The role of one electron orbitals in Many Body Theory and the Generalized Sudden Approximation is reviewed. Various approximations to the exact Hartree Fock static exchange potentials are discussed and a new, screened exchange potential is derived. Phase shifts for the elastic scattering of electrons from Helium, Neon and Argon and Photoionization cross sections for Lithium, Carbon, Oxygen, Neon and Argon were calculated and compared with the exact static exchange results. The screened exchange potential is the best approximation for Photoionization and the Hara exchange potential is the best for Scattering. Ground state eigenvalues, ionization energies and oscillator strengths have been calculated for the 2t2-la1 transition in Methane. The calculations were carried out using the Xalpha Multiple Scattering Method. The ground state eigenvalues were correctly predicted and the oscillator strengths lie within experimental limits.