Gamma Ray Multiplicity Correlation Neutron spectra from 40 Xe for each gamma-ray multiplicity Probability 0.2 Probability 0.2 Probability Multiplicity Multiplicity Multiplicity

24 Initial Spin Distribution Important Multiplicity depends on average spin in CN (σ 2 doubled case) Probability 0.2 Probability 0.2 Probability Multiplicity Multiplicity Multiplicity

25 Conclusion MCHF: Monte Carlo Hauser-Feshbach Method In this study we performed Monte Carlo simulations for neutron and γ-ray emissions. CGM: Monte Carlo Hauser-Feshbach code developed at LANL The evaporation spectrum does not give a correct asymptotic shape at low energies, which should be ɛ. Correlated neutron - gamma-ray emission from excited nucleus; with the MCHF technique it is possible to calculate: correlated neutron and γ-ray emissions neutron energy spectra for individual gamma-ray multiplicity Perspective Neutron and γ-ray generator in a transport simulation radiation shielding, detector efficiency simulation, etc. More detailed comparison with experimental data MCHF method sensitive to nuclear structure

26 Level Density Parameter Systematics Level Density Parameter [MeV - ] a(from D 0 data) a(asymptotic) Least-Squares Fit Washing-out of shell effects shell correction (δw ) and pairing energies ( ) taken from KTUY05 mass formula { a = a + δw ( e γu )} U a = 26A A 2 at low excitation energies, the constant temperature model is used with Mass Number T = 47.A 0.89 δw obtained from discrete level data of more than 000 nuclei TK, S. Chiba, H. Koura, J. Nucl. Sci. Technol., 43, (2006) and updated parameters by TK in 2009

27 Gamma Ray Strength Function and Transmission Standard Lorentzian ɛ γ Γ f E (ɛ γ ) = Cσ 0 Γ 0 0 (ɛ 2 γ E2 0 )2 + ɛ 2 γ Γ2 0 Generalized Lorentzian, finite value at low energies, energy dependent width f E (ɛ γ ) = Cσ 0 Γ 0 ɛ γ Γ(ɛ γ, T ) (ɛ 2 γ E2 0 )2 + ɛ 2 γ Γ2 (ɛ γ, T ) + 0.7Γ(ɛ γ = 0, T ) E where C = mb MeV 2 in CGM, E, M, and E2 are considered pygmy resonance and scissors mode can be included if necessary γ-ray transmission coefficient is given by T γ (ɛ γ ) = 2π m E 2L+ γ f m (ɛ γ ) Strength Function, f(e) Generalized Lorentzian Standard Lorenzian E [MeV]