An analytical perturbation treatment of the rotating Morse oscillator

Abstract

An analytical perturbation treatment to determine the energy levels of the rotating Morse oscillator is proposed. The method is based on making an exponential expansion of the rotational term about a suitably chosen internuclear distance rb, and on solving the equations obtained in this way using analytic perturbation theory. The value of the parameter rb is chosen as the minimum of the Morse–Pekeris oscillator or as the minimum of the third-order Morse–Pekeris expansion, both of which can be evaluated analytically. The resulting zero-order system is then a modified version of the original Morse–Pekeris oscillator model. The perturbation treatment is carried out using the hypervirial perturbation method and by rearranging the energy corrections in terms of inverse powers of dissociation energy of the zero-order system. The accuracy of the analytical expression derived for the energy levels of the rotating Morse oscillator is checked by making a numerical application to the H2 molecule.

Rotating Morse wave packet dynamics of diatomic molecule

“…These semi-analytical models are based on the idea of building up Morse potentials with parameters dependent on the rotational quantum number, which represent adequately the effective potential curves of the rotating Morse oscillator. There are various other numerical and proposed methods to study the rotating Morse potential [5,6,7,8,9,10,11,12,13]. These studies are very useful to obtain more accurate energy eigen values.…”