Intensities of rotational lines in first overtone bands for axially symmetric molecules of the group C3 v

Abstract

The interaction of vibration and rotation is considered in the computation of the intensities of rotational lines in the first overtone bands of axially symmetric molecules of the group C 3 v . The calculation utilizes the contact transformation method through first order of approximation as outlines by Hanson and Nielsen. General formulas for the intensities of the lines in the first overtone bands 2 ν n and 2 ν m are obtained, where n and m denote normal modes of species A 1 and E, respectively. It is found that to this order of approximation the usual selection rules Δ J = 0, ±1 and Δ K = 0 are observed for the parallel overtone band 2 ν n . For the overtone band 2 ν m , the selection rules are more complicated, being Δ J = 0, ±1; Δ l m = 0 and Δ K = 0, Δ l m = ±2 and ΔK = ⊣1 , or Δ l m = ±2 and Δ K = ±2.