Abstract
The variable-phase approach is applied to scattering and bound states in screened Coulomb potentials in two and three dimensions. The degree of ionisation for the electron—hole plasma is calculated taking into account scattering in the continuum. A two-dimensional formulation of Levinson's theorem is used for bound-state counting and a simple relationship between the screening length and the number of bound states is found for an attractive Coulomb potential screened by a two-dimensional electron gas.
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