B_c meson spectrum and hyperfine splittings in theshifted large-N-expansion technique

In the framework of potential models for heavy quarkonium, we compute the mass spectrum of the bottom-charmed $B_{c}$ meson system and spin-dependent splittings from the Schr\"{o}dinger equation using the shifted-large-N expansion technique. The masses of the lightest vector $B_{c}^{+}$ and pseudoscalar $B_{c}$ states as well as the higher states below the threshold are estimated. Our predicted result for the ground state energy is $% 6253_{-6}^{+15}$ $MeV$ and are generally in exact agreement with earlier calculations. Calculations of the Schr\"{o}dinger energy eigenvalues are carried out up to third order of the energy series. The parameters of each potential are adjusted to obtain best agreement with the experimental spin-averaged data (SAD). Our findings are compared with the observed data and with the numerical results obtained by other numerical methods.