  The corrections to the $E_2^*$ energy level of hydrogenic impurities in
semiconductors with wurtzite crystal structure are calculated using first-order
perturbation theory in the envelope-function approximation. We consider the
intrinsic (Dresselhaus) spin-orbit effective Hamiltonian in the conduction band
and compare its effects to the renormalized extrinsic (Rashba) spin-orbit
interaction which is analogous to the spin-orbit interaction in the bare
hydrogen atom. In order to evaluate the extrinsic spin-orbit interaction we
obtain the renormalized coupling constant $\lambda^*$ for wurtzite
semiconductors from 8-band Kane theory. We apply our theory to four
representative binary semiconductors with wurtzite crystal structure, namely,
GaN, ZnO, InN and AlN, and discuss the relative strength of the effects of the
intrinsic and extrinsic spin-orbit contributions.
