  The luminosity ratio of electrons to protons as it is produced in stochastic
acceleration processes in cosmic ray sources is an important quantity relevant
for several aspects of the modeling of the sources themselves. It is usually
assumed to be around 1:100 in the case of Galactic sources, while a value of
1:10 is typically assumed when describing extragalactic sources. It is
supported by observations that the average ratios should be close to these
values. At this point, however, there is no possibility to investigate how each
individual source behaves. When looking at the physics aspects, a 1:100 ratio
is well supported in theory when making the following assumptions: (1) the
total number of electrons and protons that is accelerated are the same; (2) the
spectral index of both populations after acceleration is $a_e=a_p\approx 2.2$.
In this paper, we reinvestigate these assumptions. In particular, assumption
(2) is not supported by observational data of the sources and PIC simulation
yield different spectral indices as well. We present the detailed calculation
of the electron-to-proton ratio, dropping the assumption of equal spectral
indices. We distinguish between the ratio of luminosities and the ratio of the
differential spectral behavior, which becomes necessary for cases where the
spectral indices of the two particle populations are not the same. We discuss
the possible range of values when allowing for different spectral indices
concerning the spectral behavior of electrons and protons. Additionally, it is
shown that the minimum energy of the accelerated population can have a large
influence on the results.
