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

TL;DR

This paper develops a multichannel algebraic scattering model to compute low-energy spectra of alpha-nucleus systems like ${}^{12}$C, ${}^{16}$O, and ${}^{20}$Ne, incorporating collective deformation effects and pairing interactions.

Contribution

It introduces a coupled-channel approach using MCAS with collective models for alpha-nucleus systems, providing a framework for accurate spectral calculations.

Findings

Spectra of ${}^{12}$C, ${}^{16}$O, and ${}^{20}$Ne are reasonably reproduced.

Inclusion of quadrupole and octupole deformations improves spectral accuracy.

Small monopole interactions are necessary to match experimental energy gaps.

Abstract

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.