On the Extension of the Resonating Group Treatment of Composite Particle Scattering to the Heavy System

Abstract

We present a new analytical method of calculating the kernels in the resonating group treatment of the composite particle scattering. It converts the calculations of matrix elements to those in terms of the Slater determinantal wave functions. By this we can extend the range of applicability of the resonating group method to systems heavier than α+α such as α+¹⁶O and possibly ¹⁶O+¹⁶O. Since our method treats the lighter particle as a cluster in the valence orbits outside the core of the heavier particle, the correspondence of the resonating group treatment to the continuum shell model is clearly displayed. As an application, kernels in the α+¹⁶O system are calculated and by using them the validity of the orthogonality condition model in this system is investigated which is originally proposed by Saito in the α+α system.