Effect of Finite Binding on the Apparent Spin-Orbit Splitting in Nuclei

The apparent splitting between orbitals that are spin-orbit partners can be substantially influenced by the effects of finite binding. In particular, such effects can account for the observed decrease in separation of the neutron $1p_{3\mathrm{/}2}$ and $1p_{1\mathrm{/}2}$ orbitals between the ${}^{41}$Ca and ${}^{35}$Si isotopes. This behavior has been the subject of recent experimental and theoretical works and cited as evidence for a proton “bubble” in ${}^{34}$Si causing an explicit weakening of the spin-orbit interaction. The results reported here suggest that the change in the separation between the $1p_{3\mathrm{/}2}$ and $1p_{1\mathrm{/}2}$ partners occurs dominantly because of the behavior of the energies of these $1p$ neutron states near zero binding.