Calculation of nuclear
transition matrix elements ofneutrinoless double-beta decay
using QRPA
J. Terasaki, Univ. of Tsukuba
1. Physical issues of neutrino
2. Neutrinoless double-beta decay
3. Nuclear matrix element
4. Status of calculation of nuclear matrix element
5. My application of QRPA
6. Summary
Mar. 4, 2014, Tokyo

What is the neutrino mass?
The neutrino is massless in the standard theory.
Other physical issues of neutrino• Dirac or Majorana particle?
• Breaking of the lepton number conservation?
• How is the right-handed neutrino
experimentally observed? Does that neutrino
have an interaction?

One of the intensively studied few methods todetermine the neutrino mass:
Application of neutrinoless double-beta (0)decay of nuclei

̅Nucleus,

Nucleus2,

Neutrino assumed to be Majorana particle.

2

The principle to determine the effective neutrinomass using
decay
1/Exp. →Cal. →

0 →0: half-life of the transition: transition matrix element of nucleus(nuclear matrix element): electron part of the transition amplitudes
squared (phase space factor): effective neutrino mass
: electron massNuclear matrix element,,,0 |
1 ·2|

|
1|02

VirtualIntermediate Initial state|0states |Final state |0M. Doi et al. Prog. Theor.
Phys. Suppl. No. 83 (1985) 1

Path of 0
decay in the calculation
via virtual intermediate states

(Relativistic) quasiparticle random-phase approximation
Status Shell modelInteracting boson model-2
Projected Hartree-Fock-Bogoliubov
Generator-coordinate method + Particle number andangular momentum projection

A. Feassler, arXiv:2103.3648 (2012)

Quasiparticle random-phase approximation (QRPA)
An approximation using only two-quasiparticle excitations
andfor the elementary mode of excitation
Application of QRPA≅||0|0| 〉〈 |:| 〉~| 〉〈 |:|0 〉Application of QRPA≅||0|0| 〉〈 |:≅|| 〉〈 |:|0|0| 〉〈 |:Like‐particle QRPA~| 〉〈 |:annihilator

QRPA states
The QRPA ground state is defined to be the vacuum to theQRPA quasiboson :0 ≅0: annihilation operator of QRPA state
100,~: product of quasiparticle creation operators: normalization factor

The overlap 〈 | 〉 are calculated using that definition ofthe QRPA ground state.
J.T. PRC 86, 021301(R) (2012); 87, 024316 (2013)

Calculation ofof 150Nd-150Sm using likeparticle QRPA. SkM*+volume pairing is used.
~0.02
2.5 ̶ 3.5 (QRPA , Tübingen),
1.8 ̶ 3.5 including various approaches (the previous figure)0.02 is too small, because the QRPA
correlations are too large; it is known thatthe correlation energy diverges in theSkyrme QRPA.
The Skyrme and the volume pairinginteraction ∝My prescription
To pick up the QRPA solutions having the largest
contributions so as to satisfy
and use only these states for calculating the QRPA groundstates.
10 like-particle QRPA states for
1.72MeV (150Nd) and18 like-particle QRPA states for
3.44MeV (150Sm)
were picked up. The pnQRPA
correlations were small.
Revised calculations are in progress.

Summary• Several physical issues of neutrino were shown.
• How the 0
decay is used for determining the effective
neutrino mass was explained.
• Status was shown of the calculations of the nuclear
matrix elements— the discrepancy problem of the results by methods• “The QRPA ground state = QRPA quasiboson vacuum” isused.
• The QRPA correlations have the effect to reduce thenuclear matrix element through the normalization factorof the ground state.