By David Bates, Benjamin Bederson
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Additional info for Advances in Atomic and Molecular Physics, Vol. 19
C. APPROXIMATETREATMENTS OF AO-CC EQUATIONS The system of diabatic equations (78) or (79) may be used for description of the charge-exchangeproblem in the intermediateenergy region, provided the wave functions ti) and l j ) contain translational phase factors and are appropriately orthogonalized, in which case the unitarity of the S-matrix is preserved. , the coupled system (79)], then the continuum states of the electron must also be included in the basis. Only for the one-center expansions is the system of coupled equations Hermitian (Polvkktov and Presnyakov, 1968).
More recently, a number of calculations including translational factors of different kinds have been performed and a list of those which have basis sets of adequate size is shown in Table I. Comparison with experiments (where these exist) suggests that the MO expansion method is accurate, at least for total capture cross sections for velocities ofat least up to = 1, good agreement is obtained for 2 = 2 and 2 = 6, but only fair agreement for Z = 3 (illustrated in Fig. 2), perhaps because only a limited basis of 6 terms was used (Kimura and Thorson, 1981b).
Both main objectives can be achieved by taking as the expansion functions members of some complete set of discrete functions and attempting to increase the size of the basis set to convergence. Among such functions are Gaussian (Dose and Semini, 1974) and Sturmians (Gallaher and Wilets, 1968; Shakeshaft, 1976; Winter, 1982). In order to allow for all the important discrete and continuum channels, the size of the basis set can become unmanageably large as u increases, and since a single center expansion is formally complete and numerically easy to use, it might be questioned whether results could be obtained by representing the wave function by a very large single center basis, obtaining charge-exchange cross sections from an integral expression.
Advances in Atomic and Molecular Physics, Vol. 19 by David Bates, Benjamin Bederson