Deformed quasiparticle random phase approximation formalism for single- and two-neutrino doubleβdecay

Abstract

We use a deformed quasiparticle random phase approximation formalism to describe simultaneously the energy distributions of the single ␤ Gamow-Teller strength and the two-neutrino double ␤ decay matrix elements. Calculations are performed in a series of double ␤ decay partners with A = 48, 76, 82, 96, 100, 116, 128, 130, 136, and 150, using deformed Woods-Saxon potentials and deformed Skyrme Hartree-Fock mean fields. The formalism includes a quasiparticle deformed basis and residual spin-isospin forces in the particlehole and particle-particle channels. We discuss the sensitivity of the parent and daughter Gamow-Teller strength distributions in single ␤ decay, as well as the sensitivity of the double ␤ decay matrix elements to the deformed mean field and to the residual interactions. Nuclear deformation is found to be a mechanism of suppression of the two-neutrino double ␤ decay. The double ␤ decay matrix elements are found to have maximum values for about equal deformations of parent and daughter nuclei. They decrease rapidly when differences in deformations increase. We remark on the importance of a proper simultaneous description of both double ␤ decay and single Gamow-Teller strength distributions. Finally, we conclude that for further progress in the field, it would be useful to improve and complete the experimental information on the studied Gamow-Teller strengths and nuclear deformations.

Nuclear matrix elements for neutrinoless double-beta decay and double-electron capture

“…Only quadrupole deformation is taken into account in the calculations [32][33][34][35][36]. The singleparticle Schrödinger equation with the Hamiltonian of a deformed Woods-Saxon mean field is solved on the basis of an axially-deformed harmonic oscillator.…”

“…It was demonstrated in Refs. [32][33][34] that deformation introduces a mechanism of suppression of the M 2ν matrix element which gets stronger when deformations of the initial and final nuclei differ from each other. A similar dependence of the suppression of both M 2ν and M 0ν matrix elements on the difference in deformations has been found in the PHFB [15] and the ISM [14].…”

“…M 2ν were calculated in Refs. [32,33] with schematic separable forces, and in Ref. [34] -with realistic residual interaction.…”

“…A QRPA approach for calculating ββ-decay amplitudes in deformed nuclei has been developed in a series of papers [32][33][34][35][36]. M 2ν were calculated in Refs.…”

Effect of deformation on two-neutrino double beta decay matrix elements

“…The formalism includes a deformed quasiparticle basis and residual spin-isospin separable interactions in both particle-hole (ph) and particle-particle (pp) channels. We consider two different deformed mean fields: a phenomenological Woods-Saxon (WS) potential and a selfconsistent Hartree-Fock (HF) with Skyrme interactions [1]. While the deformation in the HF calculation is obtained selfconsistently, in the WS case it is an input parameter taken to reproduce the experimental quadrupole moments.…”