  In this work, we study higher $B_c$ mesons to the $L=S$, $P$, $D$, $F$, $G$
multiplets using the Cornell potential model, which takes account of the
screening effect. The calculated mass spectra of $B_c$ states are in reasonable
agreement with the present experimental data. Based on the spectroscopy,
partial widths of all allowed radiative transitions and strong decays of each
state are also evaluated by applying our numerical wave functions. Comparing
our results with the former results, we point out the difference among various
models and derive new conclusions obtained in this paper. Our theoretical
results are valuable for searching more $B_c$ mesons in experiments.
