Variational scattering theory using a functional of fractional form. II. AnL2approach

An $L^2$ approach to our variational method which is based on a functional of fractional form is proposed. As in the $R$-matrix theory, configuration space is divided into two parts. However, unlike the $R$-matrix theory, the associated wave function is always smooth. The resulting $K$ matrix is anomaly-free and symmetric (and hence the $S$ matrix is unitary). Application of this method to an exactly soluble two-channel model problem shows that our new approach gives much better results than the other standard variational principles.