Back-of-the-envelop photon estimates

[Elton Smith <elton@jlab.org>]

Hi Will,

At the last Bcal readout meeting you showed some estimates of photons
expected in the Bcal that were (factor of 3) lower than the 10,000
photons/side I have used. I promised to get back on a quick estimate of
this number. Here it is:

1. Number of photos/MeV of scintillator = 10,000/MeV (PDG July 2008 Sec
28.2)
2. 1 GeV photon deposits 120 MeV in scintillator (0.12 sampling fraction)
3. Capture fraction/side in fiber is 5.4% double clad, 3.1% single clad,
corresponding to 26deg and 20 deg total internal reflection angles. I take
4% because we have double clad, but these do not seem to yield full
capture relative to single clad.
4. Attenuation from center to one side
(atten length=280 cm) = exp(-200/280) = 0.5

Putting all this together gives
Number of photons at end of Bcal = 10^4/MeV x 120 MeV x 0.04 x 0.5 =
24,000 photons per side.

The number we get is smaller than this by a factor of 2, but is normalized
to the measurements of Bcal prototypes. The Montecarlo estimates of the
shower actually yield somewhat higher estimates (40k/side), but losses at
different stages reduce the calculated number.

I believe the main difference from your estimate from
http://www.jlab.org/Hall-D/software/wiki/images/5/58/LightCollection.pdf
and the one above is due to the assumed loss of light due to attenuation
(factor of 20 instead of 2). The PDG claims the loss can be "95%... in a
large collider tracker." This is not consistent with our calorimeter
design or measurements and I'm not sure why this would be so large, but it
is for a different application.

Hope this helps.

Cheers, Elton.



Elton Smith
Jefferson Lab MS 12H5
12000 Jefferson Ave
Suite # 16
Newport News, VA 23606
elton@jlab.org
(757) 269-7625
(757) 269-6331 fax