The Emission, and Absorption of Radiation

Inasmuch as a thoroughly satisfactory quantum-mechanical theory of systems containing radiation as well as matter has not yet been developed, we must base our discussion of the emission and absorption of radiation by atoms and molecules on an approximate method of treatment, drawing upon classical electromagnetic theory for aid. The most satisfactory treatment of this type is that of Dirac,1 which leads directly to the formulas for spontaneous emission as well as absorption and induced emission of radiation. Because of the complexity of this theory, however, we shall give a simpler one, in which only absorption and induced emission are treated, prefacing this by a general discussion of the Einstein coefficients of emission and absorption of radiation in order to show the relation that spontaneous emission bears to the other two phenomena. 

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The Kinetics of Collision and Ionization.—In the last section we have been considering the emission and absorption of radiation as a mechanism for the transfer of atoms or molecules from one energy level to another. The other important mechanism of transfer is that of collisions with another atom, molecule, or more often with an electron. In such a collision, the colliding particles can change their energy levels,... 

Gustav Robert Kirchhoff (1824-1887) first formulated and published the laws named after him for electrical networks when he was still a student at university in Konigsberg. In 1850 he was nominated professor in Breslau and in 1854 he became a professor in Heidelberg. It was here that he worked with R. Bunsen for over 10 years and carried out investigations into the emission and absorption of radiation. Their results became known as Kirchhoff s radiation laws and as Bunsen-Kirchhoff spectral analysis. In 1875 he became Professor of Theoretical Physics of the University of Berlin. Alongside his teacher F. Neumann, Kirchhoff was a founder of mathematical (theoretical) physics in Germany. 

In a real radiation source this perfect equilibrium cannot exist and there are losses of energy as a result of the emission and absorption of radiation, which also have to be considered. However, as long as both only slightly affect the energy balance, the system is in so-called local thermal equilibrium and ... 

F. London, Zur Theorie und Systematik der Molekularkrafte. Zeits. fur Phys. 63 (1930) 245. P.A.M. Dirac, The Quantum Theory of the Emission and Absorption of Radiation. Proc. Roy. Soc. Lond. A114 (1927) 243. 

There have been developed two essentially different wave-mechanical perturbation theories. The first of these, due to Schrodinger, provides an approximate method of calculating energy values and wave functions for the stationary states of a system under the influence of a constant (time-independent) perturbation. We have discussed this theory in Chapter VI. The second perturbation theory, which we shall-treat in the following paragraphs, deals with the time behavior of a system under the influence of a perturbation it permits us to discuss such questions as the probability of transition of the system from one unperturbed stationary state to another as the result of the perturbation. (In Section 40 we shall apply the theory to the problem of the emission and absorption of radiation.) The theory was developed by Dirac.1 It is often called the theory of the variation of constants the reason for this name will be evident from the following discussion. 

The wave theory of electromagnetic radiation can explain a number of observed phenomena associated with light, such as diffraction, refraction, and interference, but fails to explain other properties. These include such things as the photoelectric effect and the emission and absorption of radiation by bodies. Instead, those phenomena involving interaction of light with matter are explained by utilizing the corpuscular character of electromagnetic radiation. 

Determination of the rate of gaseous ion-neutral reactions in electrical discharges rests on the measurement of the ion composition. The most common technique is to monitor the ion composition with a mass spectrometer, although the emission and absorption of radiation, beam probing, and wire probes are also employed. No attempt is made to give a definitive review of each of these. The reader is referred to the cited references for more detailed discussion. 

The next important step forward was taken by Einstein in 1916 in his famous work entitled The emission and absorption of radiation by the quantum theory (Einstein 1916), wherein he introduced two types of quantmn transition of an atom or molecule between discrete quantum states, namely ... 

We shall now apply the concepts developed in Chapter 9 to a discussion of the emission and absorption of radiation by an excited gas. We start by deriving the equation of radiative transfer in terms of the volume emission and absorption coefficients for line radiation and consider simple solutions for the case of uniformly excited sources. The terms source function and optical thickness are defined and the effect of self absorption and self reversal in optically thick sources is outlined. 

The hydrogen maser. The hyperfine structure of atomic hydrogen is shown as a function of the external magnetic field strength in Fig.18.16. When we study this diagram and recall our discussion of the emission and absorption of radiation in Chai tcr 9, it becomes apparent that... 

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