Finite range momentum and density dependent effective interaction and analysis of nuclear incompressibility

Extraction of the nuclear matter incompressibility ${\mathit{K}}_{\mathrm{\infty }}$ from the experimental giant monopole resonance (GMR) data via liquid drop type expansion of compression modulus of finite nuclei ${\mathit{K}}_{\mathit{A}}$ is found to be fraught with uncertainties. Hence a realistic finite range effective interaction is constructed that reproduces the bulk properties of nuclear systems as well as the GMR data in the Thomas-Fermi approximation. The nuclear matter incompressibility calculated with this interaction is found to be 226 MeV. A numerical scheme is also proposed which enables us to extract the various coefficients occurring in the expansion of ${\mathit{K}}_{\mathit{A}}$ employing this effective interaction.