On the excitation mechanism of the 21-cm (radio-frequency) interstellar hydrogen emission line.

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Abstract
The mechanism proposed here is a radiative one: as a consequence of absorption and re-emission of Lyman-a resonance radiation, a redistribution over the two hyperfine-structure components of the ground level will take place. Under the assumption here certainly permitted that induced emissions can be negelcted, it can easily be shown that the relative distribution of the two levels in question, under stationary conditions, will depend solely on the shape of the radiation spectrum in the I~a region, and not on the absolute intensity. The shape of the spectrum of resonance radiation, quasi-imprisoned in a large g~s cloud, could only be determined by a careful study of the "scattering" process (absorption and re-emission) in a cloud of definite shape and dimensions. The spectrum will turn out to depend upon the localization in the cloud. Some features can be inferred from more general consider~tions. Take a gas in a large container, with perfectly reflecting walls. Let the gas be in equilibrium at temperature T, together with Planck radiation of that same temperature. The scattering processes will not affect the radiation spectrum. One can infer from this fact that the photons, after an infinite number of scattering processes on gas atoms with kinetic temperature P, will obtain a statistical distribution over the spectrum proportional to the Plauck-radiation spectrum of temperature P. After a finite but large number of scattering processes the Planck shape will be produced in a region around the initial frequency. Photons reaching a point far inside an interstellar gas cloud, with a frequency near the La resonance frequency, will have suffered on the average a tremendous number of collisions. Hence in that region, which is wider the larger the optical depth of the cloud is for the Lyman radiation, the Plauck spectrum corresponding to the gas-kinetic temperature will be established as far as the shape is concerned. Because, however, the relative occupation of the two hyperfine-structure components of the ground state depends only upon the shape of the spectrum near the La frequency, this occupation will be the one corresponding to equilibrium at the gas temperature. The conclusion is that the resonance radiation provides a long-range interaction between gas atoms, which forces the internal (spin-)degree of freedom into thermal equilibrium with the thermal motion of the atoms. Institute for Theoretical Physics of the City University, Amsterdam.

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