Systematics of alpha-cluster states above double shell closures

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