Decay and structure of the Hoyle state

TL;DR

This study investigates the structure and decay process of the Hoyle state in carbon-12 using a three-alpha particle model and Faddeev formalism, revealing dominant two-alpha resonant decay and specific geometric configurations.

Contribution

It provides a detailed three-body analysis of the Hoyle state, showing decay mechanisms and density distributions independent of interaction models when calibrated to the state energy.

Findings

Decay mainly occurs via a two-alpha resonant state.

Interior density shows peaks for equilateral and isosceles triangle configurations.

Results are consistent across different alpha interaction models.

Abstract

The first $0^+$ resonant state of the $^{12}$C nucleus ${}^{12}$C$(0_2^+)$, so called the Hoyle state, is investigated in a three-$\alpha$-particle (3-$\alpha$) model. A wave function for the photodisintegration reaction of a $^{12}$C bound state to 3-$\alpha$ final states is defined and calculated by the Faddeev three-body formalism, in which three-body bound- and continuum states are treated consistently. From the wave function at the Hoyle state energy, I calculated distributions of outgoing $\alpha$-particles and density distributions at interior region of the Hoyle state. Results show that a process through a two-$\alpha$ resonant state is dominant in the decay and contributions of the rest process are very small, less than 1 \%. There appear some peaks in the interior density distribution corresponding to configurations of an equilateral- and an isosceles triangles. It turns out that these results are obtained independently of the choice of $\alpha$-particle interaction models, when they are made to reproduce the Hoyle state energy.