A method has been devised to calculate the cross sections of inelastic electron-atom collisions under near-resonance conditions. This method (referred to as the method of resonance distortion) consists of solving the limiting exact-resonance problem as the zeroth-order approximation and using this solution to obtain the first-order solution by an iteration procedure, and is particularly suitable for treating optically allowed transitions produced by electron impact where the coupling between the initial and final states is strong and of long-range type. Application of this method has been made to a schematic model with an isotropic inverse-square interaction potential and to the problem of electron-atom collisions with $\mathrm{ns}\to \mathrm{np}$ transition. The general results indicate that (i) for weak coupling the collision strengths calculated by the resonance-distortion scheme reduce to those calculated by the method of distorted waves, (ii) the resonance-distortion method and Seaton's B'II method give nearly equal partial cross sections for large $l$, and (iii) at very low $l$, the B'II partial cross sections are substantially larger than those determined from the resonance-distortion method. The total cross sections for the $3s\to 3p$ transition in Na have been calculated by the resonance-distortion method for various incident electron energies, and the results show better agreement with experiment than do those of the Born approximation and of Seaton's version of the modified Born approximation.

• Received 3 September 1963

DOI:https://doi.org/10.1103/PhysRev.133.A947