Ground state energy for confined diatomic molecules: case of Morse interaction

Abstract

In this work, we study the cavity size effect on the eigen-energies of one-dimensional Schroedinger equation for certain diatomic molecules governed by Morse potential interaction confined in the cavity. To avoid the dissociation of the molecule, we have realised the confinement by introducing two barriers on both sides of the minimum of the potential: the first, at the left, is fixed at $x_L=-ln2/\alpha$ and the second at the right i.e. $x_R={\lambda }_i=-ln2/\alpha +{\gamma }_i{r}_e$ where ${\gamma }_i$ is a parameter that allows us to vary the size of the cavity. It turns out that the confinement gives rise to additional energy levels and that the number of these levels increases with the size of the cavity (i.e. by increasing ${\gamma }_i$ or by decreasing the confinement). We used Green's function approach and reported our results on ${\mathrm{H}}_2,\mathrm{HCl}$ and $\mathrm{LiH}$ molecules.

GRAPHICAL ABSTRACT

KEYWORDS:

• Diatomic molecules
• confined molecules
• Morse potential
• eigen-energies
• cavity

PACS CLASSIFICATIONS:

• 33.15.Dj
• 33.15.Hp
• 33.20.Xx
• 34.20.Cf

Acknowledgements

Authors would like to thank Prof. Mansour Abdelouahab, head of Mathematics Department at University of El-Oued (Algeria). They also thank all referees for their precious comments. We have accomplished this work in part at Hamma Lakhdar University of El-oued (Algeria) and in the other part at Physics department at Kasdi Merbah University of Ouargla (Algeria) without financial support. The only support was the use of the informatics tools of the laboratories to do our work. We also declare that all authors participate equally in the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

No funding has support this work, apart the logistic aid as computers and work desks from both universities.