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Vibrational description of the LiAr molecule in its X 2Σ+ and A 2Π electronic states in the framework of an algebraic model

In this work, the vibrational energy levels, the kinetic energy and the potential energy of the LiAr molecule in its X 2Σ+ and A 2Π electronic states are studied using the Morse potential and so(2, 1) spectrum generating algebra approach. An algorithm for the recursive evaluation of the expectation value of Zq=e−α(r−re)q for a given state of Li (X 2Σ+) Ar and Li (A 2Π) Ar are proposed. As an application closed-form estimations for the value rn of Li (X 2Σ+) Ar and Li (A 2Π) Ar were derived using Jensen’s inequality. This allows us to obtain several inequalities relating the radial expectation value rn of Li (X 2Σ+) Ar and Li (A 2Π) Ar at the logarithme of the expectation value of Zq=e−α(r−re)q . These obtained outcomes are compared to the published results, both theoretical and experimental, and show a good agreement.