3-ALPHA MODEL OF C-12 NUCLEUS

The C12 nucleus is studied from the three-α-particle point of view based on a wave-function method in which the Hermiticity of the Fredholm kernel is preserved. The interaction between two α particles, obtained from the resonating-group calculation of Okai and Park, is recast in a separable form with the aid of Hille's formula. For the numerical calculation, we have employed three simpler types of the potential: Gaussian, Tabakin, and Yamaguchi. It is shown that Harrington's theory, based on the T-matrix method, reduces to a result of the present study, but not to those of other wave-function methods. Contrary to a conclusion of the previous work, we have succeeded in finding an excited state with the same (J,π) as the ground state. The present method also supplies the mean height and side of the equilateral triangles formed by three α particles. These values are found to imply a root-mean-square radius of the C12 nucleus which agrees well with the experimental value. © 1969 The American Physical Society.