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D hyperfine structure finally nuclear spins introduce

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Unformatted text preview: uite coincide. Molecular rotation splits the vibrational lines of a molecule into a band. To see this, we note that the value of J for upper and lower levels is not the same. We 1 From the NIST database: http://physics.nist.gov/PhysRefData/MolSpec/Diatomic/index.html focus first on closed ­shell molecules. Selection rules tell us that for electric dipole transitions, Ju−Jl=±1 (0 is parity forbidden for the closed shell case). In a decay, the frequency is given by the sum of both the change in vibrational energy and the change of rotational energy: Ⱥν + 2 B( J l + 1) J u − J l = +1 ν = ν vib + B[ J u ( J u + 1) − J l ( J l + 1)] = Ⱥ vib . J u − J l = −1 Ⱥ ν vib + 2 B − J l The solution with Ju=Jl+1 emits at higher frequency and is called the R branch, while the solution with Ju=Jl−1 is at lower frequency and is called the P branch. € Each is made up of many lines corresponding to different values of Jl. The individual rotation ­vibrational lines are denoted by e.g. CO 0—1 R(3), in which the two numbers indicate the vibrational quantum numbers (lower level given first by convention), then the type of branch (P or R) and then the angular momentum of the lower level. In special cases, Ju−Jl may be different from ±1. The two examples are: Electronic states with open shells, in which two levels with the same J may have different parity. In this case, Ju−Jl=0 is possible. This is called a Q branch. Electric quadrupole transitions, as occurs with the vibrations of homonuclear molecules, most importantly H2. For this case, the selection rules allow Ju−Jl=0,±2. The latter cases give rise to O ­ and S ­branches. Among th...
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