ABSTRACT
The wavefunction for electron collisions with an N-electron atom is expanded in the form Ψ = ∑ i Θ i + ∑ j Φ j c j https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203746608/2f2626dc-8555-4899-8d1e-59e7f2e652dc/content/eq2107.tif"/>
where Θ i is an antisymmetrized product of an atomic eigenfunction times an orbital function θ i for the colliding electron; θ i contains a radial function Fi ; Φ j has the form of a bound state function for the (N+1)-electron problem. The condition is imposed that (P γ |F i ) = 0 if l γ = l i , where P γ is an atomic radial function and where l γ and l i are orbital angular momenta associated with P γ and F i ; this condition does not imply a restriction on Ψ so long as a suitable set of states Φ; 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 F i . The coefficients C j 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 F i and the coefficients C j .
