Decay and structure of the Hoyle state

Abstract

The first ${0}^{+}$ resonant state of the $^{12}\mathrm{C}$ nucleus, $^{12}\mathrm{C}({0}_{2}^{+})$, the so-called Hoyle state, is investigated in a three-$\ensuremath{\alpha}$-particle (3-$\ensuremath{\alpha}$) model. A wave function for the photodisintegration reaction of a $^{12}\mathrm{C}$ bound state to 3-$\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ particles and density distributions at interior region of the Hoyle state. Results show that a process through a two-$\ensuremath{\alpha}$ resonant state is dominant in the decay and contributions of the rest process are very small, less than 1%. There appear to be some peaks in the interior density distribution corresponding to configurations of equilateral and isosceles triangles. It turns out that these results are obtained independently of the choice of $\ensuremath{\alpha}$-particle interaction models, when they are made to reproduce the Hoyle state energy.