Representations of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>Matrix in Terms of Its Angular Momentum Poles

Abstract

The asymptotic distribution of poles of the nonrelativistic $S$ matrix for potential scattering in the complex angular momentum plane is investigated, and so is the nature of the pole trajectories near $E=0$. As a consequence of the behavior of the distant poles and of their residues the $S$ matrix is shown to be representable in the form of an infinite (Weierstrass-Hadamard) product as well as in the form of a (Mittag-Leffler) series of partial fractions.