Coulomb off-shell T-matrix and its Haar scalet projection

Abstract

Several new analytical forms for the off-the-energy-shell transition matrix are presented which, in some cases, have hypergeometric functions appearing in the expressions for them. The scale of deviation of the Coulomb T-matrix from the Coulomb potential is determined. The Coulomb T-matrix derived by Shastry et al (1970 Phys. Rev. A 1 1137) is corrected by an additional term. Further, the study derives the energy shell limit for the hypergeometric forms using the Padé approximation, in which these forms are compared to the limit of exact off-shell forms in the vicinity of the energy shell. Finally, wavelet theory and multiresolution analysis are employed to arrive at a new approximate form for the Coulomb off-shell T-matrix in the Haar scalet basis.