238
THE COEFFICIENT OF OPACITY
paribus be proportional to the density, so that it will give rise to differences
between dense and rarefied stars; hence the discrepant factor 10 which
affects dense and diffuse stars alike cannot be accounted for in this way.
Other sources of Opacity.
165. The success of the correspondence principle as applied in Kramers’
theory seems to be greater than we could have expected. The general idea
of the principle is that the results of the classical and the quantum theory
will converge ; but, for example, in dealing with K absorption from a 1-
quantum orbit we are as far as possible from the convergence point and it
is fortunate that the difference is no greater. The discussion has shown
that the use of Kramers’ theory (or of the classical theory) to calculate
astronomical opacity is practically equivalent to using the laws ascertained
by terrestrial experiment. Consequently, the discordance found in § 158
is a matter of very serious concern.
It is not as though any wide extrapolation were required in applying
experimental results to the interior of a star. The approximate treatment
of the electron orbits as parabolic is as satisfactory in the stars as in
laboratory conditions*. The main point of difference is that in the stars
the outer part of the electron system is missing and this may conceivably
make some difference to the ease of expelling an inner electron by radia
tion. We should also like to know more about Kulenkampff’s spectrum B.
Does it remain at frequency y 0 when the atoms are ionised, or does it
move on to correspond with the last occupied level ? 166
166. We must consider whether there are any further sources of
absorption responsible for an appreciable part of the stellar opacity. This
brings us to the question of line absorption due to excitation of the atoms.
Rosseland, in pointing out the distinction between opacity and absorption,
suggested that this could be disregarded since fine absorption lines can
have no appreciable effect on opacity. We dare not trust to this because,
as J. Woltjerf has urged, the lines may be broadened in the stellar interior
and effectively screen the whole spectrum. As before, we attack this
problem by calculating emission rather than absorption.
If we are dealing with a large number of excited electrons, a certain
proportion will relapse and emit quanta within a given time, so that there
will be an average rate of emission of energy per excited electron. Not
very much is known about this emission for deep-lying electrons, since
experimental values have only been obtained for the outermost electrons.
But according to the general principles of the quantum theory the emission
* Some further discussion of the applicability of Kramers’ formulae to stellar
conditions will be found in Monthly Notices, 84, p. 115.
f Bull. Astr. Inst. Netherlands, No. 82.