A Study on Three-Alpha Structure of 12C in the Faddeev Formalism

Abstract

Three-alpha structure of "C is investigated in the Faddeev formalism by adopting a one-term nonlocal separable a-a potential to reproduce the damped inner oscillation of the relative wave functions, which represents the most important effect of the Pauli principle between composite particles. This boson model enables us to obtain several important lowlying states of "C. In particular, we can predict two o+ states with markedly different properties; the spatially compact ground state with large binding energy arising from the internal correlation of the relative S, D and G waves and the well-developed cluster state with the "a+'Be(O+)" structure weakly coupled in the S wave. Components of the wave functions are examined in detail. Discussion is also given for the mixture of redundant components, which should be forbidden when the effect of the Pauli principle is treated exactly as the fermion system. 1. Introduction Study on two-body cluster systems from the viewpoint of alpha-like four-body correlations and molecular structures in light nuclei has revealed the essential features of composite-particle interactions in the wide region of light nuclei.v' 21 This success provides us with the basis to investigate the aspects of three-(or more generally many-) cluster systems. Typical multi-cluster states are expected to appear near the threshold energy for the decay into subunit nuclei, according to the "Ikeda Diagram. " 31 41 Various modes of relative motion are possible in multi-cluster systems. Microscopic treatments usually adopted in studying these systems, such as the generator coordinate method, take the Pauli principle into account exactly, while relative motion between clusters is solved in more or less restricted way. 51 ~91 Since the effective interaction between clusters is weak compared with the cluster-constructive interaction owing to the exchange repulsion due to the Pauli principle, the fluctuation from the mean relative distance is generally very large. Therefore, it is important to solve relative motion in the sense of few-body problems as exactly as possible. In this paper we study the structure of 12 C by adopting the boson model for the 3a system in the Faddeev formalism. 101 We employ an a-a effective potential which reproduces the characteristics of the a-a interaction extracted micro-