Alpha-cluster spectroscopy in 40Ca and in the sd-shell closure region

The low-energy 36Ar(α,α) elastic scattering data of Gaul et al. are analyzed within the frame of the optical model, using energy-independent Woods-Saxon squared or model-independent geometries for the real part of the potential. The optical-model scattering amplitude is decomposed into its barrier and internal wave components to understand the rapid and complicated evolution of the angular distributions with incident energy. The properties of the low-energy bound and quasibound states supported by this potential are compared with those of the states of the deformed 4p-4h rotational band in 40Ca, built on the Jπ=0+, Ex=3.35 MeV state. The possibility of extending this local potential model approach to neighboring nuclei near the sd-shell closure is discussed. A negative-parity band of states with appreciable α-cluster character, starting around the α-particle threshold, is expected to be systematically present in this mass region