Isobaric analog resonances of Mg-31 and the border of the island of inversion

The evolution of the nuclear shell structure in the region of the neutron-rich shell-breaking nucleus Mg-32 has been the subject of considerable interest. We present here the first determination of the overlap of the ground and two first excited states in Mg-31 with a neutron coupled to the ground state in Mg-30 based on studies of its isobaric analog resonances in Al-31. The excitation function for proton resonant elastic scattering on Mg-30 was measured close to 0 degrees in the laboratory frame by bombarding a thick polyethylene target with a Mg-30 beam at an energy of 2.92 MeV/nucleon at the REX-ISOLDE facility at CERN. Three resonances were successfully resolved, and angular momenta and total and proton resonance widths were determined by using R-matrix analysis. The deduced spectroscopic factor for the ground state in Mg-31 is consistent with the shell-model calculation, whereas those for the first and second excited states could not be reproduced. These results show that a drastic change in structure occurs between Mg-30 and Mg-31 and that the onset of structural change in this region therefore occurs between these two isotopes.