Description of the giant monopole resonance in the even-ASn112−124isotopes within a microscopic model including quasiparticle-phonon coupling

Abstract

We have calculated the strength distributions of the isoscalar giant monopole resonance (ISGMR) in the even-$A$ tin isotopes ($A=112\text{\ensuremath{-}}124$) that were recently measured in inelastic $\ensuremath{\alpha}$ scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation (QTBA), which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the Hartree-Fock$+$Bardeen-Cooper-Schrieffer approximation. Within the RPA the self-consistency is full. The single-particle continuum is also exactly included at the RPA level. The self-consistent mean field and the effective interaction are derived from the Skyrme energy functional. In the calculations, two Skyrme force parametrizations were used: T5 with a comparatively low value of the incompressibility modulus of infinite nuclear matter (${K}_{\ensuremath{\infty}}=202$ MeV) and T6 with ${K}_{\ensuremath{\infty}}=236$ MeV. The T5 parametrization gives theoretical results for tin isotopes in good agreement with the experimental data including the resonance widths. The results of the ISGMR calculations in $^{90}\mathrm{Zr}$, $^{144}\mathrm{Sm}$, and $^{208}\mathrm{Pb}$ performed with these Skyrme forces are discussed and compared with the experiment.