The Hoyle state and its relatives

TL;DR

This paper investigates the Hoyle state and related resonances in carbon-12 using a microscopic cluster model, emphasizing the importance of continuum treatment for higher states and analyzing resonance properties.

Contribution

It introduces a comprehensive microscopic cluster model with continuum treatment for studying resonances in 12C, including the Hoyle state and higher-lying states.

Findings

The Hoyle state is a sharp resonance well-described by bound state approximation.

Higher-lying states require explicit continuum treatment for accurate description.

Resonance properties such as radii and transition strengths are quantitatively analyzed.

Abstract

The Hoyle state and other resonances in the continuum above the 3 alpha threshold in 12C are studied in a microscopic cluster model. Whereas the Hoyle state is a very sharp resonance and can be treated reasonably well in bound state approximation, the other higher lying states require a proper treatment of the continuum. The model space consists of an internal region with 3 alpha particles on a triangular grid and an external region consisting of the 8Be ground state and excited (pseudo)-states of 8Be with an additional alpha. The microscopic R-matrix method is used to match the many-body wave function to the asymptotic Coulomb behavior of bound states, Gamow states and scattering states. 8Be-alpha phase shifts are analyzed and resonance properties like radii and transition strengths are investigated.