Isospin dependence of incompressibility in relativistic and nonrelativistic mean field calculations

Abstract

The isospin dependence of incompressibility is investigated in Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility and the isospin-dependent term of the finite nucleus incompressibility is elucidated using the Thomas-Fermi approximation. The Coulomb term is also studied by using various different Skyrme Hamiltonians and RMF Lagrangians. Microscopic $\mathrm{HF}+\mathrm{random}$ phase approximation (RPA) calculations are performed with Skyrme interactions for $^{208}\mathrm{Pb}$ and Sn isotopes to study the strength distributions of isoscalar giant monopole resonances. The symmetry term of nuclear incompressibility is extracted to be ${K}_{\ensuremath{\tau}}=\ensuremath{-}(500\ifmmode\pm\else\textpm\fi{}50)$ MeV from the recent experimental data of isoscalar giant monopole resonances (ISGMR) in Sn isotopes.