8.2.2 Molecular oxygen

  

Figure: The rotational energy level diagram of molecular oxygen

Molecular oxygen, although homonuclear, hence with zero electric dipole moment, has a triplet electronic ground state, with two electrons paired with parallel spins. The resulting electronic spin couples efficiently with the magnetic fields caused by the end-over-end rotation of the molecule, yielding a ``large'' magnetic dipole moment, $\mu^{mag}$= 10^-20 emu. The magnetic dipole transitions of O₂ have intrinsic strengths $\sim10^{2-3}$ times weaker than the water transitions. O₂, however, is 10^2-3 times more abundant than H₂O, so that the atmospheric lines of the two species have comparable intensities.

The spin of 1 makes of the ground electronic state of O₂ a triplet state ($^3\Sigma$). N, the rotational angular momentum couples with S, the electronic spin, to give J the total angular momentum: N +S = J. The N$\cdot$S interaction (and the electronic angular momentum-electronic spin interaction L$\cdot$S) split each rotational level of rotational quantum number $N\geq1$ into three sublevels with total quantum numbers

$$J= N+1, J=N {\rm ~~~~and~~~~} J=N-1$$

the J= N+1 and J=N-1 sublevels lying below the J= N sublevel by approximately 119 (N+1)/(2N+3)GHz and 119/(2N-1)GHz, respectively ([Townes & Schawlow 1975] p.182). Note that the two identical ¹⁶O nuclei have spins equal to zero and obey the Bose-Einstein statistics; there are only odd N rotational levels in such a molecule.

The magnetic dipole transitions obey the rules $\Delta{N}= 0, \pm 2$ and $\Delta{J}= 0, \pm 1$. Transitions within the fine structure sublevels of a rotational level (i.e. $\Delta{N}= 0$) are thus allowed. The first such transition is the $(J,N)= 1,1\leftarrow0,1$ transition, which has a frequency of 118.75 GHz. The second, the $1,1\leftarrow2,1$ transition, has a frequency of 56.26 GHz. It is surrounded by a forest of other fine structure transitions with frequencies ranging from 53 GHz to 66 GHz. The first "true" rotational transition, the $N= 3\leftarrow 1$ transitions, have frequencies above 368 GHz (368.5, 424.8, and 487.3 GHz).

The rare isotopomer ¹⁸O¹⁶O is not homonuclear, hence has odd N levels and a non-zero electric dipole moment. This latter, however, is vanishingly small (10^-5D). ¹⁸O¹⁶O, moreover, has a very low abundance (few hundred times smaller than the main isotopomer), so that its magnetic dipole transitions (even the $\Delta{N}=2$, which have stronger intrinsic strengths), can be neglected.

The line opacity and absorption coefficients of ¹⁶O₂ are given by relations similar to Eq.8.24 and Eq.8.25.