Relativistic energies for diatomic molecule nucleus motions with the spin symmetry

• Solutions of the Dirac equation with the improved Manning–Rosen potential energy model are explored.
• Relativistic energies for the X1Σ+X1Σ+ state of SiF+ molecule with the spin symmetry have been computed.
• The impact of the relativistic effect of the nuclear motion on the vibrational energies has been observed.

The analytical solutions of the Dirac equation with the spin symmetry for the improved Manning–Rosen potential energy model have been explored. We present the bound state energy equation and the corresponding upper and lower radial wave functions. The degeneracy between the two states of the spin doublet for the nucleus motions of the X1Σ+X1Σ+ state of SiF+ molecule has been observed. When the vector potential is equal to the scalar potential, the relativistic effect of the nuclear motion leads to a little decrease in the vibrational energies, while to an increase in those if the vector potential is greater than the scalar potential.