Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--

TL;DR

This paper develops a rigorous method to calculate the overlap of QRPA excited states based on different nuclei's ground states, with mathematical analysis and test calculations for light nuclei.

Contribution

It introduces a detailed formulation for QRPA state overlaps using the explicit ground state equations and investigates their mathematical properties.

Findings

Overlap matrix properties are mathematically characterized.

Test calculations confirm the validity of the truncation methods.

The approach is applicable to light nuclei with Skyrme and delta-pairing functionals.

Abstract

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume delta-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.