Binding energy of on-axis hydrogenic and nonhydrogenic donors in a GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum-well wire of circular cross section

In the present work we calculate, by a variational approach, the binding energy of an on-axis hydrogenic donor as a function of the radius of the quantum-well wire. In addition, we also discuss the screening of a (point) donor ion by the valence electrons of GaAs and calculate, again by a variational approach, the binding energy of an on-axis nonhydrogenic donor as a function of the radius of the quantum-well wire. In these calculations we use a wave function suggested a few years ago by Lee and Spector.