Structure of the Transitional Nucleus $^{28}$Mg Studied with the $^{26}$Mg(t,p)$^{28}$Mg Reaction

Past studies of the nuclei surrounding $^{32}$Mg discovered inversions in the usual ordering of shell-model states. Shell-model interactions that incorporate the evolution toward this ``island of inversion" predict low-lying deformed intruder states for nearby nuclei. One such nucleus is $^{28}$Mg, which exists in the transition between stability and the inverted region. The two-neutron transfer reaction $^{26}$Mg(t,p)$^{28}$Mg has been used to study the properties of the ground state and excited 0$^+$ states. This experiment was carried out at Argonne National Laboratory using the HELIcal Orbit Spectrometer (HELIOS). Multi-nucleon transfer is known to be sensitive to the the amplitude and phase of configuration-mixed states, and enhances transfer to those states which are similar to the ground state of the target plus two nucleons in single-particle orbitals. Because multi-nucleon transfers are more complex than single-particle transfers, a shell-model calculation must guide the understanding of which configurations will be strongly populated. A new shell-model calculation using the SDPF-MU interaction provided the structure-related transfer amplitudes, and results comparing the experimental cross sections to those predicted by the transfer amplitudes and DWBA will be presented.