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Two physically important potentials (Manning-Rosen and P\"oschl-Teller) areconsidered for the ro-vibrational energy in diatomic molecules. An improved newapproximation is invoked for the centrifugal term, which is then used for theirsolution within the Nikiforov-Uvarov framework. This employs a recentlyproposed scheme, which combines the two widely used Greene-Aldrich andPekeris-type approximations. Thus, approximate analytical expressions arederived for eigenvalues and eigenfunctions. The energies are examined withrespect to two approximation parameters, $\lambda$ and $\nu$. The originalapproximations are recovered for certain specials values of these twoparameters. This offers a simple effective scheme for these and other relevantpotentials in quantum mechanics.

Ro-vibrational energy analysis of Manning-Rosen and P\"oschl-Teller potentials with a new improved approximation in the centrifugal term