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We reproduce masses of the self-conjugate and non-self-conjugate mesons inthe context of the spinless Salpeter equation taking into account therelativistic kinematics and the quark spins. The hyperfine splittings for the${\rm 2S}$ charmonium and ${\rm 1S}$ bottomonium are also calculated. Further,the pseudoscalar and vector decay constants of the $B_{c}$ meson and theunperturbed radial wave function at the origin are also calculated. We haveobtained a local equation with a complete relativistic corrections to a classof three attractive static interaction potentials of the general form$V(r)=-Ar^{-\beta}+\kappa r^{\beta}+V_{0},$ with $\beta =1,1/2,~3/4$ decomposedinto scalar and vector parts in the form $V_{V}(r)=-Ar^{-\beta}+(1-\epsilon)\kappa r^{\beta}$ and $V_{S}(r)=\epsilon \kappa r^{\beta}+V_{0};$ where $0\leq \epsilon \leq 1.$ We have used the shiftedlarge-N-expansion technique (SLNET) to solve the reduced equation for thescalar $(\epsilon =1),$ equal mixture of scalar-vector $(\epsilon =1/2),$ andvector $(\epsilon =0)$ confinement interaction kernels. The energy eigenvaluesare carried out up to the third order approximation.Comment: 35 page

MASS SPECTRA OF HEAVY QUARKONIA AND Bc DECAY CONSTANT FOR STATIC SCALAR-VECTOR INTERACTIONS WITH RELATIVISTIC KINEMATICS

MASS SPECTRA OF HEAVY QUARKONIA AND B_c DECAY CONSTANT FOR STATIC SCALAR-VECTOR INTERACTIONS WITH RELATIVISTIC KINEMATICS