Consistent alpha-cluster description of the 12C (0^+_2) resonance

TL;DR

This paper models the 12C (0^+_2) resonance using an alpha-cluster approach, accurately reproducing its properties and providing insights into its structure relevant for stellar helium burning.

Contribution

It introduces a consistent alpha-cluster model with tuned potentials that accurately describes the 0^+_2 resonance properties and structure of 12C.

Findings

Calculated resonance width matches experimental data

Transition matrix elements agree with observations

Resonance structure shows oscillation between configurations

Abstract

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9.