# Odd-mass nuclei in the cluster shell model

## TL;DR

This paper introduces a cluster shell model for odd-mass nuclei, focusing on three-alpha-particle configurations and their symmetry properties, and applies it to the nucleus 13C to analyze its rotational band structure.

## Contribution

The paper develops a cluster shell model analogous to the Nilsson model, incorporating discrete symmetries of alpha-particle configurations, and demonstrates its application to 13C.

## Key findings

- Identification of unique rotational band structures linked to alpha-particle symmetry
- Application of the model to 13C reveals specific spectral features
- Symmetry considerations serve as fingerprints for geometric configurations

## Abstract

In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.