Giant Monopole Resonances and nuclear incompressibilities studied for   the zero-range and separable pairing interactions
  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 208Pb.   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 1 MeV) 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. 
P. Vesely, J. Toivanen, B.G. Carlsson, J. Dobaczewski, N. Michel, A.   Pastore
nucl-th