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

Abstract

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-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 $N=34$ 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 effect should be ${}^{48}$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 ${}^{48}$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.

6 pages, 2 figures, 3 tables

References in corpus (8)

• Nuclear magic numbers: new features far from stability
• Collapse of the N=28 shell closure in ${}^{42}$Si
• The limits of the nuclear landscape explored by the relativistic continuum Hatree-Bogoliubov theory
• Measurement of excited states in 40Si and evidence for weakening of the N=28 shell gap
• Magicity of the ${}^{52}$Ca and ${}^{54}$Ca isotopes and tensor contribution within a mean--field approach
• Matter distribution and spin-orbit force in spherical nuclei
• Pairing in spherical nuclei: quasi-particle random phase approximation calculations with the Gogny interaction
• Neutron gas and pairing