Mass systematics for<i>A</i>=29–44 nuclei: The deformed<i>A</i>∼32 region

Abstract

Further evidence for the presence of an anomaly in binding energies for the ``island of inversion'' centered at Z=11, N=21 is obtained by comparison of shell-model calculations to experiment. The calculations were done with a shell-model interaction that is applicable to nuclei with active valence nucleons in both the (1s,0d) and (0f,1p) major shells. This interaction is described in detail as are its predictions for binding energies and energy spectra of Z=8--20, N=18--25 nuclei. These calculations provide the background for the exploration of the ``island of inversion.'' The extent of the ``island'' and the magnitude of the anomaly is explored by calculating the binding energies of 2\ensuremath{\Elzxh}\ensuremath{\omega} excitations of neutrons from the (1s,0d) shell to the (0f,1p) shell relative to the 0\ensuremath{\Elzxh}\ensuremath{\omega} ground state. The reason why mixed (0+2)\ensuremath{\Elzxh}\ensuremath{\omega} calculations are not considered reliable is addressed. Truncation schemes and a weak-coupling approximation are used to extend the range of the calculations. It is found that for Z=10--12, N=20--22 (and possibly N&gt;22) nuclei the lowest 2\ensuremath{\Elzxh}\ensuremath{\omega} state is more bound than the 0\ensuremath{\Elzxh}\ensuremath{\omega} ground state. The role of odd n n\ensuremath{\Elzxh}\ensuremath{\omega} excitations is considered and it is found that the 1\ensuremath{\Elzxh}\ensuremath{\omega} ground state always lies below that of 3\ensuremath{\Elzxh}\ensuremath{\omega}, and for N=19, 21, and 23, the lowest 1\ensuremath{\Elzxh}\ensuremath{\omega} state is in close competition with 2\ensuremath{\Elzxh}\ensuremath{\omega} for the lowest binding energy. Collectivity is considered via E2 observables and energy spectra for the 2\ensuremath{\Elzxh}\ensuremath{\omega} ground-state bands. The reason for the existence of the ``island'' is discussed.