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 $h_{9/2}$.

Figure 1

The upper part of the figure is a schematic level diagram of single-particle states, arising from different oscillator shells. Pairs of states with highest angular momentum in each shell are labeled to emphasize the proximity of a high-$j$ $(\ell +1)+\frac{1}{2}$ intruder state to the $\ell -\frac{1}{2}$ state from the lower shell. The lower part of the figure shows the neutron-excess dependence of the binding energy of the last proton in $Z=51$ nuclei. The stars correspond to the $11/2^{-}$ states and the circles to the $7/2^{+}$ states. The open symbols designate states where spin assignments have been made but there is no information from transfer reactions about the single-particle character of the states. The points for ${}^{133}\mathrm{Sb}$ are from [5] and those in parentheses are unpublished [6].

Figure 2

The upper part of the figure shows a triton spectrum arising from the ($\alpha ,t$) reaction on a ${}^{124}\mathrm{Sn}$ target. The two relevant peaks are indicated by shading. The lower part of the figure shows angular distributions for the $7/2^{+}$ (dots) and $11/2^{-}$ (stars) states in two Sn isotopes, together with DWBA calculations.

Figure 3

Comparison of energy differences between pairs of high-$j$ single-particle states for single nucleons outside the $Z=50$ or $N=82$ shells as a function of the neutron excess of the core. In the upper part the energy differences for proton single-particle states are shown that are the subject of the present work. Below are the available data on neutron single-particle states. The solid dots indicate that information is available from transfer reactions; the open circles represent cases where these configurations have been assigned using methods which are less sensitive to the single-particle nature. The parentheses indicate less certain or indirect assignments. The pronounced minimum in the two curves is near the neutron excess corresponding to maximum stability.