1. Futoshi Minato JAEA Nuclear Data Center, Tokai Theoretical calculations of beta-delayed neutrons and sensitivity analyses 1

2. 2 1.Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model (HFSM) 2.Incident Neutron Energy Dependence of DN Yields 3.Sensitivity Analysis of DN with JENDL evaluated libraries 4.Important Precursors in r-process Nucleosynthesis Contents of This Talk

3. 3 1.Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model 2.Incident Neutron Energy Dependence of DN Yields 3.Sensitivity Analysis of DN with JENDL evaluated libraries 4.Important Precursors in r-process Nucleosynthesis Contents of This Talk

4. 4 1. DN Emission Probabilities by SHF+QRPA plus HFSM Calculations of DN Emission Probability β-β- Parent/ Precursor (Z,N) Daughter (Z+1,N-1) (Z+1,N-2) n g.s. γ

5. 5 1. DN Emission Probabilities by SHF+QRPA plus HFSM β-β- Parent/ Precursor (Z,N) Daughter (Z+1,N-1) (Z+1,N-2) n QRPA HFSM g.s. T 1/2 Strength Function P n (P 1n, P 2n, P 3n ) Neutron Spectrum γ Calculations of DN Emission Probability

6. 6 1. DN Emission Probabilities by SHF+QRPA plus HFSM QRPA On top of Skyrme-Hartree-Fock+BCS Deformation (cylind. coordinate space) Volume-type Pairing force in BCS Residual Interaction : Same as G.S. Include All Terms self-consistently SkOSAMi Strength of Pairing (p,n) Odd Nuclei Skyrme Effective Force p or n core (330,323)(256,258) Valence Particle is assumed to follow Indep. Particle Model Blocking Effect in QRPA

7. 7 1. DN Emission Probabilities by SHF+QRPA plus HFSM QRPA Prescription to determine T=0 pairing strength V pp 1.Search appropriate V pp reproducing T 1/2 of E-E Nuclei 2.Calculate Average V pp ave (Z) from V pp of same Z 3.Calculate T 1/2 of isotope chains systematically with V pp ave (Z) SkO Atomic Number Z Isospin T=0 pairing Attractive in GT channel Strong pairing  Low 1+ state in daughter  Shorter T 1/2 V pp (Z) Daughter g.s. 1+

8. 8 1. DN Emission Probabilities by SHF+QRPA plus HFSM 233 nuclei rms=5.09 T 1/2 (calc) / T 1/2 (exp) SKO

9. 9 1. DN Emission Probabilities by SHF+QRPA plus HFSM HF Hauser-Feshbach Models implemented in the nuclear reaction calculation code, “CCONE”. Neutron Transmission Coefficient : Koning-Delaloche Optical Pot. Gamma-ray Transmission Coefficient : Kopecky-Uhl’s EGLO Level-Density: Fermi Gas Model with Mengoni-Nakajima parameter set at high excitation energy (Z+1,N-2) n g.s. Daughter (Z+1,N-1) γ n γ β-β- Parent (Z,N) Q β =1.SHF+BCS 2.Experiment

10. DN Emission Prob. for Z=35-44 (Q β : SHF+BCS) 10 1. DN Emission Probabilities by SHF+QRPA plus HFSM SKO

11. 11 1. DN Emission Probabilities by SHF+QRPA plus HFSM DN Emission Prob. for Z=27-30 (Q β : exp. or KTUY)

12. 12 1. DN Emission Probabilities by SHF+QRPA plus HFSM P2n & P3n (Q β : exp. or KTUY) A (Co isotopes) P2n or P3n SAMi(P2n) SkO(P2n) SAMi(P3n) SkO(P3n)

13. 13 DN Spectra 1. DN Emission Probabilities by SHF+QRPA plus HFSM Cu-81 Zn-83 g.s. Daughter (Z+1,N-1) β-β- Parent (Z,N) φ n (MeV -1 )/ 1 fission E (MeV)

14. 14 1.Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model 2.Incident Neutron Energy Dependence of DN Yields 3.Sensitivity Analysis of DN with JENDL 4.Important Precursors in r-process Nucleosynthesis Contents of This Talk

15. 15 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Energy Dependence of DN Yields in Nuclear Data

16. 16 Fission Yield Data Decay Data Activity of DN DN Yield 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Detail can be found in [2]. Calculation is performed with Code [3].  Bateman Equation Energy Dependent 137 Te 137 I 137 Xe 137 Cs 137 Ba 137m Ba 炉物理の研究 第 64 号（ 2012 年 3 月）吉田先生 β-β- β-β- β-β- β-β- β-β- 0.4% 0.1% 3.2% 2.7% Indep. FY 2.6m IT 2.5s24.5s 3.8m 30.1y βn=2.9%βn=7.1%

