Nuclear Structure Information from the (p, t) Reaction,A=46toA=70

The ($p, t$) reaction has been studied with 40-MeV protons for a sequence of isotopes from titanium to zinc. Angular distributions have been obtained for ground-state ($L=0\mathrm{}$) and first-excited-state, or lowest $L=2\mathrm{}$ group, transitions. The shapes of the angular distributions are nearly identical for a given angular-momentum transfer $L$. The reaction seems to proceed by the direct pickup of a neutron pair coupled to angular momentum $L$. Energy spectra of the outgoing tritons were obtained for some of the elements, showing that the predominant strength goes to the lowest $L=0\mathrm{}$ (usually the ground state) and $L=2\mathrm{}$ transitions. The general features of the ($p, t$) reaction are discussed, showing that the reaction is a powerful tool for studying the angular-momentum coupling of pairs and pair correlation effects. A sketch of the distorted-wave Born-approximation (DWBA) theory for two-nucleon transfer reactions is presented together with a discussion of the spectroscopic factors predicted by neutron seniority, pairing theory, the degenerate model, and exact shell-model calculations within a pure $f_{\frac{7}{2}}$ configuration. Since reliable DWBA calculations are not available, we have compared our integrated cross sections with spectroscopic factors predicted by the various models. The agreement is very good for the $L=0\mathrm{}$ transitions in the $f_{\frac{7}{2}}$ shell. Appreciable configuration mixing is evident in the $2p-1f_{\frac{5}{2}}$ shell, where both the degenerate model and pairing theory are in qualitative agreement with the data, predicting however too rapid a rise with increasing neutron number for the nickel isotopes. The behavior of the lowest $L=2\mathrm{}$ transitions in the $2p-1f_{\frac{5}{2}}$ shell indicates that the first 2+ states are not very pure in neutron seniority. Reliable DWBA calculations, including finite-range effects, are needed to remove uncertainties in the intepretation of the data.