Shell clusure at N=34 and the 48Si nucleus

By using a non-relativistic independent particle model we investigate the mechanism promoting 34 as new magic number. We carried out Hartree-Fock plus Bardeen-Cooper- Schrieer and Quasi-particle Random Phase Approximation calculations by consistently using the same nite-range interaction in all the three steps of our approach. We used four Gogny-like interactions, with and without tensor terms. We nd that the shell clo- sure for N = 34 neutrons appears in isotones with Z < 26 protons. The smaller is the proton number, the more evident is the shell closure at N = 34. An ideal nucleus to investigate this eect should be 48Si, as it has been recently suggested. However, some discrepancies occur between the results obtained with the four eective interactions we used concerning the position of the two-neutron drip line and, therefore, the existence of 48Si. The experimental identication of this nucleus could shed light about the shell evo- lution in nuclei far from the stability valley and put stringent tests on nuclear structure theories.