Systematics of two-neutron transfer cross sections near closed shells: A sum rule analysis of (p,t) strengths on the lead isotopes

We report the study of the (p,t) reaction on 208Pb, 206Pb, and 204Pb at E = 35 MeV and on the application of the two-neutron-transfer sum rule of Bayman and Clement to these data. Analysis of the sum rule shows that the observed dramatic increase in J = 0 (p,t) cross section as one goes from targets of 208Pb to 206Pb to 204Pb and the nearly-as-dramatic decrease in J not = 0 cross sections reflect general features of the shell-model character of these nuclei. Application to the present series of nuclei shows that this two-neutron-transfer sum rule can be applied with nearly the same accuracy as the corresponding single-nucleon-transfer sum rules. The relationship between the shell-model and pairing-vibration (p,t) strengths is discussed