Franck–Condon Factors, r-Centroids, Electronic Transition Moments, and Einstein Coefficients for Many Nitrogen and Oxygen Band Systems

Abstract

Air fluorescence models require accurate Franck–Condon factors and Einstein coefficients for analyzing the intensities of N2, N+2, and O+2 emissions produced by electron bombardment of air, such as in the aurora, high-altitude nuclear explosions, and rocket-borne electron gun experiments. In our previous report, improved vibrational and rotational constants based on the latest available spectroscopic measurements for several excited and ionic states important in air fluorescence modeling were derived. These constants have been used in the present work to calculate band origins, Franck–Condon factors, and r-centroids for many band systems of nitrogen and oxygen. These results, together with electronic transition moments obtained from published papers or derived here from published emission data and measured upper-state lifetimes, have been used to compute Einstein coefficients by the r-centroid method. Einstein coefficients by integration of the product of the electronic transition moment function and vibrational wavefunctions have also been computed for comparison. For band systems involving ‘‘perturbed’’ electronic states, Einstein coefficients have been derived by simply normalizing published emission data to measured upper-state lifetimes. In this report, tables of band origin wave-lengths and wavenumbers, Franck–Condon factors, r-centroids, electronic transition moments, and Einstein coefficients are presented for 17 N2, N+2, and O+2 band systems. Plots of most of the electronic transition moment functions used in these calculations are also given. In addition, tables of Franck–Condon factors only are presented for 16 other band systems of nitrogen and oxygen, and tables of band wavelengths and Einstein coefficients are presented for 3 band systems having ‘‘perturbed’’ upper states.