  Electronic bound states around charged impurities in two-dimensional systems
with structural inversion asymmetry can be described in terms of a
two-dimensional hydrogen atom in the presence of a Rashba spin-orbit
interaction. Here, the energy levels of the bound electron are evaluated
numerically as a function of the spin-orbit interaction, and analytic
expressions for the weak and strong spin-orbit coupling limits are compared
with the numerical results. It is found that, besides the level splitting due
to the lack of inversion symmetry, the energy levels are lowered for
sufficiently strong spin-orbit coupling, indicating that the electron gets more
tightly bound to the ion as the spin-orbit interaction increases. Similarities
and differences with respect to the two-dimensional Fr\"ohlich polaron with
Rashba coupling are discussed.
