THE COEFFICIENT OF OPACITY 
223 
152. It seems natural to assume that the target is an actual sphere 
round the centre of the atom which the electron track must intersect as 
the condition for capture. This idea is the basis of the theory of nuclear 
capture investigated in § 170. But there are certain considerations which 
weigh strongly against this assumption. The frequency of the X ray 
emitted when an electron changes its velocity is presumably dependent 
on the abruptness of the stoppage. Electrons aimed to pass within a 
distance a of the nucleus suffer an extremely rapid change of velocity as 
they swing round at pericentron. It appears that the corresponding 
X rays would have a frequency much greater than the range 2-5RT/h to 
iRTjh to which the stellar opacity corresponds. It is now generally 
believed that radiation from these close penetrating electrons is inhibited; 
but it is not very important for us to decide here whether that is so or 
not. If we are right in concluding that they would yield radiation of 
frequency considerably above 7 RT/h, then clearly these are not the captures 
calculated in the last section as responsible for the astronomical opacity. 
To give radiation in the required frequency range the stoppage of the 
electron must be not too abrupt and not too slow. This points to a target 
of annular section. 
The theory of emission and absorption, which seems to be in close 
accordance with laboratory experiment and expresses the most modern 
ideas on the subject, is due to H. A. Kramers*. We regard this as likely 
to be correct, at least in its main essentials. There are some subtleties in 
Kramers 5 theory, vital for its application to terrestrial experiments but 
only of subsidiary importance in the determination of stellar opacity. 
As simplified for stellar applications, Kramers’ theory really amounts to 
this: we may calculate the stellar opacity just as if all electrons radiated 
according to the laws of the classical electromagnetic theory. 
For this reason we take as our first problem the determination of stellar 
opacity according to classical theory. This is not a preliminary exercise; 
it is the quickest route to the formulae which we accept as definitive. 
Afterwards Kramers’ theory will be invoked to explain why so antiquated 
a procedure is justified notwithstanding the advent of the quantum theory, 
and to introduce those subtleties which are needed in order to check the 
theory by laboratory experiment. 
Classical Theory of Emission. 
153. According to the electromagnetic theory an accelerated electron 
radiates energy. If T is the acceleration, the energy radiated in time dt is 
(153-1). 
* Phil. Mag. 46, p. 836 (1923). 
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