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Statistical Analysis of Accidental Coincidences in Channel Events

Understand the conditions for coincidences between events on Channel A and Channel B, with focus on gate settings and probabilities. Explore typical values and expected rates using statistical analysis.

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Statistical Analysis of Accidental Coincidences in Channel Events

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  1. Accidental Coincidences Statistical Analysis By Steve Kliewer 2008 SCIPP Workshop

  2. w w Conditions for a Coincidence A B1 B2 Given an event on Channel A, any event on channel B from B1 to B2 (i.e. before or after up to w away), will trigger a coincidence when the gate has been set to w.

  3. Typical Values: RA = 10 kHz RB = 10 kHz Gate: w = 1 s = 10-6 s In a 1 second interval: # of counts on A = NA = RA = 103 # of counts on B = NB = RB = 103 # of gate windows = NW = 1/w = 106

  4. The probability of an event on a channel is: PA = PB1 = PB2 = NA / Nw = RA w = RB1 w = RB2 w The probability of a random coincidence on both is: PC = PA * (PB1 + PB2 ) = 2*RA * RB w2 The expected rate of coincidences is: RC = PC * Nw = 2*RA * RB w = 2* 103 * 103 * 10-6 = 2 Hz

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