Towards a Unified Description of Isoscalar Giant Monopole Resonances in a Self-Consistent Quasiparticle-Vibration Coupling Approach

TL;DR

This paper develops a self-consistent quasiparticle-vibration coupling approach to better understand the isoscalar giant monopole resonances in tin and lead isotopes, addressing the longstanding softness problem of tin's equation of state.

Contribution

It introduces a fully self-consistent QRPA plus QPVC method based on Skyrme-Hartree-Fock-Bogoliubov to unify the description of ISGMR in different isotopes.

Findings

QPVC shifts ISGMR energies in Sn isotopes by about 0.4 MeV.

The approach accurately reproduces experimental strength functions.

Incompressibility values of 226 and 229 MeV best fit the data.

Abstract

"Why is the EoS for tin so soft?" is a longstanding question, which prevents us from determining the nuclear incompressibility $K_\infty$ accurately. To solve this puzzle, a fully self-consistent quasiparticle random phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) approach based on Skyrme-Hartree-Fock-Bogoliubov is developed. We show that the many-body correlations introduced by QPVC, which shift the ISGMR energy in Sn isotopes by about 0.4 MeV more than the energy in $^{208}$Pb, play a crucial role in providing a unified description of the ISGMR in Sn and Pb isotopes. The best description of the experimental strength functions is given by SV-K226 and KDE0, which are characterized by incompressibility values $K_\infty=$ 226 MeV and 229 MeV, respectively, at mean field level.