Partial Wave Expansion

Abstract

Especially at low energies it is advantageous to expand in- and outgoing particle waves into partial waves, i.e. sums over asymptotic scattering states for each orbital angular momentum. Such an expansion, at least for short-range forces such as the hadronic nuclear force, can be truncated after few partial waves. For particles with spin and their polarization the method is equally useful by coupling orbital angular momenta with spin states to conserved total-angular momentum states and forming polarization obervables. The universal formulas by Welton and Heiss are obtained by applying Racah algebra, and the point-Coulomb interaction is taken into account.