Rotational Lines of Molecular Oxygen

An energy level diagram for the first three rotational levels can be viewed here. It shows the possible transitions and their frequencies in GHz. The lines that ODIN will be able to observe are the (1,1) to (1,0) 118.75 GHz line, and the two lines from the J=3 levels down to the (1,2) level with frequencies of 424.76 GHz and 487.25 GHz.

Molecular oxygen, like molecular hydrogen, is a diatomic molecule formed from two identical atoms in most cases since one isotope dominates the mass spectrum of the atom. So one may wonder why molecular oxygen has rotational lines while molecular hydrogen does not. There are two reasons why molecular hydrogen (ignoring the presence of deuterium) has no rotational transitions: first, the molecule has no electric dipole moment, so dipole transitions are not going to occur. Second even if the molecule had a dipole moment the symmetry requirements involved [due the two nuclei being identical and needing to have antisymmetric wavefunctions, because the proton is a Fermion and so the two protons cannot have exactly the same state] cause half the rotational levels to be forbidden. If the nuclear spin state is symmetric it turns out that the symmetric rotational levels (those with even angular momentum quantum number J) are forbidden while if the nuclear spin state is antisymmetric then the antisymmetric rotational levels (odd J) are forbidden. This is the cause of the ortho- and para- forms of the hydrogen molecule. As normal rotational transitions change J by 1 when the even or odd levels are removed the normal type of transition cannot occur.

For oxygen the nuclear spin is 0, so rather than having ortho- and para- forms of the molecule there is no para-oxygen (the antisymmetric form, odd J values when the electronic ground state is antisymmetric) because the overall wavefunction must be symmetric when the nuclei are bosons. The molecule has no electric dipole moment. However due to having two unpaired electrons the molecule has a magnetic dipole moment. Magnetic dipole transitions are possible and actually are quite strong since the molecular magnetic moment is large. It is the magnetic dipole rotational transitions that are observed. The selection rules for a magnetic dipole transition are different than those of an electric dipole transition -- they allow J to change by 0 or 2 instead of 0 or 1 as in the usual case. So even with half the rotational levels absent the transitions occur.

The electron spins in molecular oxygen add up to give a spin angular momentum quantum number of 1, so for a given J the total angular momentum quantum number N can be J-1, J, or J+1. The energies of these three levels are different. There are fine-structure transitions (which change N but not J) which mostly fall at frequencies around 60 GHz and there are normal rotational transitions which change J by 2.

Kevin Volk, October 2001
last update 2006 January 17, 19:12 UTC by Steve Torchinsky. See changelog.