Systematic Approximations for the Single-Channel Scattering Amplitude

The scattering amplitude for two-particle single-channel scattering may be computed by inverting a Hilbert-space operator 1-K, where K is compleely continuous and depends on the real energy as a parameter. This inversion can always be accomplished by obtaining a finite number of eigenvalues and eigen-functions of K together with a modified Born expansion which is guaranteed to converge. Another method consists in the inversion of a finite matrix, the elements of which are computed by a convergent perturbation series.