Band nonparabolicity and central-cell corrections for ${\mathit{D}}^{\mathrm{-}}$ centers in GaAs quantum wells

A one-electron effective Hamiltonian, previously found to describe quite accurately quantum-well energy levels of both free electrons and donor electrons in magnetic fields, is generalized to account for localized two-electron centers. The two-electron effective Hamiltonian derived is applied to the problem of finding energies for optical transitions originating from the ground state of ${\mathit{D}}^{\mathrm{-}}$ centers in seven different quantum wells with widths ranging from 9.5 to 52.0 nm. Central-cell corrections for the ${\mathit{D}}^{\mathrm{-}}$ centers are included. Comparison with experiments in magnetic fields below 10 T gives agreement to within 2 ${\mathrm{cm}}^{\mathrm{-}1}$ for all well widths without any adjustable parameters.