  The occupancies and vacancies of the valence neutron orbitals across the
stable tin isotopic chain from $112\leq A\leq 124$ have been determined. These
were inferred from the cross sections of neutron-adding and -removing
reactions. In each case, the reactions were chosen to have good
angular-momentum matching for transfer to the low- and high-$\ell$ orbitals
present in this valence space. These new data are compared to older systematic
studies. The effective single-neutron energies are determined by combining
information from energy centroids determined from the adding and removing
reactions. Two of the five orbitals are nearly degenerate, below $N=64$, and
approximately two MeV more bound than the other three, which are also
degenerate.
