Pseudospin Symmetry: Microscopic origin of the ground-state inversion in neutron-rich odd-A Cu isotopes

The role of the pseudospin symmetry in the inversion of the ground-state spin in Cu isotopes is investigated within the covariant density functional theory (CDFT). The density functional PC-PK1 gives a good agreement with the observed ground-state properties of the odd-A ${}^{69-79}$Cu. In particular, the inversion of the ground-state spin at $A=75$ is reproduced nicely, which can be explained by the level crossing between the proton pseudospin partners $\pi 2p_{3\mathrm{/}2}$ and $\pi 1f_{5\mathrm{/}2}$. It is found that the pseudospin symmetry plays a dominant role in the evolution of the energy splittings between the pseudospin partners. By comparing with the results of the nonrelativistic DFTs, our studies suggest that the pseudospin symmetry is essential to the shell evolution around this region.