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Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass

Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass. Kazuo Muto Tokyo Institute of Technology (TokyoTech). in collaboration with F. Simkovic and R. Dvornicky , Comenius Univ., Bratislava. Single beta decay: 187 Re Double beta decay.

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Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass

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  1. Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass Kazuo MutoTokyo Institute of Technology (TokyoTech) in collaboration withF. Simkovicand R. Dvornicky, Comenius Univ., Bratislava • Single beta decay: 187Re • Double beta decay International School of Nuclear Physics, 31st CourseNeutrinos in Cosmology, in Astro-, Particle- and Nuclear PhysicsErice, SicilySeptember 16-24, 2009

  2. flavoreigenstates masseigenstates neutrino oscillation experiments No absolute mass scale b decay 187Rebb decay 76Ge, 100Mo, etc. Neutrino Mass and Mixing Neutrino Mixing Mass differences Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  3. Part 1Single Beta Decay: 187Re Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  4. Electron spectra of single b decay Effects of neutrino mass can be observed in the electron energy spectra near the end point(in the last eV). Decays with a small Q-value are favored. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  5. Single b decay: 3H and 187Re Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  6. Calc. Exp. A rather large ft value among unique first-forbidden decays reproduced from B. Singh et al.,Nuclear Data Sheets 84, 487 (1998) ft-value Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  7. Neutrino p-wave (p3/2) Electron s-wave (s1/2) in total Jp = 2- Neutrino s-wave (s1/2) Electron p-wave (p3/2) in total Jp = 2- Fermi function Electron s- and p-wave emission Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  8. Electron p-wave dominance • The electron is attracted by the Coulomb potential of the nucleus. • Huge enhancement for very low-energy p-wave electron. • No attraction for neutrino See, C. Arnaboldi, et al.,Phys. Rev. Lett. 96, 042503 (2006) Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  9. Unique first-forbidden beta decay Only one nuclear matrix element Nuclear reduced transition probability • If a s.p. transition from d5/2 to p1/2 is assumed, • from the experimental half-life The parent and daughter nuclei are well deformed,and the nuclear transition is strongly hindered. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  10. Part 2Double Beta Decay Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  11. Double beta decay can be observed when single beta decays are energetically forbidden or strongly hindered. Second order process of the weak interactionDZ = 2 Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  12. n = n Two decay modes • Allowd in the SM • Observed for about ten nuclides • Shortest half-life: T1/2 = 1019 y 2n mode • Forbidden in the SM • No observations so far • Can occur when neutrinos have a finite mass and are Majorana particles 0n mode Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  13. neutrino mass nuclear structure calculation experiment Neutrino mass from 0nbb decay 0n mode 2n mode Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  14. V.A. Rodin, A. Faessler, F. Simkovic and P. Vogel, Nucl. Phys. A766 (2006) 107: A793 (2007) 213 a)different model spaces b) different NN interactions c) different QRPA models d) gA = 1.25 and gA = 1.00 Theoretical nuclear matrix elements are stable. The best prediction by QRPA models 0nbb • Short-range correlation • Nucleon form factor • Use the measured 2nbb-decay half-life for the calibration of theoretical spin-isospin correlations. the uncertaintyof about 30% Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  15. V-A V-A A • A V • V A • A Mass term of 0nbbdecay The momentum integral of the virtual neutrino gives rise to a neutrino potential, which acts on the nuclear wave functions, being a long-range Yukawa-type (“range” ~ 20 fm). There appear three nuclear matrix elements, nuclear intermediate states with two-body nuclear transition operators. GT-term Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  16. The GT term dominatesM0n. The tensor term reducesM0nby about 10%. The multipole components contribute in the same sign. Multipole decomposition (QRPA) The 2- component corresponds to unique first-forbidden b decay. The 1+ component is strongly hindered by the g.s. correlations. spin-parities of nuclear intermediate states Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  17. The largest uncertainties lie in the 1+ component, which is sensitve to the spin-isospin g.s. correlations. pp-ph ; Jp pp-nh ; 1+ np-nh ; Jp ph-np ; 1+ The spin-isospin correlations come mainly from quadrupole deformation with Jp = 2+. Spin-isospin correlation andquadrupole deformation