On 12C + Scattering by the Coupled Channel Resonating Group Method: Solution of the Redundancy and Non-Orthogonality Problem

Abstract

A microscopic treatment of 12C + α scattering is formulated in the framework of the coupled channel resonating group method (CCRGM), using Feshbach's formulation for nucleon scattering. The ground rotational band states of 12C of spins L = 0, 2 and 4 adopted in the channel coupling, and the wave functions of these three states are assumed to be described by the SU3 model wave functions of (0,4) representation. Since in the interaction region three channels which are based on the three states L = 0, 2, 4 of 12C are not orthogonal and even not independent of each other, we need to classify the states which are independent and orthogonal. The answer to this problem of the classification of the states is given systematically by solving the eigenvalue problem of the overlap kernel, whose eigenfunctions are classified entirely by the irreducible representation of the SU3 group. In order to clarify the meaning of the CCRGM approach, we classify some important shell model states of a few-particle-hole excitation by means of our CCRGM scheme and give α-spectroscopic factors of these states, by using the solutions of the eigenvalue problem of the overlap kernel. As an approximation of the CCRGM equation the equation of the coupled channel orthogonality condition model is formulated.