Local Potential Model of the Hoyle Band in 12C

TL;DR

This paper models the Hoyle state in 12C using a local potential cluster approach, successfully describing its energy, width, and charge radius, including the recently observed 2+ state, and compares different quantum number choices.

Contribution

It introduces a local potential cluster model for the Hoyle band in 12C and identifies the optimal quantum number G=6 for describing experimental data.

Findings

G=6 provides the best description of state properties.

The model reproduces energies, widths, and charge radii.

The approach aligns with recent experimental observations.

Abstract

We describe the excited 0+ state of 12C at 7.654 MeV, often called the Hoyle state, in terms of a local potential 8Be+alpha cluster model. We use a previously published prescription for the cluster-core potential to solve the Schroedinger equation to obtain wave functions for this state, and also for higher angular momentum states of the same system. We calculate energies, widths and charge radii for the resulting band of states, with particular emphasis on the recently discovered 2+ state. We examine various choices of the oscillator quantum number 2n + L = G for the cluster-core relative motion, and find that G = 6 leads to the most coherent description of the properties of the states and is consistent with recent experimental data on the L = 2 state.