Computer programs for the calculation of electron-atom collision cross sections. I. General formulation

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Abstract
The wavefunction for electron collisions with an N-electron atom is expanded in the form Psi = Sigma i Theta i+ Sigma j Phi jcj where Theta i is an antisymmetrized product of an atomic eigenfunction times an orbital function theta i for the colliding electron; theta i contains a radial function Fi; Phi j has the form of a bound state function for the (N+1)-electron problem. The condition is imposed that (Pgamma mod Fi)=0 if lgamma =li, where Pgamma is an atomic radial function and where lgamma and li are orbital angular momenta associated with Pgamma and Fi; this condition does not imply a restriction on Psi so long as a suitable set of states Phi j is included. The variational principle is discussed and two approximations are described: (i) The distorted wave (DW) approximation is valid when the coupling is not too strong. Particular attention is paid to the normalization of the DW functions Fi. The coefficients cj are determined using the variational principle. (ii) The variational principle is used to obtain a set of coupled integro-differential (ID) equations for the determination of the functions Fi and the coefficients cj.

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