FORMAL SCATTERING THEORY AND THE COULOMB PROBLEM.
PITTSBURGH UNIV PA
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It is attempted to salvage the usual apparatus of formal scattering theory in the case when there is a Coulomb field present. For this purpose, the time dependent approach to formal scattering theory is here presented without the use of adiabatic switching. Asympototic limits are investigated with the help of the Riemann-Lebesgue lemma. For scattering by a regular potential, the usual golden rule and the Lippmann-Schwinger equation are obtained. The same formalism is applied to the case of the Coulomb potential, and is found to bypass the ambiguities and wrong factors which were encountered by a number of authors, and which are due to the anomalous behaviour of the Coulomb T-matrix on the energy shell. Other mathematical pathologies still remain in the Coulomb case, but these now take the form of infinite phase factors, and are presumbably fairly innocuous. Author