The conversion of nonlocal one-body operators into local ones: The   Slater potential revisited
  One-particle Schrodinger equations are considered, e.g., the Hartree--Fock equations, that contain a nonlocal operator, e.g., the Hartree--Fock exchange operator, where this operator depends on the one-particle density-matrix of a determinantal state. One-body nonlocal operators of this type are converted into approximate local potentials that depend on the kernel of the nonlocal operator and, also, the one-particle density matrix that, as mentioned above, the nonlocal operator also depends on. When the non-local operator is the exchange operator, the method yields the Slater potential. 
James P. Finley