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.Comment: 18 pages including 7 figure

Further evidence for three-nucleon spin-orbit interaction in isotope shifts of Z=magicZ=\mathrm{magic} nuclei

It was pointed out [Phys. Rev. C \textbf{91}, 021302(R)] that the isotope shifts of the Pb nuclei, the kink at $N=126$ in particular, can be well described by the Hartree-Fock-Bogolyubov calculations if a density-dependent LS interaction derived from the $3N$ interaction is incorporated. Effects of the density-dependence in the LS channel on the isotope shifts are extensively investigated for the Ca, Ni and Sn isotopes, using the semi-realistic M3Y-P6 interaction and its LS modified variant M3Y-P6a, as in the Pb case. It is found that almost equal charge radii between $^{40}$Ca and $^{48}$Ca are reproduced, as well as the isotope shifts in a long chain of the Sn nuclei, owing to the density-dependence in the LS channel. A kink is predicted at $N=82$ for the isotope shifts of the Sn nuclei, in clear contrast to the interactions without the density-dependence.Comment: 7 pages including 4 figures, to appear in PR

Shell structure in neutron-rich Ca and Ni nuclei under semi-realistic mean fields

Shell structure in the neutron-rich Ca and Ni nuclei is investigated by the spherical Hartree-Fock calculations with the semi-realistic $NN$ interactions. Specific ingredients of the effective interaction, particularly the tensor force, often play a key role in the $Z$ dependence of the neutron shell structure. Such examples are found in N=32 and N=40; N=32 becomes magic or submagic in $^{52}$Ca while its magicity is broken in $^{60}$Ni, and N=40 is submagic (though not magic) in $^{68}$Ni but not in $^{60}$Ca. Comments are given on the doubly magic nature of $^{78}$Ni. We point out that the loose binding can lead to a submagic number N=58 in $^{86}$Ni, assisted by the weak pair coupling.Comment: 14 pages including 5 figures, to appear in Physical Review C (Rapid Communication