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The radial Schr\"odinger equation for a modified Coulomb field is separated into two first-order equations for a "phase" function and an "amplitude" function which vary only in the non-Coulomb region r<r₀. At r=r₀, these functions are related to the mixing parameter and normalization constant of quantum-defect theory. Integrals over the range [0,r₀] give the scattering phase shift and the wave function's amplitude near the nucleus. Phase shifts for negative energies serve to calculate the discrete eigenvalues of an atom or positive ion. A numerical procedure for this approach is outlined.
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Dehmer et al. (1970) studied this question.
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