Is the Nuclear Spin-Orbit Interaction Changing with Neutron Excess?

The difference in the energies of the lowest states corresponding to the two nodeless single-particle orbitals outside the $Z=50$ closed proton shell, $h_{11/2}$ and $g_{7/2}$, increases with neutron excess. We have measured the Sn$(\alpha ,t)$ reaction for all seven stable even Sn isotopes and found that the spectroscopic factors are constant for these two states, confirming their characterization as single-particle states. The trend in energies is consistent with a decrease in the nuclear spin-orbit interaction. A similar trend, also suggesting a decreasing spin-orbit splitting, is seen in the energies of the neutron single-particle states outside the $N=82$ core, $i_{13/2}$ and $h_{9/2}$.