Intensity distribution in the rotation-vibration spectrum of the OH molecule

Abstract

The rotation-vibration spectrum of OH has been observed byMeinel in the light of the night sky. For the purpose of establishing the mechanism leading to this emission calculations have been made of the intensity distribution in the vibration spectrum of a Morse oscillator equivalent to the OH molecule. On the assumption of a linear dipole moment variation an explicit formula for the transition probabilities is obtained and the numerical values are evaluated up toν=12. If the assumption is made that the OH molecules in the night sky are first formed in theν=9 level and then cascade down toν=0 an intensity distribution similar to the observed is found. The effect of a quadratic term in the dipole moment is also considered. The matrix elements of this quadratic term are evaluated up toν′=8 andν″= 3. By introducing these quadratic terms into the transition probabilities a fair quantitative agreement is obtained between observed and calculated relative intensities. Predictions are made for the intensities of the OH bands of theΔ ν= 1, 2, and 3 sequences which lie in the farther infrared not yet investigated in the night sky. A rough estimate of the number of OH molecules formed in the upper atmosphere in theν= 9 level per second and per cm2 column is 9×1011.