Kazuo Muto Tokyo Institute of Technology (TokyoTech) 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: 187Re Double beta decay International School of Nuclear Physics, 31st Course Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics Erice, Sicily September 16-24, 2009

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

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

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

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

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

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

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

Only one nuclear matrix element Unique first-forbidden beta decay 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

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

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

Two decay modes n = n 2n mode 0n mode 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 n = n Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

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

The best prediction by QRPA models 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 0nbb Short-range correlation Nucleon form factor Use the measured 2nbb-decay half-life for the calibration of theoretical spin-isospin correlations. the uncertainty of about 30% Theoretical nuclear matrix elements are stable. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

nuclear intermediate states Mass term of 0nbb decay V-A 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, A • A V • V 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

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 The GT term dominates M 0n. The tensor term reduces M 0n by about 10%. The multipole components contribute in the same sign. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

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

Universal feature of pn interaction Proton-neutrion particle-hole matrix elements deduced experimental spectra, normalized by the monopole strengths for each multiplet. particle-hole particle-particle reproduced from J.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

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

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

Summary Single beta decay of 187Re Double beta decay (0nbb) 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

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

Neutrino mass hierarchy in 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

0n-mode decay nuclear 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

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

Mass term of 0nbb decay 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

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

Gamow-Teller transition operator Weak transition operators non-relativistic approximation multipole expansion long wavelength limit 　lowest order terms 　　vector ： Fermi transition 　　axial vector ： Gamow-Teller transition Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009

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

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

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

Decomposition of the 1+ component L = 0 L = 2 The tensor term is small. The L = 2 term stays constant. The L = 0 term determines the behavior of the matrix element as 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

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

Summary Single b decay of 187Re 0n-mode decay nuclear matrix element 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

Key Parameter gpp 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