Predicting magic numbers of nuclei with semi-realistic nucleon-nucleon interactions

Magic numbers are predicted in wide range of the nuclear chart by the self-consistent mean-field calculations with the M3Y-P6 and P7 semi-realistic $NN$ interactions. The magic numbers are identified by vanishing pair correlations in the spherical Hartree-Fock-Bogolyubov regime. We also identify submagic numbers when energy gain due to the pairing is sufficiently small. It is found that the results with M3Y-P6 well correspond to the known data, apart from a few exceptions. For some of the magic or submagic numbers the prediction differs from that with the Gogny-D1S or D1M interaction. Roles of the tensor force and the spin-isospin channel originating from the one-pion exchange potential are investigated in the $Z$- or $N$-dependence of the shell gap.