Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations and $\beta$-decay half-lives

TL;DR

This paper develops a relativistic QRPA method based on RHFB theory to study charge-exchange excitations and beta-decay half-lives, emphasizing the importance of self-consistency and specific residual interactions.

Contribution

It introduces a self-consistent relativistic QRPA approach within the RHFB framework and applies it to charge-exchange excitations and beta-decay predictions, highlighting the role of residual interactions.

Findings

Self-consistent treatment of residual interactions is crucial for accurate IAS and GTR predictions.

Coulomb exchange significantly affects IAS energy calculations.

The approach accurately reproduces beta-decay half-lives for certain isotopes, with noted discrepancies discussed.

Abstract

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.