Low energy collective modes of deformed superfluid nuclei within the finite amplitude method

TL;DR

This paper introduces an efficient finite amplitude method (FAM) based approach to compute low-energy collective modes in deformed superfluid nuclei, improving the ability to predict nuclear responses and vibrational states across the nuclear chart.

Contribution

The paper develops a novel FAM-QRPA method using contour integration to accurately find low-lying collective modes in deformed nuclei, compatible with superfluid density functional theory.

Findings

FAM-QRPA reproduces conventional QRPA results for low-lying states.

Method successfully applied to deformed 24Mg, Yb, and Er isotopes.

Efficiently calculates vibrational modes and beta-decay rates.

Abstract

Background: The major challenge for nuclear theory is to describe and predict global properties and collective modes of atomic nuclei. Of particular interest is the response of the nucleus to a time-dependent external field that impacts the low-energy multipole and beta-decay strength. Purpose: We propose a method to compute low-lying collective modes in deformed nuclei within the finite amplitude method (FAM) based on the quasiparticle random-phase approximation (QRPA). By using the analytic property of the response function, we find the QRPA amplitudes by computing the residua of the FAM amplitudes by means of a contour integration around the QRPA poles in a complex frequency plane. Methods: We use the superfluid nuclear density functional theory with Skyrme energy density functionals, FAM-QRPA approach, and the conventional matrix formulation of the QRPA (MQRPA). Results: We demonstrate that the complex-energy FAM-QRPA method reproduces low-lying collective states obtained within the conventional matrix formulation of the QRPA theory. Illustrative calculations are performed for the isoscalar monopole strength in deformed 24Mg and for low-lying K = 0 quadrupole vibrational modes of deformed Yb and Er isotopes. Conclusions: The proposed FAM-QRPA approach allows one to efficiently calculate low-lying collective modes in spherical and deformed nuclei throughout the entire nuclear landscape, including shape-vibrational excitations, pairing vibrational modes, and beta-decay rates.