Shell-model calculations for two-neutron transfer near the N=20 island of inversion

We describe connections between shell-model calculation results and predictions for two-nucleon transfer reactions. Measurements of the ^30 Mg( t,p ) ^32 Mg reaction were used to identify a low-lying shape-coexisting 0 ^+ state in ^32 Mg. Interpretations of those early, limited data were based on simple empirical models. The cross sections for two-nucleon transfer are, however, extremely sensitive to the details of the nuclear-structure. Motivated by the possibility of new high-resolution two-nucleon transfer measurements around the N=20 Island of Inversion, we have performed shell-model calculations wave functions for states in the nuclei ^30,32 Mg using the SDPF-M and SDPF-MU interactions, and from those calculations obtain the two-nucleon transfer amplitudes that we use to predict cross sections for the ^28,30 Mg( t,p ) ^30,32 Mg reactions. The combined results show how the nuclear structure properties influence experimental observables for the ( t,p ) reaction. We compare our results with the existing data.