From the form of the exact ground-state wavefunction psi , of a helium-like atom, the dependence on the first power of the interparticle coordinates r 1, r2 and r12 is easily obtained. The authors construct a simple model wavefunction phi that (a) agrees with the exact wavefunction to first order in r1, r2 and r12, (b) is finite everywhere, is normalisable and satisfies the derivative cusp conditions as r1, r2 or r12 to 0, and (c) satisfies the virial theorem. If the exact wavefunction psi is written psi = phi chi , then chi satisfies a transformed Schrodinger equation, H' chi =E chi where H' has no poles at the electron-nucleus or electron-electron coalescences. It is shown, by a linear transformation of the interparticle coordinates, that all integrals required for the evaluation of the energy reduce to products of gamma functions.
|Number of pages||11|
|Journal||Journal of Physics B: Atomic and Molecular Physics|
|Publication status||Published - 1 Dec 1986|