Theoretical Calculations of Beta-Delayed Neutrons and Sensitivity Analyses

In this talk by Futoshi Minato from JAEA Nuclear Data Center, topics covered include delayed neutron emission probabilities, incident neutron energy dependence, sensitivity analysis with JENDL evaluated libraries, and important precursors in r-process nucleosynthesis. Theoretical calculations are presented using the Skyrme-HF+QRPA and Hauser-Feshbach statistical model, exploring various aspects such as parent/precursor relationships, neutron spectra, and pairing forces. The discussion delves into the theoretical framework for understanding beta-delayed neutrons and their implications in nuclear processes.

• Theoretical calculations
• Beta-delayed neutrons
• Sensitivity analyses
• Nuclear data
• Skyrme-HF+QRPA

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

2. Contents of This Talk 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 2

3. Contents of This Talk 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 3

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

5. 1. DN Emission Probabilities by SHF+QRPA plus HFSM Calculations of DN Emission Probability g.s. - n Parent/ Precursor (Z,N) g.s. (Z+1,N-2) QRPA HFSM Pn(P1n, P2n,P3n) Neutron Spectrum T1/2 g.s. Strength Function Daughter (Z+1,N-1) 5

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 SkO SAMi (330,323) Skyrme Effective Force Strength of Pairing (p,n) (256,258) Odd Nuclei Valence Particle is assumed to follow Indep. Particle Model p or n core Blocking Effect in QRPA 6

7. 1. DN Emission Probabilities by SHF+QRPA plus HFSM QRPA Isospin T=0 pairing Attractive in GT channel Strong pairing Low 1+ state in daughter Shorter T1/2 1+ 1+ 1+ Prescription to determine T=0 pairing strength Vpp 1. Search appropriate Vppreproducing T1/2of E-E Nuclei 2. Calculate Average Vppave(Z) from Vppof same Z 3. Calculate T1/2of isotope chains systematically with Vppave(Z) g.s. Daughter SkO Vpp(Z) 7 Atomic Number Z

8. 1. DN Emission Probabilities by SHF+QRPA plus HFSM 233 nuclei rms=5.09 SKO T1/2(calc) / T1/2(exp) 8

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 - Parent (Z,N) n n g.s. (Z+1,N-2) g.s. Daughter (Z+1,N-1) Q =1.SHF+BCS 2.Experiment 9

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

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

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

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

14. Contents of This Talk 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 14

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

16. 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Decay Data Fission Yield Data Energy Dependent Activity of DN ??(?) = ???(?) ??(?) ? ????= ??(?)?? DN Yield Indep. FY 137mBa 0.4% 3.2% 2.7% 0.1% - 2.6m IT - - - - 137Cs 30.1y 137Xe 3.8m 137Te 2.5s 137I 24.5s 137Ba n=2.9% n=7.1% 64 2012 3 Bateman Equation ??1(?) = ?1?1(?) ?10 = ?1, ??0 = 0(2 ?) ?? ???(?) ?? = ????? + ?? 1?? 1? (2 ?) ? ? 1?? ?=1 ??? ??? ??? = ?? ??= 2 ? ? ? ?=1,? ? (?? ??) ?=1 Detail can be found in [2]. Calculation is performed with Code [3]. 16 ??= 1 ? = ? = 1

17. 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Decay Data JENDL/FPD-2011 J. Katakura, JAEA-DATA/Code2011-025(2011) Fission Yields 5 Gaussian Model Wahl, IAEA-TECDOC-1168(2000) 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) Bad Reproduction 17

18. 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Energy Dependence of charge distribution: 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) DN Yield/fission E (eV) 18

19. Contents of This Talk 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 19

20. 3. Sensitivity Analysis of Delayed Neutron with JENDL Sensitivity Test ???=( ??/??) ( ??/??) Fission Yields ( ??/??) ( ???/???) DN Emission Prob. ????= ????= ??(?) ??? = 0.1 20

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

22. 3. Sensitivity Analysis of Delayed Neutron with JENDL Uncertainties in JENDL/FPY & FPD-2011 Indep. Fission Yields Pn(%) 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%) 22 Red represents uncertainty > 5%

23. Contents of This Talk 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 23

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

25. 4. Important Precursors in r-process Nucleosynthesis Ye=0.3, =16.6ms, s/k=105 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 Ye=0.3, =16.6ms, s/k=155 1. Sb-137 9.63E-02 2. Sb-135 8.06E-02 3. Ag-129 6.75E-02 4. P-41 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 6.72E-02 25

26. 4. Important Precursors in r-process Nucleosynthesis Ye=0.3, =16.6ms, s/k=205 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 26

27. Thank you for you attention 27