Effective three-body interactions in the α-cluster model for the 12C nucleus

Abstract

Properties of the lowest 0 + states of 12 C are calculated to study the role of three-body interactions in the α-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the α-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width

Consistent α-cluster description of the 12C(0 2 + ) “hoyle” resonance

“…Next, the assumption on the "frozen" nucleon distribution in the α-particles is used to calculate the experimentally observable nucleonic structural characteristics, e. g., the root-mean-square (r. m. s.) radii and the transition radius R 12 . This extended α-cluster model leads generally to a satisfactory description of the 12 C nucleus [10,[13][14][15]20]. In particular, the calculated Γ and M 12 [13,14] are in reasonable agreement with experimental data (up to a factor two) even for the simplified local α -α interactions.…”

“…Using this form, one obtains from the usual definitions [13,14,26] that the monopole transition matrix element is expressed merely via the three-body wave functions,…”

“…As the experimental data at these conditions are lacking, the reliable theoretical results are especially desired; nevertheless, the calculated non-resonance reaction rates [4][5][6][7] differ by many orders of magnitude. There is vast literature on the 12 C states above the 3α threshold, and it is possible to notice just some of the recent papers, e. g., with concern of astrophysical aspects [7][8][9], distribution of decaying particles [10,11], dilute-gas variational calculations [12], and different approaches to precise description of the 12 C properties [13][14][15][16][17]. Besides much interest in the 12 C(0 + 2 ) state owing to its role in the astrophysical applications, the structure of this state has been widely discussed for a long time, in particular, a linear chain configuration was suggested in [18] and a triangle configuration was considered in [19].…”

Structure of low-lying 12C resonances

“…We choose to ignore the two bound states because they, and especially the ground state, have a smaller size and their structure can then be expected to involve more nucleonic (less α-cluster) degrees of freedom. Although it is possible to construct a three-body potential which reproduces energies of both the ground state and the lowest 0 + resonance [33,34] it is uninteresting in the present context since the important intermediate and large distancestructure would remain unchanged.…”

Nuclear clusters as the first stepping stones for the chemical evolution of the universe

“…It is a two-step process, in which the first step of 4 He+ 4 He produces a very short-lived 8 Be. The equilibrium abundance of this configuration allows a third α-capture process, through a three α-cluster configuration in the 12 C compound nucleus, the Hoyle state [16][17][18]. The α-cluster configuration of the compound nuclei involved, such as 8 Be, 12 C, and 16 O, is well established and is responsible for facilitating helium burning through the α-process in Red Giant Stars.…”