Using a variational procedure for a hydrogenic donor-impurity we have investigated the influence of an axial magnetic field and hydrostatic pressure in the binding energy and the impurity-related photoionization cross-section in 1D and 0D GaAs low dimensional systems. Our results are given as a function of the radius, the impurity position, the polarization of the photon, the applied magnetic field, the normalized photon energy, and the hydrostatic pressure. In order to describe the gamma-X mixing in the Ga1-xAl xAs layer, we use a phenomenological procedure to describe the variation of the potential barrier that confines the carriers in the GaAs layer. Our results agree with previous theoretical investigations in the limit of atmospheric pressure. We found that the binding energy and the photoionization cross-section depend on the size of the structures, the potential well height, the hydrostatic pressure, and the magnetic field.