The stellar coefficients of absorption and opacity

1. The evaluation of the atomic absorption and opacity coefficients* due to atomic nucleii in an enclosure containing free electrons distributed according to the Fermi-Dirac statistics, apart from its theoretical interest, has of late gained some physical importance since Professor Milne’s recent analysis of stellar structure has disclosed the possibility ofall the stars possessing at least a zone of complete degeneracy. It is proposed, therefore, to examine this question in this paper. The formulæ here arrived at for the degenerate case are true only for high degeneracy. It has not been found possible to evaluate them for “ incipient ” degeneracy. 2.Absorption by an Atomic Nucleus in an Electron-gas obeying the Fermi-Dirac Statistics .—We shall definea 0 (E,v ) to be the rate of absorption of energy from radiation of frequencyv and unit intensity, by electrons of energy E, and unit mean density. Then it is known from the work of Kramers and Gaunt thata 0 (E,v ) = 4π Z2 e 6 /3√ 3hcm 2 v 3 v , where Ze is the charge of the atomic nucleus, andv the velocity of the electrons, the other symbols having their usual significance. Let this nucleus be in an enclosure of unit volume containing Ne free electrons distributed according to the Fermi-Dirac statistics. We want then the total absorption of energy Qv from the incident radiation by all the electrons with velocityv , in the enclosure, in unit time. On the classical theory we should have clearly Qv dv =a 0 (E,v )Nv dv .