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 $\ensuremath{\beta}$-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 ${}^{24}$Mg 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 $\ensuremath{\beta}$-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.
Accepted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call