Systematics of alpha-cluster states above double shell closures

Abstract

Alpha particle cluster models have been very successful in reproducing energy spectra, static and dynamic electromagnetic properties, \ensuremath{\alpha}-emission widths and \ensuremath{\alpha}-nucleus elastic scattering data in light nuclei around the double shell closures at $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$. We extend the application of one such model to the heavier mass regions above $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$. In all cases we employ a potential of given geometric form with all parameters fixed except for the radius that is tailored to each nucleus in turn. We find that the potentials needed for $^{20}\mathrm{Ne}$ and $^{44}\mathrm{Ti}$ are very similar to the real parts of the optical potentials used in an accurate description of \ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{16}$O and \ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{40}$Ca elastic scattering up to high energies. By suitable choice of the quantum numbers that describe the relative motion of the \ensuremath{\alpha} particle and the core nucleus we are able to give a good account of the spectra, the reduced E2 transition strengths, and the \ensuremath{\alpha}-particle emission widths (or lifetimes) of the members of the ground state bands in the four nuclei $^{20}\mathrm{Ne}$, $^{44}\mathrm{Ti}$, $^{94}\mathrm{Mo}$, and $^{212}\mathrm{Po}$. The potential chosen also allows a consistent description of the half-lives for favored \ensuremath{\alpha} decay throughout the Periodic Table.