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

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, as well as individual nuclear excitations. 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 superfluid nuclear density functional theory with Skyrme energy density functionals, the FAM-QRPA approach, and the conventional matrix formulation of the QRPA. 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 Mg-24 and for low-lying K = 0 quadrupole vibrational modes of deformed Yb and Er isotopes. Conclusions: The proposed FAM-QRPA approach, in addition to providing a quick estimate of various strength functions, allows one to efficiently calculate the individual QRPA amplitudes of the low-lying collective modes in spherical and deformed nuclei throughout the entire nuclear landscape, in particular shape-vibrational and pairing-vibrational modes and beta-decay rates. It can also be employed in microscopic approaches to large-amplitude nuclear collective motion based on the adiabatic self-consistent collective coordinate method.