Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions.

P. Veselý, J. Toivanen, B. G. Carlsson, J. Dobaczewski, N. Michel, and A. Pastore

Date: February 28, 2012

Abstract:

Background:

Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than $^{208}$Pb.

Purpose:

We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei.

Methods:

We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing.

Results:

We found that the difference between centroids of Giant Monopole Resonances measured in lead and tin (about 1MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility.

Conclusions:

The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data.