Nuclear Structure Studies in the Tin Isotopes with (d, p) and (d, t) Reactions

Abstract

The neutron single-particle states in the odd isotopes of tin are identified by ($d, p$) angular distribution studies. The cross sections for exciting these states by ($d, p$) and ($d, t$) reactions are measured, and the results are analyzed to give values of ${{V}_{j}}^{2}$ (in Kisslinger-Sorens$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{o}}$n notation), the fraction by which each of the single-particle states is full, for each subshell in each isotope. These are used to calculate ${\ensuremath{\epsilon}}_{j}$, the unperturbed single-particle energies; the results are reasonably consistent. If the observed energies of single-particle states are used to predict the ${V}_{j}$, the agreement is generally good, but some discrepancies are noted and an explanation is offered.Other weakly excited states are found in the region of the single-particle states. At higher excitation energies, several rather sharp levels are strongly excited in ($d, p$) reactions. Their energy, cross section, and regularities among the isotopes suggests that these are single-particle levels from the next major shell ($82lN\ensuremath{\le}126$); however, their angular distributions cannot be used for identification as they are the same for all levels in this region and show little structure. This last fact is not easily explained.Some of the two quasi-particle excitation states in the even isotopes of Sn are identified and the apparent pairing energy is thereby measured; it is surprisingly found to vary rapidly with mass number. Spectra from ($d, p$) and ($d, t$) reactions in isotonic pairs ${\mathrm{Cd}}^{114}$-${\mathrm{Sn}}^{116}$ and ${\mathrm{Cd}}^{116}$-${\mathrm{Sn}}^{118}$ are compared to show that the single-particle neutron states are much more radically affected by the addition of two protons than by the addition of two neutrons, contrary to the usual assumption in shell model theory.$Q$ values for ($d, p$) and ($d, t$) reactions on the major isotopes of tin are measured.