Semi-realistic nucleon-nucleon interactions with improved neutron-matter properties

New parameter-sets of the semi-realistic nucleon-nucleon interaction are developed, by modifying the M3Y interaction but maintaining the tensor channels and the longest-range central channels. The modification is made so as to reproduce microscopic results of neutron-matter energies, in addition to the measured binding energies of doubly magic nuclei including $^{100}$Sn and the even-odd mass differences of the Z=50 and N=82 nuclei in the self-consistent mean-field calculations. Separation energies of the proton- or neutron-magic nuclei are shown to be in fair agreement with the experimental data. With the new parameter-sets M3Y-P6 and P7, the isotropic spin-saturated symmetric nuclear matter remains stable in the density range as wide as $\rho\lesssim 6\rho_0$, while keeping desirable results of the previous parameter-set on finite nuclei. Isotope shifts of the Pb nuclei and tensor-force effects on shell structure are discussed.