Modified Lippmann-Schwinger equations for two-body scattering theory with long-range interactions

Abstract

Two kinds of modified Lippmann-Schwinger equations are derived for the case of long-range potentials. The equations of the first kind are homogeneous and are a direct result of the fact that the standard Lippmann-Schwinger equations do not hold when long-range forces are present. The equations of the second kind depend on the existence of an operator Z such that W± = s-lim exp (iHt)Z exp(−iH0t). A general recipe for constructing Z is given and its computation is carried through for the case of asymptotically Coulombic potentials. The resulting equations are used to compare the long-range theory with the theory with a space cutoff (i.e., screened potential) in the limit in which that cutoff is being removed.