Description of double beta decay within continuum-QRPA

TL;DR

This paper develops a continuum-QRPA method to calculate double beta decay amplitudes, showing that continuum effects have minimal impact on two-neutrino decay but suppress neutrinoless decay amplitudes, with implications for nuclear models.

Contribution

The paper introduces a continuum-QRPA approach for double beta decay calculations, incorporating continuum effects into the nuclear transition amplitudes.

Findings

M^{2 u} amplitudes are unaffected by the continuum.

Neutrinoless decay amplitudes are suppressed due to continuum correlations.

Future inclusion of pairing may offset suppression.

Abstract

A method to calculate the nuclear double beta decay ($2\nu\beta\beta$- and $0\nu\beta\beta$-) amplitudes within the continuum random phase approximation (cQRPA) is formulated. Calculations of the $\beta\beta$ transition amplitudes within the cQRPA are performed for ^{76}Ge, ^{100}Mo and ^{130}Te. A rather simple nuclear Hamiltonian consisting of phenomenological mean field and zero-range residual particle-hole and particle-particle interaction is used. The calculated M^{2\nu} are almost not affected when the single-particle continuum is taken into account. At the same time, a regular suppression of the $0\nu\beta\beta$-amplitude is found that can be associated with additional ground state correlations due to collective states in the continuum. It is expected that future inclusion of the nucleon pairing in the single-particle continuum will somewhat compensate the suppression.