Homonuclear diatomic molecules show neither pure vibrational nor pure rotational spectra. However, as the absorption of a photon requires the molecule to take up one unit of angular momentum, vibrational transitions are accompanied by a change in rotational state, which is subject to the same selection rules as for the pure rotational spectrum. For a molecule in a Σ Σ state, the transitions between two vibration-rotation (or rovibrational) levels ( v , ℑ ℑ ) and ( v ′ , ℑ ℑ ′ ) , with vibrational quantum numbers v and v ′ = v + 1 , fall into two sets according to whether Δ Δ ℑ ℑ = + 1 or Δ Δ ℑ ℑ = − − 1 . The set corresponding to Δ Δ ℑ ℑ = + 1 is called the R branch. The corresponding frequencies are given by: ℏ ℏ ω ω R = E ( v + 1 , ℑ ℑ + 1 ) − − E ( v , ℑ ℑ ) = 2 B ( ℑ ℑ + 1 ) + ℏ ℏ ω ω 0 ; ℑ ℑ = 0 , 1 , 2 , . . . . . .