Vibrational description of the LiAr molecule in its X2Σ+ and A2 Π 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-2 Sigma(+) and A(2)Pi 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 Z(q) = (e(-alpha(r-re)))(q) for a given state of Li (X-2 Sigma(+)) Ar and Li (A(2)Pi) Ar are proposed. As an application closed-form estimations for the value < r >(n) of Li (X-2 Sigma(+)) Ar and Li (A(2)Pi) Ar were derived using Jensen's inequality. This allows us to obtain several inequalities relating the radial expectation value < r >(n) of Li (X-2 Sigma(+)) Ar and Li (A(2)Pi) Ar at the logarithme of the expectation value of Z(q) = (e(-alpha(r-re)))(q). These obtained outcomes are compared to the published results, both theoretical and experimental, and show a good agreement.

Automated summary

In this work, the vibrational energy levels, kinetic energy, and potential energy of the LiAr molecule in different electronic states were studied using the Morse potential and so(2, 1) spectrum generating algebra approach. An algorithm for calculating the expectation value of Z(q) = (e(-alpha(r-re)))(q) for specific states of Li (X-2 Sigma(+)) Ar and Li (A(2)Pi) Ar was proposed. Closed-form estimations for the expectation value < r >(n) of Li (X-2 Sigma(+)) Ar and Li (A(2)Pi) Ar were derived using Jensen's inequality. The obtained results were compared to existing theoretical and experimental results, showing good agreement.