  The influence of a Lorentz-violating fixed background on fermions is
considered by means of a torsion-free non-minimal coupling. The
non-relativistic regime is assessed and the Lorentz-violating Hamiltonian is
determined. The effect of this Hamiltonian on the hydrogen spectrum is
determined to first-order evaluation (in the absence of external magnetic
field), revealing that there appear some energy shifts that modify the fine
structure of the spectrum. In the case the non-minimal coupling is
torsion-like, no first order correction shows up in the absence of an external
field; in the presence of an external field, a secondary Zeeman effect is
implied. Such effects are then used to set up stringent bounds on the
parameters of the model.
