1. 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

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

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

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

6. 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 , 2009

7. 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 , 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, (2006)
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept , 2009

9. 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 , 2009

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

11. 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 , 2009

12. 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 , 2009

13. 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 , 2009

14. 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 , 2009

15. 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 , 2009

16. 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 , 2009

17. 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 states
daughter ground state
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept , 2009

18. 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 , 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 , 2009

20. 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 , 2009

21. 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 , 2009

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

23. 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 , 2009

24. 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 , 2009

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

26. 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 , 2009

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

28. 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 , 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 , 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 , 2009

32. 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 , 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 , 2009

34. 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 , 2009

35. 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 , 2009