Perturbation treatment of the molecular helium ion

Abstract

The binding energy of the /sup 1/Eu state of the molecular calculated by the method of distorted waves, the resonance approximation and of Seaton's version of the modified Born 3 x 3 cross-section matrix involved in the electron impact excitation of the ground state of H atom to the 2s and 2p levels. The method of solution is that of atomic eigenstates expansion. Instead of the iterative technique used by others, the definite integral terms in the coupled radial differential equations are eliminated through some linear transformation of the radial functions, thus avoiding iteration of these equations. The accuracy of the numerical integration is tested by satisfying the equation of reciprocity and the equation of continuity of currents with an error-to-value ratio less than 1 per 1000 on the average; and the maximum of this ratio, except for a few cases, was kept below 5%. The results are in agreement with the results of an iterative technique. To evaluate the effect of the long range and the centrifugal potential, a simple perturbation theory is developed. Only the 2s yields 2p and the 2p yields 2p cross more » sections are reported. The 2p yields 2p cross section requires the solution of the sets of differential equations with different parities. Assuming the validity of the eigenstates expansion, it is found by comparison with the eigenstates expansion calculation that the Born approximation, despite its simplicity, gives meaningful results for low and closeto-the-threshold energies of the bombarding electrons. The effect of the exchange potentials on the cross sections is also investigated. Finally, an interesting structure of the 1s yields 2s excitation cross section above threshold is found. (auth) « less