(d,p) and (d,t) Reactions on the Isotopes of Tin

Energy levels up to ∼4-MeV excitation energy are studied using the ($d,p$) and ($d,t$) reactions. Spectroscopic factors for most of the levels are obtained with the aid of distorted-wave Born-approximation (DWBA) calculations. The ${\frac{7}{2}}^{+}$ state is not identified in ${\mathrm{Sn}}^{123}$ and ${\mathrm{Sn}}^{125}$. Several new $l=2\mathrm{}$ states are identified as well as several $l=1\mathrm{}$ and $l=3\mathrm{}$ states belonging to the 82-126-neutron shell. A renormalization of the DWBA absolute cross sections is performed to eliminate systematic inconsistencies in the sum of ${U_j}^2+{V_j}^2$. The factors of renormalization are found to be within the well-known uncertainties of the DWBA calculations. The values of relative single-particle energies (${\epsilon }_j-{\epsilon }_{\frac{5}{2}}$) are calculated both from the occupation numbers (${U_j}^2 or {V_j}^2$) and from the single-quasiparticle energies ($E_j$) using pairing theory. The results are in disagreement by as much as 1 MeV or more. From the reactions on the odd isotopes, spin and parity information is obtained for many states in ${\mathrm{Sn}}^{114}$, ${\mathrm{Sn}}^{116}$, ${\mathrm{Sn}}^{118}$, and ${\mathrm{Sn}}^{120}$.