Magnetic-dipole transitions are observed in molecular-beam studies of methane . It can be shown that all three laboratory-fixed components of the magnetic dipole moment operator are of species A1. Thus, magnetic dipole transitions between hyperfine components are rigorously forbidden unless υr nΓ′ × υr nΓ″ contains A1.
Figure 5 illustrates a number of electric-dipole rovibrationally allowed transitions observed in methane. Solid vertical lines indicate strongly allowed vibration-rotation transitions of the υ3 fundamental band [43-45]. Dashed lines indicate weakly allowed vibration-rotation transitions . Dotted lines indicate very weakly allowed pure rotational transitions seen in double-resonance experiments [47-49].
The strong transition F1(2)-F2(2) nearly coincides with the 3.39 µm line of the He-Ne laser. Shimoda suggested  using this near coincidence and the Lamb-dip effect to achieve extreme stabilization [51-54] of the laser line. In such experiments Hall and Bordé  have resolved the hyperfine structure [25, 56] of this methane transition and have convincing line-shape evidence for the observation of photon-recoil effects .
We now turn to two brief examples of the construction of individual interaction terms for the Hamiltonian operator. These constructions are best carried out using molecule-fixed components of the various vector operators, since molecule-fixed components are automatically invariant to those operations which correspond simply to rotating the molecule in space without permuting any identical particles and which are associated with changes in the m quantum number (see Sec. 15).
Consider first a vibration-rotation Coriolis operator which is to be bilinear in the (molecule-fixed) components of L and J. Since L and J both belong to the F1 representation, and since F1 × F1 contains the A1 representation only once, there is only one bilinear form allowed in the Hamiltonian. It can be seen from the matrices in Table 3 that JxLx + JyLy + JzLz is the desired operator.
Very similar considerations apply to the construction of the proton-spin - overall-rotation interaction operator , except that Table 19 contains two proton-spin vector operators belonging to the species F1. Thus there are two spin-rotation operators, having the forms: JxIx + JyIy + JzIz and Jx(I1y + I2y - I3y - I4y - I1z + I2z + I3z - I4z) + Jy(I1x + I2x - I3x - I4x + I1z - I2z + I3z - I4z) + Jz(- I1x + I2x + I3x - I4x + I1y - I2y + I3y - I4y), respectively.