Single-particle states outside the N=82 core

A systematic study of the high-$j$ single-neutron states outside the $N$=82 isotones was carried out with the ($\alpha$,$^{3}$He) reaction on $^{138}$Ba, $^{140}$Ce, $^{142}$Nd and $^{144}$Sm at a beam energy of 51~MeV. The separation between the i$_{13/2}$ and h$_{9/2}$ single-neutron states, was measured. Spectroscopic factors for the states populated in the high-$\ell$ transfers indicate significant fragmentation for the $\ell$=5 and $\ell$=6 strength, but the summed strengths on these targets are constant. The centroids of the single-particle strength display a change in the relative energies of these two nodeless single-particle orbits, similar to the trend observed in the Sb isotopes$^{1}$. The centroid shifts with neutron number are in agreement with those expected from the monopole term in the tensor component of the residual interaction between nucleons of Otsuka et al.$^{2}$. This research was supported by the DOE Office of Nuclear Physics under Contract Nos. DE-FG02-91ER-40609 and DE-AC02-06CH11357. $^{1}$J.P. Schiffer et al. Phys. Rev. Lett. {\bf 92}, 162501 (2004). $^{2}$T. Otsuka et al. Phys. Rev. Lett. {\bf 95}, 232502 (2005).