The N=50 and Z=28 shell closure revisited

TL;DR

This paper revisits the N=50 and Z=28 shell closure by analyzing proton spectra in nickel isotopes, highlighting the roles of mean-field interactions and tensor forces in reproducing observed level crossings.

Contribution

It demonstrates that the crossing of proton levels in nickel isotopes is mainly driven by mean-field effects and assesses the necessity of tensor interactions across different models.

Findings

Tensor interactions are crucial in some models for reproducing level crossings.

Certain mean-field models can explain experimental data without tensor forces.

The impact of tensor interactions varies depending on the effective interaction used.

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 2$p_{3/2}$ 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.