Natural boundary condition methods for nuclear reactions (II)

Two natural boundary condition methods are used to calculate both the elastic and inelastic scattering cross sections for an exactly soluble model comprising two square well potentials coupled by a square well interaction. The necessary modification of one of the methods (R-matrix approach with energy-dependent basis states) for the case of several open channels and a simple correction which greatly improves the rate of convergence of the other (Barrett and Delsanto) method are given. The methods are investigated for weak, intermediate and strong coupling interactions and the results are compared where possible with those of other related methods. It is concluded that for the practical calculation of reaction cross sections from a basic physical model, the natural boundary condition methods offer the most tractable approach particularly for problems involving strong channel coupling.