Limiting Forms of the Screened Coulomb T Matrix

Abstract

In the complex energy plane, the pure Coulomb T matrix possesses branch points which would not appear if the force were properly defined. This is demonstrated by a study of the screened Coulomb T matrix in the limit as the screening radius R tends to infinity. No branch points develop if the proper order of limiting processes is observed and the results agree with previous calculations; however, the T matrix is discontinuous in the limit. A formula for the screened Coulomb T matrix is given which is valid to order 1/R for all energies.