This work was done while the author was a guest scientist conducting research through the National Research Council-NASA Research Associateship Program. Cornputer costs were funded by NASA-RTOP Grant No. 681-170-10-01-08.
Physical Review A
Fourier transformations, Coulomb functions, Feynman integrals, Orthogonalization methods, Atomic orbitals
The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.
Straton, Jack C. "Fourier transform of the multicenter product of 1s hydrogenic orbitals and Coulomb or Yukawa potentials and the analytically reduced form for subsequent integrals that include plane waves." Physical Review A 39.10 (1989): 5062. DOI: http://dx.doi.org/10.1103/PhysRevA.39.5062