Both the variational approach and the method of separable expansion have proved to be very useful for the solution of scattering equations. Connections are established between these two approaches. It is shown that an underlying variational principle is responsible for the good convergence obtained with the method of separable expansions. It is pointed out that a proper choice of expansion functions is essential for the rapid convergence of the method of separable expansion. Several types of separable expansions are tested numerically for the Reid ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$ soft-core potential. It is shown that with proper choices of expansion functions these separable expansions yield more rapid convergence than those obtained previously in other studies of separable expansions. In the case of the three-body scattering equations the usual separable expansions are shown to follow from the general expansion schemes studied here with special choices of expansion functions.

• Received 9 March 1987

DOI:https://doi.org/10.1103/PhysRevC.36.1275