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By using a non-relativistic independent particle model we investigate themechanism promoting 34 as new magic number. We carried out Hartree-Fock plusBardeen-Cooper-Schrieffer and Quasi-particle Random Phase Approximationcalculations by consistently using the same finite-range interaction in all thethree steps of our approach. We used four Gogny-like interactions, with andwithout tensor terms. We find that the shell closure for $N=34$ neutronsappears 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 toinvestigate this effect should be $^{48}$Si, as it has been recently suggested.However, some discrepancies occur between the results obtained with the foureffective interactions we used concerning the position of the two-neutron dripline and, therefore, the existence of $^{48}$Si. The experimentalidentification of this nucleus could shed light about the shell evolution innuclei far from the stability valley and put stringent tests on nuclearstructure theories.

Shell closure at $N=34$ and the $^{48}$Si nucleus