Table 1. shows the expected mean number of photoelectrons for different gases, due to the difference in index of refraction. The value for Freon-12 is about 6.0 ph.e., however, this number varies significantly from point to point, - Fig. 3 shows the number of detected photoelectrons for an initial electron energy of 0.8 GeV as a function of the polar ( Theta) and azimuthal ( Phi) angles.
Table 1: Indices of refraction for various radiate
gases and estimated mean number of photoelectrons.
Figure 3: Mean numbers of photoelectrons in
Freon-12 gas versus angles Theta and Phi. Initial
energy of electrons is 0.8 GeV.
The coefficient in parentheses is the ratio to the Freon-12 value.
One can see that, for example, Perfluorobutane
provides
additional 2.5 photoelectrons due to the index of refraction alone.
To estimate the effect of one additional photo-electron,
we consider the
electron detection efficiency dependence on
( 
)
In simple cases, when it is possible to neglect geometry factors, the number of detected photoelectrons is distributed according to Poisson's law :
We define the detection threshold as the minimum number of photoelectrons necessary to detect a signal from the PMT. The detection efficiency for a one-photo-electron threshold is
For
to be less than 
,
should be greater than 7. Actually the ``real''
distribution is wider
than the Poisson distribution, and the probability to obtain zero
photoelectrons is greater than the value estimated using Poisson's law.
In order to obtain a value of
for the electron inefficiency,
we need an additional 2-3 photoelectrons.
If one is forced to raise the threshold to a few
photoelectrons,
for example due to background events,
the mean number of photoelectrons should be even higher.
