Einstein A coefficient, integrated band intensity, and population factors: application to the a [formula omitted] O 2 band

Abstract

Literature values of the Einstein A coefficient for spontaneous emission for the a 1Δ g→X 3Σ g − (0,0) band of O 2 differ by as much as a factor of 2. The corresponding integrated band intensity values found in the literature show maximum differences of a factor of 4. The reason for these differences is not only the spread in the measured absorption band intensities but also in the improper use of population factors relating the Einstein A value to the line intensity or integrated band intensity. Here, the relationships between the Einstein A coefficient for spontaneous emission and the integrated band intensity and line intensity are developed with application to the a 1Δ g←X 3Σ g − bands of O 2. These relationships serve to eliminate the previously demonstrated confusion about the proper use of the lower and upper state population factors, with some using a ratio of 3 : 1 and the others 3 : 2 . A slightly modified expression for the line intensity in terms of the integrated band intensity is proposed which corrects for some approximations used in earlier expressions. Finally, recommendations are made for the most accurate values of the electronic–vibrational Einstein A coefficient and integrated band intensity for the a 1Δ g(0)←X 3Σ g −(0) band of O 2.