Resonance charge transfer between H(1 s ) and H + calculated by means of an approximation based on an expansion in molecular eigenfunctions

The cross-section for the process H + + H(1 s ) → H(1 s ) + H + has been calculated for proton energies between 1 and 50 keV by means of the perturbed stationary-state approximation, with allowance for momentum transfer effects. Allowance for momentum transfer is found to decrease the cross-section by 5% at 2 keV, by 16% at 5 keV and by 45% at 20 keV. For energies below about 20 keV, the calculations are within 5% of those of McCarroll (1961), who uses an approximation based on atomic eigenfunctions. The results are in satisfactory accord with the experimental data of Fite, Stebbings, Hummer & Brackmann (1960) in the lower part of the energy range covered (where capture into excited states is unimportant).

Equivalent functions: hybrids and Wannier functions

In the last two decades a family of closely related functions have been introduced for the solution of quantum-mechanical problems. In dealing with atomic and molecular systems Pauling (12) introduced in 1928 linear combinations of the eigenfunctions of a single atom, which were called hybrids. These have specific symmetry properties which were utilized by Kimball (6) to construct a group-theoretical method for their determination. More recently Lennard-Jones (8) defined linear combinations of molecular eigenfunctions which he called equivalent orbitals. These are formally similar to the hybrids and Lennard-Jones took over the Kimball method for their determination.