Accidental Coincidences Learning Objectives Understand the difference between real and accidental coincidences in an experiment using  2 scintillators Understand the relevance of accidental coincidences in CROP experiments Learn how to evaluate the contribution of accidental coincidences to a measurement you are making Aim: minimize accidental vs. real coincidences

Outline Coincidence counting in CROP experiments Typical coincidence circuit set-up Mt. Michael Benedictine High School experience A careful look at accidental coincidence rates Formula for estimating accidental rate Quantitative discussion of Mt. Michael observation Power of adding 3rd, 4th detector in coincidence decision Accidental Coincidences

We will be dealing with coincidences among CROP detectors in almost all measurements. Mini-experiments during the first academic year 1. Cosmic-ray rate (coincidences per second) vs. barometric pressure Vertical telescope 2. Coincidence rate vs. detector separation Extensive air showers Optimization of detector geometry on rooftops Detectors spread horizontally

Accidental Coincidences Typical coincidence circuit set-up Det1 Det2 Analog signals Discriminator Coincidence unit Logic unit Logic pulse Digital, i.e. on or off Logic unit fires when it receives overlapping “on” signals from Det1 and Det2. Det1 Det2 Two overlapping “on” signals Coincidences come from: Real cosmic rays traversing both detectors. Accidental overlap of random triggers in Det1 and Det2. Cosmic rays hitting only one detector. Electronic noise. Each detector has its own “singles rate” which will determine the rate of accidental coincidences.

Accidental Coincidences Mt. Michael Benedictine High School Experience CROP 2000 first-year participating school Mini-experiment Coincidence rate vs. horizontal separation Two detectors only Report at April 2001 CROP meeting at UNL Note constant rate for separation > 5 meters 25 coincidences / 10 minutes  0.04 coincidences / second Real or accidental?

Accidental Coincidences Mt. Michael Benedictine High School Experience

Accidental Coincidences Discriminator threshold scans for 3 detectors Vertical scale: linear Vertical scale: log

Accidental Coincidences Mt. Michael Benedictine High School Experience Data from experiment: 2-fold coincidence rate vs. detector separation in meters

Accidental Coincidences 100 nsec Assume Det1 and Det2 fire their discriminators at random times (4 counts/second) and that the discriminator output widths are 100 nsec. For a typical second, the random firings can happen anytime within that 1 second period. Det1 and Det2 logic pulses from discriminator 1 second 100 nsec width Det 1 discriminator output Det 2 discriminator output A simple, specific example How often, on average, do the Det1 and Det2 signals happen to overlap?

If any Det2 pulse comes within a 2  100 nsec = 200 nsec window of any Det1 pulse, the coincidence unit will fire. Estimate of accidental coincidence rate: S 1 S 2  t Det1 singles rate Det2 singles rate Logic pulse width 4 counts/sec  4 counts/sec  (2  100 nsec) = 3.2  per second General formula: Accidental coincidence rate = S 1  S 2  (2  t) (coincidences/second) !! Formula assumes the two logic pulses have the same width and that the coincidence unit requires minimal overlap to fire!! Accidental Coincidences Close-up view Det1 Det2 100 nsec 200 nsec

Accidental Coincidences Confirm that Mt. Michael’s coincidence rate for separations greater than 5 m is consistent with accidental coincidences. Discuss the power of adding a 3rd and 4th detector in the coincidence decision to drastically reduce accidental coincidence rate.

Accidental Coincidences Counts per 5 minutes Approximately 50 mV threshold chosen for A and B Detector B singles rate = S 1 = 80,000/5 min = 267/sec Detector A singles rate = S 2 = 110,000/5min = 366/sec Predicted accidental coincidence rate: S 1  S 2  (2  t) = 267/sec  366/sec  2  sec = 0.02 / sec accidentals Observed: 0.04 / sec observed coincidence rate We may conclude that all or most of observed coincidences are due to accidentals!! 100 nsec