nuclear structure aspects of single and double beta decays for neutrino mass

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


Part 1Single Beta Decay: 187Re


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.


Single decay: 3H and 187Re


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)


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


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)


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


Part 2Double Beta Decay


Double beta decay can be observed when single beta decays are energetically forbidden or strongly

hindered.Second order process of the weak interactionZ = 2


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

=


Neutrino mass from 0 decay

neutrino mass

nuclear structure calculationexperiment

2 mode

0 mode


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


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


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.


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+.


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


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.


GT transition with momentum transfer

QRPA in a large model space :

0 1+ component:

probed by charge-exchange reactions

not yet confirmed


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


THE END

Thank you for your patience.


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.


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


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.


1+ component of the 0 mode


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


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.


Effect of ground-state correlations

Quasi-particle RPA


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.


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.


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.


Key Parameter gpp

QRPA を用いた核行列要素の計算結果

nuclear structure aspects of single and double beta decays for neutrino mass

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