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核行列要素計算の現状と問題点

核行列要素計算の現状と問題点. Status and problems of nuclear matrix elements calculations. Kazuo M UTO Tokyo Institute of Technology. Nuclear transition operators Quasi-particle RPA calculation Problems of calculations. Part 1. Nuclear transition operators. Two decay modes. 2 n mode Allowed in SM

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核行列要素計算の現状と問題点

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  1. 核行列要素計算の現状と問題点 Status and problems ofnuclear matrix elements calculations Kazuo MUTO Tokyo Institute of Technology • Nuclear transition operators • Quasi-particle RPA calculation • Problems of calculations 二重ベータ崩壊研究懇談会

  2. Part 1 Nuclear transition operators 二重ベータ崩壊研究懇談会

  3. Two decay modes 2n mode • Allowed in SM • Observed for 10 nuclides • Shortest half-life：T1/2 = 1019 y 0n mode • Forbidden in SM • No observation so far 二重ベータ崩壊研究懇談会

  4. Momentum transfer Weak Hamiltonian 1. Nonrelativistic reduction of nucleon current2. Multipole expansion into spherical tensors 2n mode 0n mode Large momentum transfer～100 MeV/c 3. Long wave length limit Gamow-Teller transitions:momentum transfer ～ 0 → nucleon form factor 二重ベータ崩壊研究懇談会

  5. Nuclear transition operators Sequential (Gamow-Teller) beta decays through virtual intermediate states. The neutrino exchange with momentum integral generates a neutrino potential, which resembles a Yukawa potential with a “range” of about 20 fm. 二重ベータ崩壊研究懇談会

  6. Part 2 Quasi-particle RPA calculations 二重ベータ崩壊研究懇談会

  7. BCS RPA Ground-state correlations bb decay : 0+gs → 0+gs • Important components of NN interaction: • Pairing between like nucleons →BCS • Proton-neutron interaction, in particular QQ force →RPA Random-Phase Approximation 二重ベータ崩壊研究懇談会

  8. BCS Ground state ansatz Variation with constraints quasiparticle RPA Excitation Operatorcharge-changing modes Equation of motion RPA equationquasi-boson approximation proton-neutron QRPA 二重ベータ崩壊研究懇談会

  9. by hand pnQRPA Calculations 0n mode 2n mode A poor predictive power for 2nbb NME 二重ベータ崩壊研究懇談会

  10. Rodin et al., NPA 793 (2007) 213 a)different model spaces b) different effective NN interactions c) different QRPA models d) gA = 1.25 and gA = 1.00uncertainties of about 30% The best pnQRPA prediction Experimental half-life of 2nbb decay is used to fix gpp. 二重ベータ崩壊研究懇談会

  11. Part 3 Problems of calculations 二重ベータ崩壊研究懇談会

  12. Model dependence of 0nbb NME Systematic differences between nuclear models Interacting Boson Model J. Barea and F. Iachello,Phys. Rev. C79, 044301 (2009) 二重ベータ崩壊研究懇談会

  13. Ratio of MGT and MF • A prediction of MF is expected to be more stable. • gV is free from quenching (no spin operator) • little affected by ground-state correlations If there is “universality” in the ratio MGT / MF,it can be used for more reliable predictions. bb decay : nn → pp A pair of nucleons with T=1, S=0 MGT / MF = -3 QRPA calculations give MGT / MF = -2 ～ -3 二重ベータ崩壊研究懇談会

  14. Nuclear intermediate states Multipole expansion of 0nbboperators bb decay :0+ → 0+ Multipole single-particle transition operators all Jp, except 0+ only natural-parity states 二重ベータ崩壊研究懇談会

  15. Spin-parity of nuclear intermediate states Violation of isospin symmetry The large 0+ component of MF is due to violation of isospin symmetry involved in the QRPA models. Isospin is a good quantum number in shell model. 二重ベータ崩壊研究懇談会

  16. Fermi, Gamow-Teller Spin-Dipole type Unique : only one transition operator spin-parity of nuclear intermediate states Classification of beta decays X X X X 二重ベータ崩壊研究懇談会

  17. Quenching of Gamow-Teller strengths A systematic shell-model calculation：(sd)A-16 Experimental data are well reproducedwith a quenching factor of 0.77. 二重ベータ崩壊研究懇談会

  18. B. Singh et al.,Nuclear Data Sheets 84, 487 (1998) Quenching of M2 strengths? Unique first-forbidden b decay quenching factor ? • A number of experimental data, which are, however, uncertain. • Many of them are in heavy nuclei, and structure calculations are difficult. • There are no systematic calculations which allow to discuss quenching. • New data are expected in neutron-rich nuclei. 二重ベータ崩壊研究懇談会

  19. Single-particle occupation probabilities J.P. Schiffer, et al.Phys. Rev. Lett. 100, 112501 (2008) B.P. Kay, et al.Phys. Rev. C79, 021301(R) (2009) Occupation probabilities ofQRPA deviate much from experimental data. g9/2 is most important in 76Ge Improved occupation probabilities reduce 0nbb NME （76Ge）by 20%. Data for other nuclei !! 二重ベータ崩壊研究懇談会

  20. Summary • Predictions of 0nbb nuclear matrix elements by nuclear structure models involve uncertainties of a factor of two. For more reliable predictions • Comparison between nuclear structure models • Multipole decomposition of NME • Violation of isospin symmetry • Ratio of MGT and MF • Experimental data and comparison with systematic nuclear structure calculations • Occupation probabilities of single-particle orbits • Spin-dependent transitions, in particular, M2 二重ベータ崩壊研究懇談会

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