Decay and structure of the Hoyle state

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.

Comments: 5 pages, 3 figures