# The algebraic molecular model in $^{12}$C and its application to the $\alpha$+$^{12}$C scattering: from densities and transition densities to optical potentials and nuclear formfactors

## TL;DR

This paper employs an algebraic molecular model to derive densities and transition densities in $^{12}$C, applying them to calculate nuclear potentials, formfactors, and scattering processes, and compares results with a three-body approach.

## Contribution

It introduces an algebraic molecular model for $^{12}$C that connects low-lying states to scattering observables and compares with three-body calculations.

## Key findings

- Densities and transition densities are successfully calculated.
- Model results agree with three-body approach for continuum effects.
- Nuclear potentials and formfactors are effectively derived from the model.

## Abstract

The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground and the Hoyle states. These densities are then used as basic ingredients to calculate, besides electromagnetic transition probabilities, nuclear potentials and formfactors to describe elastic and inelastic $\alpha$+$^{12}$C scattering processes. The calculated densities and transition densities are also compared with those obtained by directly solving the problem of three interacting alpha's within a three-body approach where continuum effects, relevant in particular for the Hoyle state, are properly taken into account.