  A multi-channel algebraic scattering (MCAS) method has been used to solve
coupled sets of Lippmann-Schwinger equations for $\alpha$+nucleus systems to
find spectra of the compound systems. Low energy spectra for ${}^{12}$C,
${}^{16}$O, and ${}^{20}$Ne are found with the systems considered as the
coupling of an $\alpha$ particle with low-excitation states of the core nuclei,
${}^8$Be, ${}^{12}$C, and ${}^{16}$O, respectively. Collective models have been
used to define the matrices of interacting potentials. Quadrupole (and octupole
when relevant) deformation is allowed and taken to second order. The
calculations also require a small monopole interaction to provide an extra
energy gap commensurate with an effect of strong pairing forces. The results
compare reasonably well with known spectra given the simple collective model
prescriptions taken for the coupled-channel interactions. Improvement of those
interaction specifics in the approach will give spectra and wave functions
suitable for use in analyses of cross sections for $\alpha$ scattering and
capture by light-mass nuclei; reactions of great importance in nuclear
astrophysics.
