Construction of the Barut-Girardello quasi coherent states for the Morse potential

The Morse oscillator (MO) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications in quantum mechanics to diatomic or polyatomic molecules, spectroscopy and so on. For this potential some kinds of coherent states (especially of the Klauder-Perelomov and Gazeau-Klauder kinds) have been constructed previously. In this paper we construct the coherent states of the Barut-Girardello kind (BG-CSs) for the MO potential, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi's and P-quasi distribution functions (for the mixed-thermal states) are also presented. Finally, we show that all obtained results for the BG-CSs of MO tend, in the harmonic limit, to the corresponding results for the coherent states of the one dimensional harmonic oscillator (CSs for the HO-1D).