17. 17 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Decay Data ： JENDL/FPD-2011 J. Katakura, JAEA-DATA/Code2011-025(2011) Bad Reproduction Fission Yields ： 5 Gaussian Model 1. Mass Distribution & Prompt Neutron:J. Katakura, JAERI-Research2003-004(2003) 2. Charge Distribution: T.F. England and B.F.Rider, LA-UR-94-3106,ENDF-349(1994). 3. Isomer states:J. Katakura, JAEA-DATA/Code2011-025(2011) Wahl, IAEA-TECDOC-1168(2000)

18. 18 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Correction in A) D.R. Nethaway, Lawrence Livermore Laboratory Report No. UCRL-51538, (1974). (see also D.R. Alexander and M.S. Krick, Nucl. Sci. Eng. 62, 627 (1977) ) B) V.A. Roshchenko, V.M. Piksaikin et al., Phys. Rev. C74, 014607 (2006) Energy Dependence of charge distribution: E (eV) DN Yield/fission

19. 19 1.Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model 2.Incident Neutron Energy Dependence of DN Yields 3.Sensitivity Analysis of DN with JENDL 4.Important Precursors in r-process Nucleosynthesis Contents of This Talk

20. 20 Sensitivity Test Fission Yields DN Emission Prob. 3. Sensitivity Analysis of Delayed Neutron with JENDL

21. 235 U: 86 Ge, 89 Br, 90 Br, 94 Rb, 137 I Thermal Neutron Fission 239 Pu: 89 Br, 90 Br, 94 Rb, 98m Y, 137 I, 138 I Remarkable Nuclei 235 U: 86 As, 88 Br, 89 Br, 90 Br, 94 Rb, 137 I 239 Pu: 88 Br, 89 Br, 90 Br, 94 Rb, 98m Y, 137 I, 138 I 21 3. Sensitivity Analysis of Delayed Neutron with JENDL

22. Nucl. Yield error Err./Yield Ge-86 0.6278 0.1005 (16%) As-85 0.1212 0.0775 (63%) As-86 0.0199 0.0127 (64%) Br-89 1.0379 0.0415 (4%) Br-90 0.5518 0.0331 (6%) Rb-94 1.5644 0.0438 (2.8%) Y-98m 1.8739 0.5996 (32%) Sb-135 0.1449 0.0116 (8%) Te-137 0.3919 0.0313 (8%) Te-138 0.0661 0.0423 (64%) I-137 2.6189 0.1048 (4%) I-138 1.4222 0.0398 (2.8%) Nucl Pn(%) err. err./Pn Ge-86 6 N/A (----) As-85 59.4 29 (48.8%) As-86 33.0 4.0 (12%) Br-89 13.8 0.4 (2.9%) Br-90 25.2 0.9 (3.6%) Rb-94 10.5 0.4 (3.8%) Y-98m 3.4 1.0 (29%) Sb-135 22 3 (13.6%) Te-137 2.99 0.16 (5.4%) Te-138 6.3 2.1 (33%) I-137 7.14 0.23 (3.22%) I-138 5.56 0.22 (3.96%) Uncertainties in JENDL/FPY & FPD-2011 Indep. Fission Yields Pn(%) Red represents uncertainty > 5% 22 3. Sensitivity Analysis of Delayed Neutron with JENDL

23. 23 1.Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model 2.Incident Neutron Energy Dependence of DN Yields 3.Sensitivity Analysis of DN with JENDL 4.Important Precursors in r-process Nucleosynthesis Contents of This Talk

24. 24 4. Important Precursors in r-process Nucleosynthesis This Work is performed with T. Kajino & Shibagaki at NAOJ Important DN precursor after freeze-out(f.o.) in r-process We define Tells information which nucleus emits neutron efficiently after f.o.

25. 25 4. Important Precursors in r-process Nucleosynthesis 1. Ag-129 4.79E-01 2. Rh-127 1.54E-01 3. Pd-128 7.33E-02 4. Cd-130 6.16E-02 5. Rh-125 5.59E-02 6. In-131 2.76E-02 7. Ru-126 1.68E-02 8. Pd-126 1.67E-02 9. Al-35 1.64E-02 10. Nb-109 1.56E-02 1. Sb-137 9.63E-02 2. Sb-135 8.06E-02 3. Ag-129 6.75E-02 4. P-41 6.72E-02 5. I-141 6.27E-02 6. Cl-46 5.67E-02 7. Cd-130 4.12E-02 8. Sn-136 3.14E-02 9. I-143 3.07E-02 10. Sn-134 2.76E-02 Ye=0.3, τ=16.6ms, s/k=105 Ye=0.3, τ=16.6ms, s/k=155

26. 26 4. Important Precursors in r-process Nucleosynthesis 1. Sb-137 1.28E-01 2. Cl-46 7.14E-02 3. P-41 7.12E-02 4. Sb-135 6.29E-02 5. I-143 3.10E-02 6. I-141 2.99E-02 7. Sn-136 2.43E-02 8. La-157 2.41E-02 9. Pr-161 2.08E-02 10. La-155 1.93E-02 Ye=0.3, τ=16.6ms, s/k=205

27. 27 Thank you for you attention