THE COEFFICIENT OF OPACITY 
247 
which agrees precisely with the result of Kramers’ theory (158-2) except 
that the numerical coefficient is 10-8 instead of 0-668. Thus the nuclear 
theory of capture gives an absorption 16-2 times greater. For example, at 
the centre of Capella the result is k = 80 which is satisfactorily close to 
the astronomical value 53. The nuclear theory predicts the absolute 
brightness of Capella to within half a magnitude; and since it also gives 
the recognised law Jc oc p/T^ the agreement for other stars will be equally 
good. 
As already stated it appears to be impossible to accept the nuclear 
theory in spite of this agreement. It is, however, instructive to find an 
entirely different theory leading to the same formula for stellar absorp 
tion as Kramers’ theory, except for a purely numerical factor. It serves 
to emphasize the very general basis of an absorption law approximating 
to p/T%. 
171. The case for the hypothesis of nuclear capture is that, although 
Kramers’ theory is presumed to be right so far as it goes, it apparently 
needs supplementing, since it leaves T 9 ^ of the absorption unaccounted 
for—if our figures are correct. Now Kramers never refers to those electron 
tracks which are interrupted by a collision with the nucleus. His target 
is an annulus; as we go inwards from the annulus and the orbits become 
sharper and sharper the frequency of capture becomes rarer; his theory 
gives good reason for this decline. But it is possible that there might be 
a recrudescence of capture when the tracks strike the nucleus and so 
introduce a state of things not discussed by him. According to mechanical 
ideas an electron would not rebound with perfect elasticity from a cushion 
composed of 86 protons and electrons (the iron nucleus). The kinetic 
energy at the impact is so enormous that the loss of part of it would 
leave the electron with negative total energy and so unable to escape. 
Unfortunately for the theory, mechanical ideas are not to be trusted, and 
according to quantum ideas capture is less probable. Our impression is 
that the impact would be of such brief duration that there would not be 
enough low frequency radiation to effect capture; the classical radiation 
would be on the wrong side of the guillotine. 
We have assumed in the calculation that the energy emitted on capture 
is the mean quantum of the stellar radiation 2-lRT. This will not be exact; 
but we are bound to assume that the emission is in this region, for other 
wise Rosseland’s argument (§77) shows that the corresponding absorption 
would not be equivalent to opacity. This means that the captures are 
required at the K level in light elements and at the L level in heavy 
elements. We at once encounter the difficulty that owing to the thermo 
dynamical relation between absorption and emission coefficients there 
would have to be a corresponding K and L absorption in un-ionised