Effective-Range Approximation Based on Regge Poles

Abstract

During the last year, a new kind of effective-range approximation1,2,3 based on singularities in the complex angular momentum plane has given interesting results in several problems concerning low-energy scattering. The expression “effective-range approximation” is used here in the customary sense for the S-matrix theory, namely, an approximation based on the idea that in a limited region of energies the scattering amplitude may be reasonably well parameterized in terms of a few nearby singularities. It is well known that such an approximation in terms of singularities in the complex energy or momentum plane provides a very good description of low-energy scattering of, for example, the n-p system. We shall see in what follows how singularities in the complex angular momentum plane can also be used for the same purpose.