Einstein A coefficients, oscillator strengths and lifetimes have been calculated by an asymptotic expansion method, introduced by Chang and Karplus, for the N 2 , B In.-A 3.I: (first positive), C 'nu-+B lJI g (second positive), W 3 Llu+2B In. (Wu-Benesch) and B 03 .I';-+B In. (infrared afterglow) band systems, using theoretical electronic transition moments, Re(r), of Yeager and McKoy. Whenever possible, comparison has been made with those calculated from the electric dipole moment functions, Re(F), which are functions of r centroids, obtained from band intensity or lifetime measurements. Excellent agreement has been obtained in the case of the second positive band system of molecular nitrogen. However, for ail other cases, conventional Re(f) functions are found to be superior to the theoretical Re(r) functions of Yeager and McKoy.
An asymptotic expansion method has been used to calculate the Morse matrix elements for the vibration-rotation transition. A general expression has been derived for the quartic matrix elements, which can be reduced to the expressions for the cubic, quadratic, and linear matrix elements. The results agree extremely well with those given by the factorization method outlined by Badawi et al., and are similar to those given by Coquant et al., who used quite complicated and lengthy equations based on the Dunham potential. Earlier works to calculate the electronic transition probability parameters utilizing the above mentioned asymptotic expansion technique have also been extended and modified.
Using an asymptotic expansion, an equation has been derived for the calculation of matrix elements involved in the vibrational transition probabilities for a Morse oscillator. Resulting matrix elements and vibrational probabilities for the OH molecule agree well with those given by Heaps and Herzberg.
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