Effects of density dependence of the effective pairing interaction on the first $2^+$ excitations and quadrupole moments of odd nuclei

TL;DR

This paper investigates how the density dependence of the effective pairing interaction influences the calculated excitation energies and quadrupole moments in odd and even tin and lead isotopes, using a self-consistent theoretical approach.

Contribution

It provides a detailed analysis of the impact of volume versus surface pairing on nuclear excitation energies and quadrupole moments within the Theory of Finite Fermi Systems.

Findings

Density dependence noticeably affects 2+ excitation energies.

Both pairing models reasonably agree with experimental data.

Quadrupole moments are highly sensitive to single-particle energies.

Abstract

Excitation energies and transition probabilities of the first $2^+$ excitations in even tin and lead isotopes as well as the quadrupole moments of odd neighbors of these isotopes are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. The effect of the density dependence of the effective pairing interaction is analyzed in detail by comparing results obtained with volume and surface pairing. The effect is found to be noticeable. For example, the $2^+$-energies are systematically higher at 200-300 keV for the volume paring as compared with the surface pairing case. But on the average both models reasonably agree with the data. Quadrupole moments of odd-neutron nuclei are very sensitive to the single-particle energy of the state $\lambda$ under consideration due to the Bogolyubov factor ($u^2_{\lambda}-v^2_{\lambda}$). A reasonable agreement with experiment for the quadrupole moments has been obtained for the most part of odd nuclei considered. The method used gives a reliable possibility to predict quadrupole moments of unstable odd nuclei including very neutron rich ones.