Quantum defect theory. XI. Clarification of some aspects of the theory

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Abstract
The theory of Coulomb functions is reviewed for complex values of energy and angular momentum, particular attention being paid to the many-valued nature of some of the functions. The theory for the motion of an electron in the field of a positive ion is simplified by considering a model problem in which a finite system of coupled differential equations contains diagonal Coulomb potentials for an attractive charge Z, together with non-Coulomb potentials Uii'( rho ) where rho =Zr and r is the radial coordinate for the electron. The energy of the electron in channel i is ki2=-Z2/ kappa i2 which defines kappa i. In the simple model problem it is assumed that the potentials Uii'( rho ) are of finite range, Uii'( rho =0 for rho > rho 1 with rho 1< infinity . For rho > rho 1, the solutions of the coupled equations may then be equated to linear combinations of Coulomb functions.

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