Shell closure at N = 34 and the 48Si nucleus

Abstract

By using a nonrelativistic independent particle model, we investigate the mechanism promoting 34 as new magic number. We carried out Hartree–Fock plus Bardeen–Cooper–Schrieffer and Quasi-particle Random Phase Approximation calculations by consistently using the same finite-range interaction in all the three steps of our approach. We used four Gogny-like interactions, with and without tensor terms. We find that the shell closure for [Formula: see text] neutrons appears in isotones with [Formula: see text] protons. The smaller the proton number, the more evident is the shell closure at [Formula: see text]. An ideal nucleus to investigate this effect should be [Formula: see text]Si, as it has been recently suggested. However, some discrepancies occur between the results obtained with the four effective interactions we used concerning the position of the two-neutron drip line and, therefore, the existence of [Formula: see text]Si. The experimental identification of this nucleus could shed light about the shell evolution in nuclei far from the stability valley and put stringent tests on nuclear structure theories.