Multiple scattering in the Compton effect. IV. Operator formalism for nonstationary electrons

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Abstract
The problem of correcting experimental Compton profiles for the effects of multiple scattering is shown to be equivalent to obtaining the solution to a nonlinear operator equation. Two methods of solving the equation are presented. One, analogous to the Newton-Raphson technique for algebraic equations, leads to a new solution to the problem. Another more efficient approach, based upon the idea of successive approximation, is seen to be equivalent to the method of Felsteiner, Pattison et al., though it fails to converge if the fraction of multiple scattering is too great. The double-scattering operator is derived and examined in some detail. Extensions to higher-order scattering are indicated.