Cm

Figure 7.8 Fine-structure splitting of the electronic ground states of O I and C II. The far-infrared lines associated with transitions between these levels are indicated. Also shown in the case of O I are the optical transitions from the first excited electronic state. No optical lines arise from the analogous transition in C II.

Oxygen exists in neutral, atomic form (O I) throughout large regions of molecular clouds. In its electronic ground state, O I has four p-electrons (l = 1). Their individual orbital angular momenta combine vectorially to yield a total orbital quantum number L =1, while the electron spins add together to S = 1. Although other values for L and S are possible, all result in greater Coulomb repulsion between the electrons and hence higher energy. The electronic ground state of O I is symbolized spectroscopically as 3P, where the symbol P denotes L =1 and the superscript is equal to 2S + 1. As sketched in Figure 7.8, the first excited state, corresponding to L = 2 and S = 0, is denoted D.

The figure also shows that the 3P state is actually a multiplet of three different levels of slightly different energy. Each level is distinguished by its degree of spin-orbit interaction. One may picture the orbital and spin angular momentum vectors, L and S, precessing about their fixed sum, J = L + S. (Compare the discussion of the OH molecule in ยง 5.5.) The spin-orbit energy is proportional to L S, which remains constant during precession. By convention, each level is labeled with the subscript J, the magnitude of the total angular momentum. This number can take the values 0,1, or 2 for the 3P state, but is restricted to 2 for the first excited (xD) state. The 3P2 level of O I is the true ground state, while the 3P0 level is highest in energy. This ordering of energies within the multiplet is called inverted, since, in the semi-classical model, L and S prefer to be antiparallel, implying that J is normally minimized in the ground state.2

2 In the electron's reference frame, the nucleus creates a magnetic field B parallel to L. For an electron with spin magnetic moment fxs, the lowest energy occurs when is parallel to B, and hence to L. Because of the electron's negative charge, is antiparallel to S. Therefore, L and S are expected to be antiparallel.

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