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

Abstract

In this work, the vibrational energy levels, the kinetic energy and the potential energy of the LiAr molecule in its X2Σ+ and A2Π 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(X2Σ+)Ar and Li(A2Π)Ar are proposed. As an application closed-form estimations for the value 〈r〉n of Li(X2Σ+)Ar and Li(A2Π)Ar were derived using Jensen’s inequality. This allows us to obtain several inequalities relating the radial expectation value 〈r〉n of Li(X2Σ+ )Ar and Li(A2Π)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.