intermediate 1+states daughter ground state Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  18. particle-particle particle-hole Universal feature of pn interaction Proton-neutrion particle-hole matrix elements deduced experimental spectra, normalized by the monopole strengths for each multiplet. reproduced fromJ.P. Schiffer and W.M. True,Rev. Mod. Phys. 48, 191 (1976) Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  19. Monopole strength of NN interaction • Most important for shell-structure evolution, especially in neutron-rich nuclei. • Due to mainly from triplet-even attraction of the central force, with second-order renormalization of tensor force. • Effective interaction theories, such as G-matrix, do not reproduce empirical monopole strengths. • Even if the monopole strengths are well determined,the 1+ matrix element is still ambiguous, since it has little effect on the monopole with the small weight 2J+1 = 3. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  20. QRPA in a large model space : probed by charge-exchange reactions not yet confirmed GT transition with momentum transfer 0nbb 1+ component: Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  21. Summary • Single beta decay of 187Re • Only one nuclear matrix element involved. • It is obtained from the measured half-life. • The nuclear transition is strongly hindered. • Double beta decay (0nbb) • Matix elements are much more stable by the standard calculation, less dependent on the nuclear structure, than 2nbb matrix elements. • Further studies on • spin-isospin correlations vs quadrupole deformation • GT(q=0) vs GT with momentum transfer • unique first-forbidden (spin-dipole) transitions, which give the largest component of 0nbb mass term Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  22. THE END Thank you for your patience. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  23. Neutrino mass hierarchyin the electron energy spectrum mlightest = 30 meV assumed for both normal and inverted neutrino mass hierarchies. A clear difference in the last 100 meV. But, it is a tiny difference even in the last 1 eV. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  24. 0n-mode decaynuclear matrix element Why does the 1+ component of the 0n-mode matrix element behave as M2n for the change of gpp? • Tensor term • L = 2 term in the GT matrix element • Finite momentum transfer q Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  25. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  26. Mass term of 0nbbdecay Three nuclear matrix elements, but the transition operators are two-body nature, since bb decay is a second-order process. multipole transition operators all Jp, except 0+ only natural-parity states Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  27. 1+ component of the 0n mode Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  28. Gamow-Teller transition operator Weak transition operators • non-relativistic approximation • multipole expansion • long wavelength limitlowest order termsvector ： Fermi transitionaxial vector ： Gamow-Teller transition Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  29. Momentum transfer in GT transitions With momentum transfer : B(GT-) : low-lying strengths are reduced, and high-lying strengths are increased very slightly. B(GT+) : low-lying strengths are reduced as B(GT-), and sizable strengths appear at high excitation region. The latter may be the Isovector Spin Monopole Resonance. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  30. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  31. Effect of ground-state correlations Quasi-particle RPA Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  32. L = 0 L = 2 Decomposition of the 1+component The tensor term is small. The L = 2 term stays constant. The L = 0 term determines thebehavior of the matrix elementas a function of gpp. The L = 0 term vanishes at the most probable gpp. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  33. 1+ component of 0n mode The L = 0 term of the 1+ component of 0n- mode matrix element behaves as the closure matrix element of the 2n-mode decay. Though the 0n decay is associated with transfer of finite momentum, it only scales the L = 0 term of the 0n mode. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  34. Summary • Single b decay of 187Re • Only one nuclear matrix element contributes, and it is obtained from the observed half-life, though the nuclear wave functions are complicated. • 0n-mode decay nuclear matrix element • Evidences to use 2n-decay half-lives. • Tensor term is small, and L = 2 term (GT) is constant. • The L = 0 term behaves as the closure matrix element of the 2n mode. QRPA predicts Isovector Spin Monopole excitation. Tests by experimental data of GT transitions. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

  35. Key Parametergpp QRPAを用いた核行列要素の計算結果 Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

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