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The isospin dependence of incompressibility is investigated in the SkyrmeHartree-Fock (SHF) and relativistic mean field (RMF) models. The correlationsbetween the nuclear matter incompressibility and the isospin dependent term ofthe finite nucleus incompressibility is elucidated by using the Thomas-Fermiapproximation. The Coulomb term is also studied by using various differentSkyrme  Hamiltonians and RMF Lagrangians. The symmetry energy coefficient ofincompressibility is extracted to be K_{\tau}=-(500\pm50) MeV from the recentexperimental data of isoscalar giant monopole resonances (ISGMR) in Snisotopes. Microscopic HF+random phase approximation (RPA) calculations are alsoperformed with Skyrme interactions for ^{208}Pb and Sn isotopes to study thestrength distributions of ISGMR. .Comment: 19pages,5figure

Isospin dependence of incompressibility in relativistic and nonrelativistic mean field calculations