Systematic of isovector and isoscalar giant quadrupole resonances in normal and superfluid spherical nuclei

TL;DR

This study systematically investigates isoscalar and isovector giant quadrupole resonances in spherical nuclei using time-dependent Skyrme Energy Density Functional, highlighting the dependence on functional choice and pairing effects, and discussing implications for symmetry energy.

Contribution

It provides a comprehensive analysis of quadrupole responses in spherical nuclei with different Skyrme functionals, including pairing effects, and explores their relation to symmetry energy.

Findings

Mean energies reproduce experimental values but not lifetimes.

Collective energies depend on the choice of Skyrme functional.

Pairing influences low-lying states and reduces collective energy.

Abstract

The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective energy but fails to reproduce their lifetimes. It is found that the mean collective energy depends rather significantly on the functional used in the mean-field channel. Pairing by competing with parity effects can slightly affect the collective response around magic numbers and induces a reduction of the collective energy compared to the average trend. Low-lying states, that can only be considered if pairing is included, are investigated. While the approach provides a fair estimate of the low lying state energy, it strongly underestimates the transition rate $B(E2)$. Finally, the possibility to access to the density dependence of the symmetry energy through parallel measurements of both the IS- and IV-GQR is discussed.