Random Coincidence between two Independent Pulses

Transcription

1 Random Coincidence between two Independent Pulses Sean O Brien June 16, Random Coincidence Rates In nuclear experimentation there are genuine coincident events, those that are detected by two or more detectors that correspond to the same event. There are in addition to these true coincidence events signals that arise for which the detectors are responding to two separate events during the detectors resolving time. These signals can be due to one of the detectors not seeing the event or due to a event that has single a emission and no partner emission to be detected by its partner detector. Due to their random distribution over time and high rate of occurrence, there is a probability that some of these unrelated events will occur simultaneously, one in each detector leading to an over estimate of the true coincidence events. The time interval during which these random signals overlap is the resolving time. The random interval s size is dependent on the two single rates. If the time duration of the signals is sufficiently small, then the resolving time distribution will be linear throughout time [1] [2]. The magnitude of the random distribution is derived as follows: Let r 1 and r 2 be the rates of two uncorrelated start and stop pulses and T be the interval of time between the two pulses. After each start pulse the probability that over the length of time T a stop pulse will not occur is: e T r2 (1). The differential probability of the arrival of a stop pulse during the following differential time dt is r 2 dt. Since both independent events must occur, the total probability of creating an interval of dt and T + T is: r 2 e T r2 dt (2) The total differential rate of the interval is the rate of arrival multiplied by the probability, r 1 r 2 e T r2 dt (3) The exponential portion, e T r2, can be approximated to T if dt T r2 = T, e = 1, T r 2 1 and is not large in comparison with the inverse of the resolving 1

2 time, then r 2 T will also be small. Now we have that the random coincidence rate, r 12, is [1]: r 12 = r 1 r 2 T (4) 2 Circuit Construction The above equation was experimentally verified in the following way. The two single rates (r 1 and r 2 ) were obtained by two independent NIM Pocket Pulsers(model 417). Each pulser generates 800mV into 50Ω, with a risetime of 1.5ns, a falltime of 5ns, with a of 6ns at a 10KHz rate. These two pulers were input into the following circuit in order to measure their random coincidence rate. Each pulser was connected to an individual channel in the ch2 pulser 1 CH1 variable 5ns Logic Logic 5ns AND CH3 ch3 Linear fan out timer pulser 2 CH2 ch2 All cable lengths 4ns. Figure 1: A Random Coincidence Circuit Constructed with NIM bins. sixteen channel discriminator(module 706), which converts the pulses into logic pulses. A copy of each pulse is sent to a scalar (module N114), so the that each pulser s rate can be determined and then to a quad majority logic unit(module 755). This module allows for adjustment of the of each signal. In this 2

3 Figure 2: Setup Coincidence Circuit circuit one channel was set at 5ns, while the other was variable, ranging from approximately 5ns to 950ns. Each pulse then was duplicated again, with one running to a channel on the oscilloscope, so that the adjustments of each pulse could be measured and the other leading back into the majority logic module set to a coincidence level of two. From here the outgoing signal, only present when the two pulses overlapped and set to a of 5ns, goes to the quad scalar to determine the random coincidence rate and to the oscilloscope. Before each scalar channel is a, this is used to tell each of the scalars to stop counting. This portion of the circuit runs from the scalar timer to a quad linear fan-in/out(module 740), this unit simply accepts the timers stop pulse and copies it and sends it to the three scalar s. 3

4 3 Data and Analysis The above circuit was then used to experimentally verify the derived expression, r 12 = r 1 r 2 T. By adjusting the (resolving time), T, of a single pulser while the other remained fixed allowed a sample of resolving times ranging from 5ns to 950ns. The data was taken over 10s intervals on the scalar and forty runs were made with each run corresponding to a different. Figure 3: Random Coincidence Plot: Resolving Time vs. Coincidence Rate 4

5 The data corresponds well to the expected result. The expected slope calculated by averaging all r 1 r 2 is in good agreement with the observed slope. 4 Summary and Conclusions The construction and principles of random coincidence circuit are important concepts and skills necessary to nuclear instrumentation. They are important for particle measurements and help weed out false data, allowing greater statistical precession by understanding how to distinguish them from genuine coincidences [1] [2]. References [1] Glen F. Knoll. Radiation Detection and Measurement: Third Edition. John Wiley and Sons, Inc. New York, [2] E. Fenyves and O. Haiman The Physical Principles of Nuclear Radiation Measurements Academic Press, New York,