Alpha-induced inelastic scattering and alpha-transfer reactions in $^{12}$C and $^{16}$O within the Algebraic Cluster Model

TL;DR

This paper uses an algebraic cluster model to describe alpha-induced inelastic scattering and transfer reactions in carbon-12 and oxygen-16, providing a reliable framework for reactions involving alpha-cluster structures.

Contribution

It introduces a molecular algebraic model based on alpha clusters to accurately describe inelastic scattering and transfer reactions in $^{12}$C and $^{16}$O, including reaction mechanisms.

Findings

Reliable description of low-lying state excitations.

Good agreement with experimental data.

Brief discussion of alpha-transfer selection rules.

Abstract

The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $\alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $\alpha$-transfer reactions from $^{12}$C and $^{16}$O.