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.Comment: 5 pages, 3 figure

Low-lying12C continuum states in three-αmodel

“…system above the 3α threshold. This is an extension of recent works [5,6], in which 3α continuum states up to E = 0.6 MeV were studied to calculate the reaction rate of the triple-α process at stellar temperature T ∼ 10 9 K, and clarify the decay mode of the Hoyle state.…”

“…In Ref. [6], it was shown that the decay of the Hoyle state is dominated by a sequential decay (SD) process, in which the decay occurs in two steps: first 3 α-particles separate to 2-α resonant state, 8 Be(0 Fig. 1.…”

“…(See Refs. [5,6,8] for the details of the calculations.) This procedure provides the amplitude F (B) (q,p, E q ), and then the E0 strength function is calculated as…”

Quartet condensation in Fermi-systems. The Hoyle state in the 12C nucleus and life on earth

“…A precise answer is obtained from the calculation of the bosonic occupation numbers which have been obtained in three different works [23,28,29] with very similar results. The ones of [29] are displayed in Figure 7.…”

“…For the microscopic description of the Hoyle state several approaches have been put forward in the past [14,16,17,19,[21][22][23]. However, only the following, so-called THSR wave function (according to the authors Tohsaki, Horiuchi, Schuck, Roepke) which was proposed in [1] concentrates on the α particle condensation aspect (the spin-isospin part is not written out)…”