Investigation of the triple-αreaction in a full three-body approach

Abstract

Background: The triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of 12 C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible. Purpose: Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the non-resonant reaction mechanisms on the same footing, to compute the triple-alpha reaction rate at low temperatures. Methods: We combine the R-matrix expansion, the R-matrix propagation method, and the screening technique in the hyperspherical harmonics basis. Results: Both the 2 + 1 bound state and the 0 + 2 resonant state in 12 C are well reproduced. We also study the cluster structure of these states. We calculate the triple-alpha reaction rate for T = 0.01 − 0.1 GK. Conclusions: We obtain the same rate as NACRE for temperatures above 0.07 GK, but the new rate is largely enhanced at lower temperatures (≈ 10 12 at 0.02 GK). The differences are caused by the direct capture contribution to the reaction when three alpha particles can not reach the resonant energies.

Alpha particle clusters and their condensation in nuclear systems

“…The structure of the 1/2 ± states of 13 C up to around E x ∼ 16 MeV has been investigated with the full fourbody 3α+n OCM [128]. The 3α OCM, the model space of which is the subspace of the 3α + n model, describes well the structure of the low-lying states of 12 [128,127] with the 3-body force V3α, compared with the experimental data. structure with a higher nodal behavior, while the 0 + 4 state is characterized by a linear-chain-like structure having the dominant configuration of 8 Be(2 + )+α with a relative Dwave motion.…”

“…This is large in comparison with the Hoyle state but still small considering that the excitation energy is about twice as high. It is tempting to say that the width is surprisingly small because the states to which it can decay, if we suppose that the 15.1 MeV state is an α condensate state, have radically different structure being either of the 12 C+α type with 12 C in a compact form or other shell model states. Let us see what the theoretical approaches tell us more quantitatively.…”

“…Next came the fully microscopic approaches solving RGM respectively GCM equations by Kamimura et al [28] and Uegaki et al [29] for 12 C. Concerning the Hoyle state the conclusions were the same as the one of Horiuchi. We cite from Uegaki et al [29]: In a number of excited states which belong to the new "phase", the 12 …”

“…with φ αi as in (12). The Brink wave function is in fact a perfect Slater determinant where always quadruples of 2 protons and 2 neutrons are placed on the same spatial position S i .…”

“…As for the case of 8 Be, this state is hold together by the Coulomb barrier. It is one of the most important states in nuclear physics because it is the gateway for Carbon production in the universe through the so-called triple α reaction [8,9,10,11,12,13,14] and is, thus, responsible for life on earth. A great part of this article will deal with the description of the properties of this state.…”