Consistent semimicroscopic algebraic description of core + α-particle systems in the A = 16 to 20 region

A standardized version of the Hamiltonian of the Semimicroscopic Algebraic Cluster Model is presented, by the use of which the spectra of several neighbouring even- and odd-mass nuclei can be parametrized in a consistent way. We extract parameters from the 12C + α, 14C + α, 15N + α and 16O + α systems and use them to construct the Hamiltonian for 13C + α by interpolation.