Generator Coordinate Treatment of Composite Particle Reaction and Molecule-like Structures

Abstract

We propose a generator coordinate method as a numerically tractable alternative to the resonating group method for treating the composite particle reaction and for the study of the molecular model of nuclear structure. Adopting the wave function used by Margenau and Brink in their α particle model as a trial function the problem of the relative motion between composite particles is discussed. We give a method of transformation of the generator function to the wave function of the relative motion, and show that the solutions of the generator coordinate method include that of the resonating group method in the interaction region. To obtain the scattering amplitude we present the formulation which uses the boundary condition constraint method. As an example our procedure is applied to the phase shift calculation of the α-α scattering case, and good agreement with experiment is obtained showing the utility of our method. We also discuss that the idea of the density localization in the molecular model can be adequately formulated in this method, using the fact that this method has a direct connection with the concept of intrinsic deformation. Some quantitative analyses are given of the α particle widths of ⁸Be by our method of generator coordinates, providing the evidence of the molecule-like structure of this nucleus.