Nuclear Structure Aspects of Single and Double Beta
Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass Kazuo Muto Tokyo Institute of Technology (Tokyo. Tech) in collaboration with F. Simkovic and R. Dvornicky, Comenius Univ. , Bratislava 1. Single beta decay: 187 Re 2. Double beta decay International School of Nuclear Physics, 31 st Course Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics Erice, Sicily September 16 -24, 2009 Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009
Neutrino Mass and Mixing Neutrino Mixing flavor eigenstates Mass differences mass eigenstates neutrino oscillation experiments No absolute mass scale b decay 187 Re bb decay 76 Ge, 100 Mo, etc. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 2
Part 1 Single Beta Decay: 187 Re Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 3
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 e. V). Decays with a small Q -value are favored. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 4
Single b decay: 3 H and 187 Re Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 5
ft-value Calc. Exp. A rather large ft value among unique first-forbidden decays reproduced from B. Singh et al. , Nuclear Data Sheets 84, 487 (1998) Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 6
Electron s- and p-wave emission Neutrino p-wave (p 3/2) Electron s-wave (s 1/2) in total J p = 2 - Neutrino s-wave (s 1/2) Electron p-wave (p 3/2) in total J p = 2 - Fermi function Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 7
Electron p-wave dominance l The electron is attracted by the Coulomb potential of the nucleus. l Huge enhancement for very low-energy p-wave electron. See, C. Arnaboldi, et al. , Phys. Rev. Lett. 96, 042503 (2006) l No attraction for neutrino Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 8
Only one nuclear matrix element Unique first-forbidden beta decay Nuclear reduced transition probability n If a s. p. transition from d 5/2 to p 1/2 is assumed, n 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 9
Part 2 Double Beta Decay Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 10
Double beta decay can be observed when single beta decays are energetically forbidden or strongly hindered. Second order process of the weak interaction DZ = 2 Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 11
Two decay modes u Allowd in the SM 2 n mode 0 n mode u Observed for about ten nuclides u Shortest half-life: T 1/2 = 1019 y u Forbidden in the SM u No observations so far u Can occur when neutrinos have a finite mass and are Majorana particles n = n Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 12
Neutrino mass from 0 nbb decay neutrino mass 0 n mode experiment nuclear structure calculation 2 n mode Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 13
The best prediction by QRPA models V. A. Rodin, A. Faessler, F. Simkovic and P. Vogel, Nucl. Phys. A 766 (2006) 107: A 793 (2007) 213 0 nbb a) different model spaces b) different NN interactions c) different QRPA models d) g. A = 1. 25 and g. A = 1. 00 ►Short-range correlation ►Nucleon form factor ►Use the measured 2 nbb-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 14
Mass term of 0 nbb decay V-A The momentum integral of the virtual neutrino V-A 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 A • A with two-body nuclear transition operators. nuclear intermediate states GT-term Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 15
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 0 n. The tensor term reduces M 0 n 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 16
Spin-isospin correlation and quadrupole deformation The largest uncertainties lie in the 1+ component, which is sensitve to the spin-isospin g. s. correlations. intermediate 1+ states daughter ground state pp-nh ; 1+ ph-np ; 1+ pp-ph ; Jp np-nh ; Jp The spin-isospin correlations come mainly from quadrupole deformation with Jp = 2+. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 17
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 18
Monopole strength of NN interaction n Most important for shell-structure evolution, especially in neutron-rich nuclei. n Due to mainly from triplet-even attraction of the central force, with second-order renormalization of tensor force. ü Effective interaction theories, such as G-matrix, do not reproduce empirical monopole strengths. ü 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 2 J +1 = 3. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 19
GT transition with momentum transfer 0 nbb 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 20
Summary Single beta decay of 187 Re n Only one nuclear matrix element involved. n It is obtained from the measured half-life. n The nuclear transition is strongly hindered. Double beta decay (0 nbb) u Matix elements are much more stable by the standard calculation, less dependent on the nuclear structure, than 2 nbb matrix elements. u Further studies on p spin-isospin correlations vs quadrupole deformation p GT(q=0) vs GT with momentum transfer p unique first-forbidden (spin-dipole) transitions, which give the largest component of 0 nbb mass term Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 21
THE END Thank you for your patience. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 22
Neutrino mass hierarchy in the electron energy spectrum mlightest = 30 me. V assumed for both normal and inverted neutrino mass hierarchies. A clear difference in the last 100 me. V. But, it is a tiny difference even in the last 1 e. V. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 23
0 n-mode decay nuclear matrix element Why does the 1+ component of the 0 n-mode matrix element behave as M 2 n for the change of gpp? 1. Tensor term 2. L = 2 term in the GT matrix element 3. Finite momentum transfer q Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 24
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 25
Mass term of 0 nbb 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 26
1+ component of the 0 n mode Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 27
Gamow-Teller transition operator Weak transition operators ① non-relativistic approximation ② multipole expansion ③ 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 28
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 29
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 30
Effect of ground-state correlations Quasi-particle RPA Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 31
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 32
1+ component of 0 n mode The L = 0 term of the 1+ component of 0 nmode matrix element behaves as the closure matrix element of the 2 n-mode decay. Though the 0 n decay is associated with transfer of finite momentum, it only scales the L = 0 term of the 0 n mode. Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16 -24, 2009 33
Summary Single b decay of 187 Re Only one nuclear matrix element contributes, and it is obtained from the observed half-life, though the nuclear wave functions are complicated. 0 n-mode decay nuclear matrix element u. Evidences to use 2 n-decay half-lives. u. Tensor term is small, and L = 2 term (GT) is constant. u. The L = 0 term behaves as the closure matrix element of the 2 n 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 34
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 35
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