1. Accidental Coincidence Rates
June 24, 2008

2. = RB • RA • Window Chance Coincidence Probability of an open window
Sci A
Probability of an open window
= Rate A • Window length
Noise Hit
Sci B
Coincidence
Chance Coincidence
Window from yesterday = 100 ns
Let rate of Sci A = 1 MHz
Ex) Probability of an opening = 10-7 • 106 = .1 = 10%
Rate of an ACCIDENTAL Coincidence= Rate of Sci B • Probability of an Opening
= RB • RA • Window

3. Rate of scintillator B seen from yesterday= 100 Hz
Set window from yesterday = 100 ns
Rate of scintillator A = 40 Hz
Rate of a ACCIDENTAL
Coincidence
= RB • RA • Window
Rate of scintillator B seen from yesterday= 100 Hz
Rate of Accidental Coincidence = 100 Hz • 40 Hz • 10-7 = .04 Hz
A fluctuation that small is obviously not seen on this graph

4. Instead of a coincidence rate changing by .04 Hz,
is it possible for the rate to fluctuate by 5 Hz?
AC = RB • RA • Window
RB = 5 Hz / (40 Hz • 10-7) ≈ 12 • 105 Hz
1.2 MHz is a much larger rate for B than was tested yesterday, but if it were to be tested, then one would see that the line for coincidence would deviate from the “plateau” by 5 Hz
RA • RB = 5 • 107 Hz2

5. Why does the coincidence rate rise?
Thermal Noise due to higher voltages
Efficiency = # coincidences / # scintillator hits
Noise in the scintillator, would cause an under-estimate of efficiency
Noise in the coincidence counter, would cause a false increase in efficiency
After-pulse can overlap with a single event, causing a false coincidence