Effects of pairing strength on the nuclear structure and double-$\beta$ decay predictions within the mapped interacting boson model

TL;DR

This study investigates how pairing strength variations in the interacting boson model, based on energy density functional calculations, affect nuclear structure predictions and double-beta decay rates, showing increased pairing improves agreement with experimental data.

Contribution

It introduces a sensitivity analysis of pairing strength effects within the mapped interacting boson model for double-beta decay predictions based on microscopic EDF inputs.

Findings

Increased pairing strength lowers excited 0+ state energies.

Enhanced pairing leads to larger predicted double-beta decay NMEs.

Standard pairing strength provides a good overall description of experimental data.

Abstract

The low-energy nuclear structure and two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay are studied within the interacting boson model (IBM) that is based on the nuclear energy density functional (EDF). The IBM Hamiltonian describing the initial and final even-even nuclei, and the interacting boson fermion-fermion Hamiltonian producing the intermediate states of the neighboring odd-odd nuclei are determined by the microscopic inputs provided by the self-consistent mean-field (SCMF) calculations employing a relativistic EDF and a separable pairing force. Sensitivities of the low-lying structure and $2\nu\beta\beta$-decay properties to the pairing strength are specifically analyzed. It is shown that the SCMF calculations with decreased and increased pairing strengths lead to quadrupole-quadrupole interaction strengths in the IBM that are, respectively, significantly enhanced and reduced in magnitude. When the increased pairing is adopted, in particular, the energy levels of the excited $0^+$ states are lowered, and the predicted $2\nu\beta\beta$-decay nuclear matrix elements (NMEs) increase in magnitude systematically. The mapped IBM employing the increased pairing force generates effective NMEs and half-lives that are in a reasonable agreement with the experimental data for the $^{76}$Ge$\to^{76}$Se, $^{82}$Se$\to^{82}$Kr, and $^{100}$Mo$\to^{100}$Ru decays in particular, whereas the calculation with the standard pairing strength is adequate to provide an overall good description of the effective NMEs in agreement with data.