Electromagnetic transition intensities

Mass Scaling Laws and Lowering of Symmetry Electromagnetic Transition Intensities Anharmonic Couplings... 

Linear Triatomic Molecules Anharmonic (Fermi) Interactions Rotational Spectroscopy Electromagnetic Transition Intensities... 

Maser The microwave equivalent of a laser that represents some of the strongest transition intensities in the radio region of the electromagnetic spectrum, e.g. the water maser at 22.235 GHz. 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

From the general considerations of transition intensities in Section 12.2, we know that the rate of absorption of electromagnetic radiation is proportional to the population of the lower energy state (N in the case of a proton NMR transition) and the rate of stimulated emission is proportional to the population of the upper state (Np). At the low frequencies typical of magnetic resonance, we can neglect spontaneous emission as it is very slow. Therefore, the net rate of absorption is proportional to the difference in populations, and we can write... 

As discussed earlier in Section lOC.l, ultraviolet, visible and infrared absorption bands result from the absorption of electromagnetic radiation by specific valence electrons or bonds. The energy at which the absorption occurs, as well as the intensity of the absorption, is determined by the chemical environment of the absorbing moiety. Eor example, benzene has several ultraviolet absorption bands due to 7t —> 71 transitions. The position and intensity of two of these bands, 203.5 nm (8 = 7400) and 254 nm (8 = 204), are very sensitive to substitution. Eor benzoic acid, in which a carboxylic acid group replaces one of the aromatic hydrogens, the... 

The set of energy levels associated with a particular substance is a unique characteristic of that substance and determines the frequencies at which electromagnetic radiation can be absorbed or emitted. Qualitative information regarding the composition and structure of a sample is obtained through a study of the positions and relative intensities of spectral lines or bands. Quantitative analysis is possible because of the direct proportionality between the intensity of a particular line or band and the number of atoms or molecules undergoing the transition. The various spectrometric techniques commonly used for analytical purposes and the type of information they provide are given in Table 7.1. 

Figures 2.13(a) and 2.13(b) illustrate the basis of a semiconductor diode laser. The laser action is produced by electronic transitions between the conduction and the valence bands at the p-n junction of a diode. When an electric current is sent in the forward direction through a p-n semiconductor diode, the electrons and holes can recombine within the p-n junction and may emit the recombination energy as electromagnetic radiation. Above a certain threshold current, the radiation field in the junction becomes sufficiently intense to make the stimulated emission rate exceed the spontaneous processes.

The angular distribution of the intensity of electromagnetic radiation is given by specific analytic functions written in terms of an angle, W(Q,mi), relative to the quantization axis, Z, and the magnetic quantum number, mi. The patterns depend on the order of the multipole, dipole, quadra pole, and so forth, but they are the same for electric and magnetic transitions with the same order. For example, the angular distributions for dipole radiation are... 

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