  We calculate the $c\bar{b}$ mass spectrum, the splitting values and some
other properties in the framework of the semi-relativistic equation by applying
the shifted large-N expansion technique. We use seven different central
potentials together with an improved QCD-motivated interquark potentials
calculated to two loops in the modified minimal-subtraction $% (\bar{MS}) $
scheme. The parameters of these potentials are fitted to generate the
semi-relativistic bound states of $ c\bar{b}$ quarkonium system in close
conformity with the experimental and the present available calculated
center-of-gravity (c.o.g.) data. Calculations of the energy bound states are
carried out up to third order. Our results are in excellent fit with the
results of the other works.
