Continuous absorption

Abstract

Astrophysical theories cannot proceed far without the introduction of an absorption coefficient for the continuous spectrum. It is generally agreed that this kind of absorption is produced by the transition of an electron from a bound state to a free state, or from one free state in the neighbourhood of an ion to another of greater energy. The absorption coefficient should therefore be calculable by means of atomic theory. The theory hitherto used is an adaptation of Kramers’ classical theory* of X-ray emission. The opacity so calculated is many times smaller than Eddington’s estimate from astronomical observations.† The present paper summarises an attempt to discover whether the quantum theory yields a value nearer to that of Eddington. Various approximations that are made prevent an accurate calculation of the opacity; but it seems fairly certain that the classical theory is not far wrong in instances of importance in astrophysics. The mathematical problem consists in the calculation of matrix-elements involving at least one state of positive energy. It is sufficient to consider a single electron in the field of a positive charge. The calculated coefficients of absorption are compared with the results of Kramers’ theory. §5 is concerned with the application of this work to astrophysics.