Hartree-Fock Theory with Exchange Cutoff

A new Fock-type operator is defined which varies between the Hartree and the Hartree-Fock operator depending on a cutoff parameter in the exchange potential. The corresponding pseudo-Hartree-Fock equations require each orbital ${\phi }_i$ to behave asymptotically as $\exp [-{(-2\mathrm{}{\epsilon }_i)}^{\frac{1}{2}}r]$. Calculations are reported for the Ne atom.