D-dimensional energies for sodium dimer

Abstract

We solve the Schrödinger equation with the improved Tietz potential energy model in D spatial dimensions. The D-dimensional rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The rotation–vibrational energies for the A1∑u+ and C1Пu states of the Na2 molecule increase as D increases in the presence of a fixed vibrational quantum number and rotational quantum number. It is observed that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. We find that the D-dimensional scaling method resembles a translation transformation from the higher dimensions to the three dimensions.