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A multi-channel algebraic scattering (MCAS) method has been used to solvecoupled sets of Lippmann-Schwinger equations for $\alpha$+nucleus systems tofind spectra of the compound systems. Low energy spectra for ${}^{12}$C,${}^{16}$O, and ${}^{20}$Ne are found with the systems considered as thecoupling of an $\alpha$ particle with low-excitation states of the core nuclei,${}^8$Be, ${}^{12}$C, and ${}^{16}$O, respectively. Collective models have beenused to define the matrices of interacting potentials. Quadrupole (and octupolewhen relevant) deformation is allowed and taken to second order. Thecalculations also require a small monopole interaction to provide an extraenergy gap commensurate with an effect of strong pairing forces. The resultscompare reasonably well with known spectra given the simple collective modelprescriptions taken for the coupled-channel interactions. Improvement of thoseinteraction specifics in the approach will give spectra and wave functionssuitable for use in analyses of cross sections for $\alpha$ scattering andcapture by light-mass nuclei; reactions of great importance in nuclearastrophysics.

A multichannel model for clusters of an $\alpha$ and select $N=Z$ nuclei