Relativistic treatment of alkaline earth dimers in the presence of non-central molecular potential in N-dimensions

Highlights: • Relativistic vibrational transition frequencies provide excellent agreement with RKR and IPA experimental values. • Pekeris approximation for alkaline earth dimers is valid around the equilibrium distance. • Insight into the surface plots of alkaline earth molecules for non-central Morse potential. • The relativistic treatment is more effective in low vibrational states. Within the framework of relativistic theory, N-dimensional non-central Morse potential as anharmonic model is considered thoroughly to describe the internuclear motion of alkaline earth dimers in the different electronic states. We illustrate the surface plots of alkaline earth dimers to examine the effect of angular potential, due to existence of molecular systems in which spherical symmetry disappears. Also, the contribution of angle dependent interaction to the relativistic energy spectra has been investigated in N-dimensions. We determine the relativistic vibrational transition frequencies in the lower vibrational states for the $X^1{\Sigma }_g^{+}$ ground state of ²⁴${\mathrm{Mg}}_2,{}^{40}{\mathrm{Ca}}_2,{}^{24}\mathrm{Mg}{}^{40}\mathrm{Ca}$ and $A^1{\Sigma }_u^{+}$ excited state of ${}^{88}{\mathrm{Sr}}_2$ alkaline earth diatomic molecules. The theoretical results have been compared with Rydberg-Klein-Rees (RKR) and the inverted perturbation approach (IPA) experimental data. We also discussed the validity of Pekeris approximation around the equilibrium distance as well as the repulsive and attractive regions for alkaline earth dimers.