1 2 8 D O C . 1 2 9 T H E O R Y O F R A D I A T I O N E Q U I L I B R I U M
theory, the processes of inverse motions to Z and Z* do not exist at all. For our con-
sideration we must rather assume that for each transition Z — Z* a transition Z* —
Z exists such that in the former process a quantum of the same direction and, in any
event, of the same type, is absorbed in the same way as it is emitted in the latter.
For the transitions thus defined, the statistical rules indicated in §1 should apply.
Now we move onward to the case that the molecules are mobile and change ve-
locity under the influence of the radiation process. In this case, the molecule’s state
is codetermined by the velocity components of its center of mass, i.e., the state do-
mains Z and Z* are codetermined by the elementary intervals of these velocity
components. ε and ε* then signify the value of the total energy including the kinetic
energy. The elementary processes of the defined type then always only involve in-
teraction with radiation from a specific directed cone. Here, too, the constants a and
b naturally also depend on the choice of elementary process to be examined. If re-
lation (9) is retained for all elementary processes of the defined type, then the tem-
perature equilibrium is always guaranteed, irrespective of how a may depend on the
particular choice of elementary process.
§3. Extension of the Statistical Elementary Rules to the Case That Many Quanta
of Radiation Participate in the Elementary Process. It is characteristic of the
elementary process of scattering that two radiation quanta participate in it, an inci-
dent one and a scattered one, which are differently directed and in general (for
moving scattering molecules, atoms, or electrons) have different frequencies. In or-
der to cover such processes and survey their relation to the radiation formula, let us
generalize the scheme of §1. In the observed elementary process, let the radiation
quanta hν1, hν2… be absorbed by the molecule and the radiation quanta hν′1,
hν′2…, which like the former belong to beams of specified direction, specifically
for each quantum, be emitted from the molecule. The associated values for the ra-
diation density shall be denoted as ρ1, ρ2…, resp. ρ′1, ρ′2…. We imagine every
such partial absorption and emission process of the elementary process as assigned
to coefficients a1b1, a2b2…resp. a1′b′1, a′2b′2….
We apply formulas (2) and (5), naturally generalized, to this process
, (10)
whereby the products are extended over the indices 1, 2, 3…, and the coeffi-
cients a1b1 depend not only on the particular molecular states of equal probability
a priori, between which the process takes place, but also on the frequency range and
directional domain to which the individual radiation quanta belong.
[p. 305]
dW b1ρ1. a′1 b′1ρ′1)dt + (
∏∏
=
∏