Stability analysis of the solution of the Dirac equation for the vibrational energies of the SiF+ molecule

Abstract

Analytical solutions of the Dirac equation with the spin symmetry in higher spatial dimensions have been explored for the improved Manning-Rosen potential energy model. We present the bound-state energy equation and the corresponding upper and lower radial wave functions. It has been found that the behavior of the higher-dimensional relativistic vibrational energies remains similar to that of the three-dimensional molecular system for the $ X^{1}\Sigma^{+}$ state of the SiF+ molecule. This symmetry phenomenon will break upon the critical point through which the system undergoes a phase transition from a stable to an unstable state.