Coincidence resolving time

The residence time was determined for our neutron counter by measuring the time intervals between beta start signals and neutron stop signals. With a residence half-time of 11 ms and a coincidence resolving time of 40 ms. 92 of the true coincidence events were included. The fraction of true events not detected does not influence the present results because we normalize the Pn measurements to a known Pn value measured under identical conditions. The coincidence rate was measured by a simple overlap coincidence module where the beta pulse Input was stretched to 40 ms by a gate and delay generator. To measure the accidental coincidence rate, the same beta pulse was sent to a second coincidence module and overlapped with neutron pulses which had been delayed 45 ms. After correcting each coincidence rate for deadtime effects, the difference was the true coincidence rate. 

Obviously, the coincidence resolving time At, shown in Fig. 4.48, has to be large enough to accept all these true coincidences. However, this finite value of At then leads to the recording of not only the desired true coincidences, but also of accidental coincidences (also called random or false coincidences). As indicated by the name, these accidental coincidences accidentally follow one another within the time At. Hence, they are due to any two electrons which match the conditions set by the experimenter for the selected double ionization process they might originate from two different double-ionization processes, two single-ionization processes, or... 

Figure 4.48 Typical spectrum of electron-electron coincidences recorded with a TDC. The data refer to a situation in which the photon beam has no time structure. True coincidences are collected in the peak while accidental coincidences give a flat and smooth background. At indicates the coincidence resolving time and dt the time resolution of the time-measuring device. The two shaded areas represent accidental coincidences, measured on the left-hand side together with the desired true coincidences, but on the right-hand side separately (and simultaneously) in the full time spectrum.

From this relation it follows that a good, i.e., large, ratio of true to accidental coincidences requires a small coincidence resolving time At and a small source strength (f J<7). However, for small values of N all counting rates, Ix, l2, and /true, are small, and therefore the ratio r is not well suited as a criterion of the quality or feasibility of coincidence experiments. Indeed, a more appropriate figure of merit follows if the relative error a of true coincidences, defined by... 

Of these requirements, two topics will be discussed further. One concerns ways to get a small coincidence resolving time At, and the other addresses how large acceptance angles of the spectrometers can modify the shape of observed angular distribution patterns. 

Nominal values of coincidence resolving times A and photoelectric efficiencies a are 10 s and 0.2 respectively. Thus for chemiluminescence intensities such that (I A) 1, Eq. 

Figure 14. Left Panel The energy resolution at 662 keV is shown a set of crystals of different volumes (from ref [6]). Right Panel Coincidence Resolving Time (CRT) for LaBrs- Ce of different volumes (from ref [3])...

Random coincidences can be partially corrected by software, provided that the single counts of each channel and the coincidence resolving time are recorded. 

From the relations quoted, the rate of accidental coincidences, /acc, recorded within the finite resolving time interval At (see Fig. 4.48) can be calculated from... 

The scanner is designed to recognise coincidences where events occur in two opposing buckets within a resolving time of 12 ns. In normal operation, only coincidences between two elements in the same ring or adjacent rings (of the 8) were accepted, but for PEPT use this restriction was removed. The data acquisition system of the scanner was also modified so that coincidence data is recorded in list mode with time stamps at 1 ms intervals. 

The light decay time constant in Nal is about 0.25 (is. Typical charge sensitive preamplifiers translate this into an output pulse rise time of about 0.5 (is. Fast coincidence measurements cannot achieve the very short resolving times that are possible with plastic, especially at low gamma ray energies. 

The explanation along this line is usually made in most textbooks. However, the ideal conditions are seldom achieved in any practical counting system, and some modifications of the fundamental equations are required in order to correct the possible effects which may disturb the ideal conditions. For example, the 47t P- proportional counter has an appreciable sensitivity to y-rays. Furthermore the y-transition is detected by the p-detector through the internal conversion process, if any. Besides, because a coincidence mixer has a finite resolving time, false accidental coincidences are inevitably produced by chance. In addition to this problem, further consideration must be given when a nuclide with a complex decay scheme is measured. Taking account of all of these effects the coincidence equation becomes... 

The conditions for the emission of a chemiluminescence photon during any small time interval A and the Independence of the reaction probability k of prior events, i.e. dependence only on the nature of M and the constant reaction conditions, are precisely the conditions for a Poisson distribution in time. Therefore, at any time during the course of a chemiluminescent reaction, the probability of finding two or more photons emitted within the resolving time A of a coincidence circuit will be given by... 

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