High Temperature Optical Spectra of Diatomic Molecules at Local Thermodynamic Equilibrium

Abstract

In the paper, several theoretical approaches to the determination of the reduced absorption and emission coefficients under local thermodynamic equilibrium conditions were exposed and discussed. The full quantum-mechanical procedure based on the Fourier grid Hamiltonian method was numerically robust but time consuming. In that method, all transitions between the bound, free, and quasi-bound states were treated as bound–bound transitions. The semi-classical method assumed continuous energies of ro-vibrational states, so it did not give the ro-vibrational structure of the molecular bands. That approach neglected the effects of turning points but agreed with the averaged-out quantum-mechanical spectra and it was computer time efficient. In the semi-quantum approximation, summing over the rotational quantum number J was done analytically using the classical Franck–Condon principle and the stationary–phase approximation and its consumption of computer time was lower by a few orders of magnitude than the case of the full quantum-mechanical approach. The approximation described well the vibrational but not the rotational structure of the molecular bands. All the above methods were compared and discussed in the case of a visible and near infrared spectrum of LiHe, Li2, and Cs2 molecules in the high temperature range.