nuclear structure aspects of single and double beta decays for neutrino mass
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
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Part 1Single Beta Decay: 187Re
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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.
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Single decay: 3H and 187Re
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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)
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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
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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)
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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
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Part 2Double Beta Decay
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Double beta decay can be observed when single beta decays are energetically forbidden or strongly
hindered.Second order process of the weak interactionZ = 2
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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
=
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Neutrino mass from 0 decay
neutrino mass
nuclear structure calculationexperiment
2 mode
0 mode
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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
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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
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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.
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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+.
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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
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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.
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GT transition with momentum transfer
QRPA in a large model space :
0 1+ component:
probed by charge-exchange reactions
not yet confirmed
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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
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THE END
Thank you for your patience.
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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.
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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
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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.
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1+ component of the 0 mode
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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
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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.
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Effect of ground-state correlations
Quasi-particle RPA
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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.
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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.
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Key Parameter gpp
QRPA を用いた核行列要素の計算結果