Coincidences resolution time

Comcidence experiments have been connnon in nuclear physics since the 1930s.The widely used coincidence circuit of Rossi [9] allowed experimenters to detennine, within tire resolution time of the electronics of the day, whether two events were coincident in time. The early circuits were capable of submicrosecond resolution, but lacked the flexibility of today s equipment. The most important distinction between modem comcidence methods and those of the earlier days is the availability of semiconductor memories that allow one to now record precisely the time relations between all particles detected in an experiment. We shall see the importance of tliis in the evaluation of the statistical uncertainty of the results. 

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.

Sum peak formation is observed when two y-rays emitted from a nucleus enter simultaneously into the detector. This is because cascade emission of the y-rays in the disintegration of the nucleus is measured as one coincidence count within the detector resolution time. Figure 19 shows a y-ray spectrum of in which displays two single peaks ofy (171.3 and 245.4 keV) and a sum peak at 416.7 keV. The sum peak... 

In the method of delayed coincidences, the coincidence counting rate between detectors responding selectively to genetically related particles, e.g., a jS- or a-par-ticle and a y-ray or an electron or between y-rays, is plotted as a function of a time delay inserted in the electronic circuits used to detect one of them. The development of this method and of improved electronic techniques has led to the use of resolution times of between 10" and 10 sec. We shall not discuss these methods here, for they have been very adequately reported by Bell [i9], 2ff]. Further analysis of the experimental data has made it possible to measure lifetimes of the order of 10 sec. The limit to the method seems to be determined by the scintillating properties of the phosphor and its physical size. 

A pulse will be involved in a summing whenever it is not preceded or followed by a certain period of time. This time, T, is the resolution time of the electronic system. Using the Poisson distribution, it can easily be demonstrated that the probability of a random coincidence, Pq, within T is ... 

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])...

W. Fichtner and W. Hacker, Time-resolution of Ge avalanche photodiodes operating as photon counters in delayed coincidence, Rev. Sci. Instrum. 47, 314-ill (1976). 

The overall separation potential of an electromigration technique can be expressed by the peak capacity ( ), which is defined as the maximum number of peaks that can be separated within a given separation time, usually coincident with the time interval between the first and last detected peak in the electropherogram, while retaining unit resolution for all adjacent peak pairs ... 

The time-resolved emission spectra (TRES) and fluorescence lifetimes, ti, of the fluorene derivatives were measured in liquid solutions at room temperature with a PTI QuantaMaster spectrofluorimeter with 0.1 ns temporal resolution [20]. At this resolution, all investigated fluorenes exhibited TRES which were coincident with the corresponding steady-state fluorescence spectra. As an example, TRES for compounds 3 and 11 in hexane, THE, and ACN are presented in Eig. 8 for different nanosecond delays 0 ns (curves 2,4,6) and 5 ns, which modeled the steady-state condition (curves 3,5,7). No differences in the fluorescence spectra for these two delays were observed, indicating that all relaxation processes in the first excited state Si are sufficiently fast for fluorene molecifles and did not exceed the time resolution of the PTI system ( 0.1 ns). 

Safford and Naumann (128) have shown that the time-of-flight spectra for 4.6M solutions of KF, KC1, CsCl, NaCl, and LiCl show peaks in the inelastic scattering region which coincide both in frequency and shape with the ice-like (structured) frequencies of pure water. Also, solutions of KSCN, KI, KBr, and NaC104 have lattice frequencies where they are found for water although in these cases apparently with less resolution and less intensity. Even an 18.5-M solution of KSCN showed a similar behavior. We take this to suggest that elements of water structure remain in these solutions (as discussed elsewhere in this paper, where we noted that the thermal anomalies occur at approximately the same temperatures, even for relatively concentrated solutions, as where they occur in pure water see also Ref. 103). 

The PBDE concentrations in the core from Lake Erie are shown in Fig. 11 as a function of deposition year. Data from the other lakes are similar except the resolution with depth is much less. In this Lake Erie core, BDE-209 was first observed at core depths corresponding to 1979. This date is similar to the result reported by Zegers et al. [52], who found BDE-209 first appeared in 1978 in a sediment core from Drammcnfjord, Norway. This advent date also coincides well with the increasing production of commercial deca-BDE beginning in the late 1970s [28]. Both the SPBDE and BDE-209 concentrations in this sediment core increased exponentially with time. This is consistent with the increasing demand for PBDEs in U.S. market over the last 30 years. 

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