Reexamination of the N=50 and Z=28 shell closure

Abstract

Recent experiments performed in neutron-rich copper isotopes have revealed a crossing in the nucleus 75 Cu between the 3/2 − and 5/2 − levels, which correspond to the ground state and the first excited state in isotopes with mass number below A = 75. Due to the strong single-particle character of these states, this scenario can be investigated through the analysis of the proton spectrum provided by mean-field models in nickel isotopes with neutron numbers between N = 40 and N = 50. In this work, we show that the aforementioned crossing is mainly driven by the mean field provided by the effective nucleon-nucleon and spin-orbit interactions. We also analyze the impact of the tensor interaction and find that in some mean-field models it is essential to reproduce the crossing of the 2p 3/2 and 1 f 5/2 proton single-particle levels, as in the case of the SAMi-T Skyrme force and the D1M Gogny interaction, whereas in other cases, as for example the SLy5 Skyrme force, a reasonable tensor force appears to be unable to modify the mean-field enough to reproduce this level crossing. Finally, in the calculations performed with the so-called simple effective interaction (SEI), it is shown that the experimental data in nickel and copper isotopes considered in this work can be explained satisfactorily without any explicit consideration of the tensor interaction.

The finite range simple effective interaction including tensor terms

“…The mean-field calculation have been performed within the QLDFT framework using the uniform blocking method to describe odd nuclei. This approximation is justified, as far as we have shown in a recent work [18], QLDFT and HF calculations give identical results in N i-isotopic series. It is shown that in case of the SEI interaction with an incompressibility value K(ρ 0 )=240 MeV, there is no requirement of explicit inclusion of a tensor part, unlike the case in Gogny and Skyrme forces, to achieve the 2p 3/2 and 1f 5/2 s.p.…”

“…Notice that the presence of a tensor term does not guarantee the crossing of these s.p. proton levels, as is the case of the Skyrme-Lyon force SLy5, as has been discussed recently in [18]. This fact point out the relevance of the underlying mean-field to describe the crossing of the aforementioned s.p.…”

“…In this work we enlarge SEI by adding a tensor force, which is taken as a zero-range force as the one used in Skyrme interactions. We have checked previously [18] that a QLDFT calculation with the Gogny D1M force together with a zero-range tensor predicts a finite nuclei description extremely close to the one obtained in full HF calculations with a finite-range tensor [12,14,15]. Although the contribution of the zero-range tensor force to the energy density functional has been discussed in detail in earlier literature [11,5], we briefly summarize it here for a sake of completeness.…”

“…As it is discussed in detail in Ref. [18], some effective forces of Skyrme and Gogny types can reproduce the crossing between the 1f 5/2 and 2p additional tensor force is added to these interactions. The main effect of the tensor force in the N i isotopes analyzed in this work is the attraction (repulsion) between the neutron 1g 9/2 s.p.…”

“…On the other hand, Anguiano et al have obtained the aforementioned crossing at A=74 by performing spherical Hartree-Fock (HF) calculations in coordinate space using the D1M Gogny interaction together with a finite-range tensor contribution [12,14,15]. This crossing predicted by the D1M set can also be obtained in the framework of quasi-local density functional theory (QLDFT) [16,17] by adding a zero-range tensor part as the one used in Skyrme forces, as has been shown in a recent work [18]. In this reference it has also been shown that the finite range simple effective interaction (SEI) predicts the crossing of the 1f 5/2 and 2p 3/2 s.p.…”