Abstract
Instead of assuming the probabilities of absorption and emission of atoms in a radiation field as equal to and (the well-known Einstein equations) Strum has in a recent paper assumed them to be respectively equal to and . This leads to a modification of Planck's law. It is shown in this paper that this assumption effectively amounts to replacing the new statistical law of interaction of Nordheim e.g. by the more general where , , , are the distribution functions for the projectiles corresponding to the numbers of each before and after collision; , the number of cells respectively associated with them. On this basis a general function defined by is considered. As a consequence of this we get a generalized distribution function given by the relation If we take only two terms we get approximately By substituting the appropriate values for in the cases corresponding to the photons and the atoms, we get Strum's modified radiation formula, and a new distribution function for a gas. Thus as a result of a generalized analysis of the -theorem we get a new statistics the successive approximations of which are a more accurate statistics which includes Strum's formula, the statistics of Bose-Einstein, Fermi-Dirac, the classical statistics of Maxwell-Boltzmann. It is suggested that this new statistics may be of importance in the study of dense matter at high temperature.
- Received 1 July 1929
DOI:https://doi.org/10.1103/PhysRev.34.1204
©1929 American Physical Society