Influence of radiation on ionization equilibrium.

Abstract

The ionization formula for an assembly of atoms, ions and electrons in thermodynamical equilibrium was first given by M.N. Saha in a series of papers (1920a, 1920b, 1921) and later extended by Darwin and Fowler (1923) and Milne (1921b) to include the different excited states of the atom. Milne (1921a) and Russel (1922) calculated the equilibrium in the case when the electron concentration can be regarded as an independent variable. In all these cases, however, the system is supposed to be in thermodynamical equilibrium, i. e. the reaction space is supposed to be traversed by radiation having the same temperature as the assembly. Let us, however, consider the case when radiation traversing an assembly consisting of the neutral atom, the ion and the electron is not in temperature equilibrium with the components of the system. The problem was attacked by M. N. Saha and R. K. Sur (1926), but the correct solution was obtained by Woltjer (1925a, 1925b) and Milne (1924) for the case of a non-relativistic non-degenerate system and was applied by Pannekoek (1926) to the explanation of the ionization of the earth's atmosphere by sunlight. Eddington (1926) in this way calculated the ionization in gaseous nebulae for which a more elaborate theory has been given later by Ambarzumian (1935). The purpose of the present communication is to extend the analysis to such systems in which the electrons are degenerate but the atoms and the ions are non-degenerate. Such cases occur in the interior of white dwarfs and of the planets as shown by D. S. Kothari (1936). For the sake of completeness we have derived in §1 the generalized ionization formula when the constituents obey any statistics. In §2 the ionization in presence of incident radiation of any composition is considered, the electrons being supposed to be either degenerate or non-degenerate.