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.

Lifetime and predissociation yield of N214 b 1Πu(v=1)

“…Therefore, we performed an uncoupled, rotationless ''adiabatic'' calculation of the bϪa (1,vЉ) oscillator strengths, employing RydbergKlein-Rees potential-energy curves for the b and a states, 35 together with an R-dependent electronic transition moment assumed to be the same as that applying to the isoconfigurational C 3 ⌸ u -B 3 ⌸ g transition. 36 The b -a fluorescence is found to be dominated by the ͑1,0͒ transition, with significant contributions only for vЉϽ7. The total transition rate, computed according to the second term in Eq.…”

Vibrational kinetics of air plasmas induced by sprites

“…The radiative transitions probabilities of 1PN2 included (see Table 5) are all those listed in Gilmore et al [1992] with transition probabilities ≥10 2 s −1 .…”

The 762 nm emissions of sprites

“…Figure 4b presents the number density of the O 2 (b 1 S g + ) substate, which is the upper state of the O 2 atm band. Figure 4c shows the temporal evolution of the related chemical reactions that lead to the production and the loss of O 2 (b 1 S g + ), which are indicated by Based on a private discussion [Liu and Pasko, 2005], the middle value of Einstein coefficient for major vibrational levels of upper state of band system [Gilmore et al, 1992, Figure 4c. These reactions are all resulting from the driving electric field as shown in Figure 4 or from the active species left behind in the streamer head and the streamer body regions after 1 ms.…”