Continuous absorption

For some years astrophysicists have been looking for an adequate theory of continuous—as opposed to line—absorption. The natural and generally accepted mechanism is 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 free state of greater energy. The theory hitherto used is KRAMERS’ theory of the converse process of emission by a free electron passing a positive nucleus. Since emission and absorption are intimately connected by thermodynamics, the absorption coefficient can be calculated from KRAMERS’ formulae. Unfortunately, although KRAMERS’ work is in good agreement with laboratory observations of X-rays, it gives an absorption coefficient many times smaller than that found from astronomical observations. KRAMERS used classical electromagnetism, and got over the difficulty of the quantisation of negative energies by distributing the classical emission that involved captures somewhat arbitrarily among the various stationary states. It was evidently desirable to do the same work by means of quantum theory, both for the sake of greater rigour, and in the hope of finding a larger absorption. The foundations of such a theory were laid by OPPENHEIMER,|| upon the bed-rock of SCHRODINGER’s equation, in a paper to which this one is much indebted. The matrix-elements involving positive energies present considerable difficulty, and the approximations used by OPPENHEIMER in his paper of 1927 are unsuitable for stellar applications.