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.
A survey of known threshold excitations of mirror systems suggests a means to estimate masses of nuclear systems that are uncertain or not known, as does a trend in the relative energies of isobaric ground states. Using both studies and known mirror-
pair energy differences, we estimate the mass of the nucleus 17-Na and its energy relative to the p+16-Ne threshold. This model-free estimate of the latter is larger than that suggested by recent structure models.
Cross-section and analyzing power data from 197 MeV $(p,p)$ scattering and longitudinal and transverse form factors for electron scattering to low lying states in $^{10}$B have been analyzed as tests of the structure of the nuclear states when they a
re described using a no-core $(0+2)hbaromega$ shell model. While the results obtained from the shell model clearly show the need of other elements, three-body forces in particular, to explain the observed spectrum, the reasonable level of agreement obtained in the analyses of the scattering data suggest that the wavefunctions from our shell model using only a two-body potential are credible. Any changes to the wavefunctions with the introduction of three-body forces in the shell model Hamiltonian should therefore be relatively minor.
Differential cross sections and analyzing powers for elastic scattering from, and for inelastic proton scattering to a set of $2^+_1$ states in, ${}^{12}$C, ${}^{20}$Ne, ${}^{24}$Mg, ${}^{28}$Si and ${}^{40}$Ca, and for a set of energies between 35 t
o 250 MeV, have been analyzed. A $g$-folding model has been used to determine optical potentials and a microscopic distorted wave approximation taken to analyze the inelastic data. The effective nucleon-nucleon interactions used to specify the optical potentials have also been used as the transition operators in the inelastic scattering processes. Shell and large space Hartree-Fock models of structure have been used to describe the nuclear states.
A Multi-Channel Algebraic Scattering (MCAS) theory is presented with which the properties of a compound nucleus are found from a coupled-channel problem. The method defines both the bound states and resonances of the compound nucleus, even if the com
pound nucleus is particle unstable. All resonances of the system are found no matter how weak and/or narrow. Spectra of mass-7 nuclei and of {}^{15}F, and MCAS results for a radiative capture cross section are presented.
Two causes of non-locality inherent in nucleon-nucleus scattering are considered. They are the results of two-nucleon antisymmetry of the projectile with each nucleon in the nucleus and the dynamic polarization potential representation of channel cou
pling. For energies $sim 40 - 300$ MeV, a g-folding model of the optical potential is used to show the influence of the knock-out process that is a result of the two-nucleon antisymmetry. To explore the dynamic polarization potential caused by channel coupling, a multichannel algebraic scattering model has been used for low-energy scattering.
