Calculation of the photoelectron orbitals

To obtain the final state wavefunctions needed in evaluating the photoelectron matrix elements, we assume a frozen-core Hartree-Fock model in which the core orbitals are taken to be those of the ion for both ionized and neutral electronic states. The photoelectron orbital, i2), is 

We use an iterative procedure, based on the Schwinger variational principle, to solve the Lippmann-Schwinger equation associated with Eq. (3.63) [250]. The procedure begins by approximating the static-exchange potential of the relaxed ion core by a separable form 

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