Rotational-Vibrational Structure of CO₂

Abstract

Laser action in any CO₂ system occurs between low-lying vibrational-rotati-onal levels of the ground electronic state. Knowledge of the rotational-vibrational structure, the corresponding energy levels, and their transition probabilities is essential for the understanding of the laser process. For a determination of these molecular properties it is necessary to calculate the wave functions. The exact solution of the wave equation describing the motion of the individual atoms of a molecule (relative to the center of mass) is a difficult problem, because molecules have, as a rule, a rather complex structure. However, the empirical results of molecular spectroscopy on CO₂ as, for instance, obtained by Dennison [2.1], show that the energy values bear a simple relationship to one another, so that the energy of the molecule can be conveniently considered to be made up of two parts, called, respectively, the vibrational energy and the rotational energy. This permits a simpler solution, because the spectroscopic data suggest that it is possible to treat the vibration and rotation of the molecule quite separately and then to combine the results of the two calculations to present the behaviour of the three atoms in the CO₂ molecule. Thus we neglect any perturbation of the vibrational state due to the rotation of the molecule, and therefore the wave functions are products of rotational and vibrational wave functions.