Variational studies of ${\mathit{D}}^0$ and ${\mathit{D}}^{\mathrm{-}}$ centers in magnetic fields in bulk crystals and in parabolic quantum wells

A linear combination of a few Gaussian functions of variable widths and anisotropy was used as a trial function for ${\mathit{D}}^0$ centers in bulk crystals and in parabolic quantum wells in the presence of a magnetic field. The same types of functions with an additional correlation factor were then used for ${\mathit{D}}^{\mathrm{-}}$ ions in the bulk and in parabolic quantum wells. All integrals including the electron-electron interaction were calculated analytically. The results obtained for the bulk are very accurate for ${\mathit{D}}^0$ centers and quite close to the experimental data for ${\mathit{D}}^{\mathrm{-}}$ ions in GaAs. The impurities in parabolic quantum wells were not yet experimentally investigated but the present results indicate that even in the case of a uniform spatial distribution they should lead to well-defined infrared absorption maxima.