  We propose a CPT-even and Lorentz-violating dimension-five nonminimal
coupling between fermionic and gauge fields, involving the CPT-even and
Lorentz-violating gauge tensor of the Standard-Model Extension. This nonminimal
coupling modifies the nonrelativistic regime of Dirac particles, inducing new
effects such as an electric-Zeeman-like spectrum splitting and an
anomalous-like contribution to the electron magnetic moment. These new effects
allow to constrain the magnitude of this nonminimal coupling in 1 part in
$10^{16}.$
