How the alternating degeneracy in rotational Raman spectra of CO₂ and C₂H₂ reveals the vibrational temperature

The contribution of higher vibrational levels to the rotational spectrum of linear polyatomic molecules with a center of symmetry (CO₂ and C₂H₂) is assessed. An apparent nuclear degeneracy is analytically formulated by vibrational averaging and compared to numerical averaging over vibrational levels. It enables inferring the vibrational temperature of the bending and asymmetric stretching modes from the ratio of even to odd peaks in the rotational Raman spectrum. The contribution from higher vibrational levels is already observable at room temperature as g˜_e/o=0.96/0.04 for CO₂ and g˜_e/o=1.16/2.84 for C₂H₂. The use of the apparent degeneracy to account for higher vibrational levels is demonstrated on spectra measured for a CO₂ microwave plasma in the temperature range of 300-3500 K, and shown to be valid up to 1500 K.