Abstract
We solve the Klein-Gordon equation with the improved Rosen-Morse empirical potential energy model. The bound-state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $3^{3}\Sigma_{g}^{+}$ state of the Cs2 molecule have been computed by using the improved Rosen-Morse potential model. The relativistic vibrational transition frequencies are in good agreement with the experimental RKR values and DPF values.
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