Intensities of rotational lines in combination bands for axially symmetric molecules of the group C 3v

Abstract

The interaction of vibration and rotation is considered in the computation of the intensities of rotational lines in the combination bands of axially symmetric molecules of the group C 3 v . The calculation utilizes the contact transformation method through first order of approximation as outlined by Hanson and Nielsen. General formulas for the intensities of the lines in the parallel combination band ( ν n + ν n′ ) and perpendicular combination band ( ν m + ν n ) are obtained. 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 combination band. For the perpendicular combination band the selection rules are more complicated, being Δ J = 0, ±1, Δ l m = +1 and Δ K = +1 or −2, Δ l m = −1 and Δ K = −1 or +2, Δ l m = ±3 and Δ K = 0. Specific intensity formulas are then given for the ( ν 1 + ν 3) parallel and ( ν 2 + ν 3) perpendicular combination bands of ammonia.