Abstract
In the previous chapters we have provided a quantum description of the radiation field in vacuum (Chap. 4) and of isolated atomic systems (Chaps. 5–9). We now move on to describe their mutual interaction by introducing some general methods, also based on quantum mechanics, with which we will be able to handle many phenomena associated with the absorption, emission and scattering of radiation, typical of laboratory and astrophysical plasmas. The combination of these methods is now commonly referred to by the name of quantum electrodynamics and represents one of the most successful achievements of theoretical physics, both from the point of view of the precision of the results obtained, and the elegance of the formalism. We will illustrate in this chapter the fundamental concepts and their simplest applications by considering only first order phenomena, i.e. phenomena involving the emission and the absorption of a single photon. We will formally derive the equations for the evolution of the populations of an atomic system in the presence of the radiation field (statistical equilibrium equations) and the equations for the evolution of the radiation field in the presence of an atomic system (equation of radiative transfer). The most relevant second order phenomena (where two photons are involved) will be treated in Chap. 15.
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Notes
- 1.
As we will see in Chap. 15, the term in \(\mathbf{A}_{\mathrm{R}}^{2}\) describes second order processes, in particular Thomson scattering.
- 2.
This fact justifies the name of the method (variation of constants) to denote the procedure followed here for the solution of the Schrödinger equation.
- 3.
The demonstration that the two types of averages are the same is far from trivial. In statistical mechanics, one usually refers to statements of this type by invoking the so-called ergodic theorem.
- 4.
For further discussions on polarisation phenomena see Landi Degl’Innocenti and Landolfi (2004).
- 5.
The diagonal matrix elements \(\mathcal{H}^{\mathrm{I}}_{\alpha\alpha}\) are effectively null in the applications that are considered in the following, where the interaction Hamiltonian is the one of Eq. (11.3).
- 6.
This property is formally derived in Sect. 16.12. Intuitively, we can think of the factor \({1 \over3}\) as the result of the average over the solid angle of a factor of the type cos2 θ, where θ is the angle between the r ba vector and the polarisation unit vector.
- 7.
The word laser is an acronym that stands for Light Amplification by Stimulated Emission of the Radiation.
- 8.
It is often improperly called absorption coefficient tout court. In reality, this latter name should be reserved for \(k_{\nu}^{(\mathrm{a})}\).
- 9.
In principle, the profiles for emission and stimulated emission can be different from each other and different from that one relative to absorption. The hypothesis to consider them equal, contained in Eqs. (11.35), is known as the approximation of total redistribution in frequency. For an in-depth discussion of this topic see, for example, Mihalas (1978).
References
Landi Degl’Innocenti, E., Landolfi, M.: Polarization in Spectral Lines. Kluwer Academic, Dordrecht (2004)
Mihalas, D.: Stellar Atmospheres, 2nd edn. Freeman, San Francisco (1978)
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Landi Degl’Innocenti, E. (2014). Interaction Between Matter and Radiation. In: Atomic Spectroscopy and Radiative Processes. UNITEXT for Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2808-1_11
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DOI: https://doi.org/10.1007/978-88-470-2808-1_11
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