  The bottom-charmed meson spectrum is studied in this work via an effective
version of the Coulomb gauge QCD Hamiltonian. The Tamm-Dancoff approximation is
employed to estimate the energies of the low-lying and radial-excited $B_c$
states with quantum numbers $J^P = 0^{-}, 0^{+}, 1^{-}, 1^{+}, 2^{+}, 2^{-}$.
In particular, we analyze the effects of incorporating an effective transverse
hyperfine interaction and spin mixing. The Regge trajectories and hyperfine
splitting of both $S$- and $P$-wave states are also examined. The numerical
results are compared with available experimental data and theoretical
predictions of other models.
