nuclear structure aspects of single and double beta decays for neutrino mass
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Nuclear Structure Aspects of Single and Double Beta Decays for Neutrino Mass
Kazuo MutoTokyo Institute of Technology (TokyoTech)
1. Single beta decay: 187Re
2. Double beta decay
International School of Nuclear Physics, 31st CourseNeutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics
Erice, SicilySeptember 16-24, 2009
in collaboration with F. Simkovic and R. Dvornicky, Comenius Univ., Bratislava
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 2
Neutrino Mass and Mixing
flavoreigenstates
masseigenstates
Neutrino Mixing Mass differences
No absolute mass scale
decay 187Re
decay 76Ge, 100Mo, etc.
neutrino oscillation experiments
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 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 decay: 3H and 187Re
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 6
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 7
Electron s- and p-wave emission
Fermi function
Neutrino p-wave (p3/2)
Electron s-wave (s1/2)
in total J = 2
Neutrino s-wave (s1/2)
Electron p-wave (p3/2)
in total J = 2
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 neutrinoSee, 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
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.
Unique first-forbidden beta decay
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 interactionZ = 2
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 12
Two decay modes
Allowd in the SM Observed for about ten nuclides
Shortest half-life: T1/2 = 1019 y
Forbidden in the SM No observations so far Can occur when neutrinos
have a finite mass and are Majorana particles
2 mode
0 mode
=
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 13
Neutrino mass from 0 decay
neutrino mass
nuclear structure calculationexperiment
2 mode
0 mode
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 14
The best prediction by QRPA modelsV.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
the uncertaintyof about 30%
►Short-range correlation►Nucleon form factor►Use the measured
2-decay half-life for the calibration of theoretical spin-isospin correlations.
Theoretical nuclear matrix elements are stable.
0
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 15
Mass term of 0 decay
There appear three nuclear matrix elements,
VAVA
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).
A • AA • A V • V
with two-body nuclear transition operators.
GT-term
nuclear intermediate
states
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 16
Multipole decomposition (QRPA)
The GT term dominates M 0.
The tensor term reduces M 0 by about 10%.
The multipole components contribute in the same sign.
spin-parities of nuclear intermediate states
The 1+ component is strongly hindered by the g.s. correlations.
The 2 component corresponds to unique first-forbidden decay.
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 17
Spin-isospin correlation andquadrupole deformation
intermediate
1+ states
The largest uncertainties lie in the 1+ component, which is sensitve to the spin-isospin g.s. correlations.
daughter ground state
p-h ; 1+
h-p ; 1+
p-h ; J
p-h ; J
The spin-isospin correlations come mainly from quadrupole deformation
with J = 2+.
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 18
Universal feature of pn interactionProton-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)
particle-particleparticle-hole
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
GT transition with momentum transfer
QRPA in a large model space :
0 1+ component:
probed by charge-exchange reactions
not yet confirmed
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 21
SummarySingle 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 (0) Matix elements are much more stable by the standard calculation, less dependent on the nuclear structure, than 2 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 0 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
A clear difference in the last 100 meV.
But, it is a tiny difference even in the last 1 eV.
mlightest = 30 meV assumed
for both normal and inverted neutrino mass hierarchies.
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 24
0-mode decaynuclear matrix
elementWhy does the 1+ component of the 0-mode matrix element behave as M2 for the change of gp
p?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 25
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 26
Mass term of 0 decay
multipole transition operators
only natural-parity states
all J, except 0+
Three nuclear matrix elements, but the transition operators are two-body nature, since decay is a second-order process.
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 27
1+ component of the 0 mode
Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics, Erice, Sicily, Sept. 16-24, 2009 28
Gamow-Teller transition operator
Weak transition operators① non-relativistic approximation② multipole expansion③ 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 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
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 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 0 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
SummarySingle 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.
0-mode decay nuclear matrix elementEvidences to use 2-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 2 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 Parameter gpp
QRPA を用いた核行列要素の計算結果
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