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J u j l 1 vib 2 b j l the solution with jujl1

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Unformatted text preview: 2 J + 1 We can see that the decay rates rise rapidly with J (due to the ω3). A special case occurs for homonuclear molecules such as H2, since these have zero dipole moment. In this case, decay occurs through electric quadrupole transitions with ΔJ=−2. The frequencies are then 6B, 10B, 14B, etc. and the decay lifetimes are much longer. In practical ISM cases, H2 is the only homonuclear molecule with sufficient abundance for the quadrupole transitions to be of interest. The rotational spectral lines are often labeled with a letter denoting the type of transition (R for electric dipole decays, S for quadrupoles) and the angular momentum of the lower level in parentheses. For example: H2 S(0) J = 20, CO R(3) J=43, H2 S(1) J = 31. Some cases of particular interest are: H2: The quadrupole lines are at: S(0) 28 μm [Radiation from lowest excitation of para ­H2] S(1) 16 μm [Radiation from lowest excitation of ortho ­H2] Rotational constants:1 Molecule 2B 12C16O 115.3 GHz 13C16O 110.2 GHz 12C32S 049.0 GHz The carbon monoxide dipole series is usually the strongest of the molecular lines. B. VIBRATION SPECTRA A vibrating molecule can often be approximated as a harmonic oscillator. In a true harmonic oscillator whose dipole moment is a linear function of position, there is a selection rule that the quantum number v changes by 1, however in practice molecular potentials are anharmonic and larger |Δv| is common. A perfectly harmonic oscillator would emit at frequencies ν equal to the natural frequency of oscillation, however in an anharmonic oscillator the frequency changes with excitation (generally becoming lower for potentials with a finite dissociation energy). Thus v=10 and 21 do not q...
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