N minus Z dependence of intruder states near the island of inversion*

Almost 3 decades after the discovery of deformed, intruder-dominated ground states in nuclei with Z $\sim$ 10 and N $\sim$ 20, many questions remain about the behavior of the N = 20 shell gap and how correlation effects can bridge the gap in this region of nuclei, later dubbed the ``Island of Inversion,'' because intruder states expected to lie at higher energies actually fall below the ``normal'' s-d states. Recent work has illustrated how some intruder dominated states fall systematically with increasing N and decreasing Z until reaching inversion. These N and Z dependences have been treated quite differently in the most successful calculations. The fall with increasing N is generally attributed to the rising Fermi level for neutrons, while the fall with decreasing Z seems to require a reduction in the N = 20 shell gap with lowering Z, perhaps due to the tensor interaction. The recent assignment of a negative-parity intruder band in $^{30}$Al at reduced energy and a subsequent survey of similar 4$^-$ bandheads in neighboring odd-odd nuclei has led to an intriguing discovery: the excitation energy of these lowest intruder states depends only on N minus Z to an accuracy of 10 to 20 keV.