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arXiv:astro-ph/0110483

Einstein's coefficients and the nature of thermal radio emission

Fedor V. Prigara

Published Oct 22, 2001• 0 citations
arXivHTMLPDF

Abstract

The relations between Einstein's coefficients for spontaneous and induced emission of radiation with account for the natural linewidth are obtained . It is shown that thermal radio emission is stimulated one . Thermal radio emission of non-uniform gas is considered .
DOI
10.48550/arxiv.astro-ph/0110483

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The spectral densities of Einstein coefficients for absorption and stimulated emission in a two-level quantum system are not equal to each other beyond the absorption (emission) line if the homogeneous broadening caused by interaction with a thermostat is much larger than the natural width. In this study, a relationship between these coefficients is derived on the basis of general thermodynamic requirements. This relationship is associated with new effects such as population inversion upon the nonresonant absorption of continuous radiation and radiation amplification without population inversion.
It is pointed out that the line profile coefficients for spontaneous and stimulated emission are identical in low-intensity radiation fields. In more intense radiation fields, however, the stimulated emission profiles in the radiative transfer equation and in the rate equations for the atomic level populations may differ from each other, owing to their different physical nature. A seeming discrepancy between the stimulated emission profiles of the usual semi-classical aproach and a recent quantum mechanical approach by Cooper et al. (1982), which should also be valid for intense 'broadband' fields, is discussed and shown to have negligible consequences for low-intensity radiation fields.
We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive.
In a famous paper where he introduces the A and B coefficients, Einstein considered that atomic decays of excited atoms can be stimulated by light waves. Here we consider that atomic decays can also be stimulated by atomic waves. It is however necessary to change the Maxwell-Boltzmann statistics of thermal equilibrium into Bose-Einstein statistics and to introduce a coefficient C which complements the list of the coefficients introduced by Einstein. Stimulated emission of light can be considered as the first step towards the laser. Similarly, stimulated production of matter waves can be considered as the basic phenomenon for an atom-laser. Most of the results that we obtain here are not new. However, the method that we use remains very close to elementary classical physics and emphasizes the symmetry between electromagnetic and matter waves from various points of view.