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where D2 is the fraction of counts in the window due to y2 ; from the window width, this fraction can be obtained from the single-crystal spectrum, analyzed as described in Section II.3.D. The term ^ q, i DA W, ^ (0) corrects for coincidences arising from "gating" events in the window from any gamma ray (yi) other than y2. Here DI is the fraction of counts in the window due to yi, and q, , i is the relative number of y1 coinci- dent with y-^. In most decay-scheme studies, the necessary 11t± values can either be measured directly in other coincidence experiments or deduced from the decay scheme. Once the "q" values have been obtained for a series of gamma-gamma coincidence experiments, they are used in conjunction with the single-crystal intensities and the decay scheme to calculate the intensity of each gamma-ray transition. This procedure usually involves a series of successive approximations until internal consistency is achieved, especially if the decay scheme is complex. Other quantitative aspects of coincidence counting which relate to the determination of disintegration rates will be found below in Section VIII.2.E. VII. LOW-LEVEL COUNTING 1. General Remarks Many chemical experiments lead to very small amounts of radioactive sample, either because of the low yield of the reaction under study, or because of the small amount of sample available. It may be found that if a conventional detector is used for counting such low-intensity samples, the sample count- ing rate is comparable to the background rate from cosmic rays and other environmental radiation sources. When choosing between detector systems, the criterion for optimum counting precision in a given time is the "figure of merit" Ni/N-,, where N., is the sample counting rate, and N_ is a a gjj i. the background rate. The system which gives the largest figure of merit is the most sensitive for the measurement of a particular nuclide. Therefore, the reduction in the background rate must be large in order to be effective, since the sample counting rate appears to the second power and the background only as the first. Increasing the sample counting rate by 111
improvement of geometry, reduction of absorption, or some other means is far more valuable. The other practical criterion for low-level counting is stability, because a single determination may extend over days or weeks. Detectors used for low-level counting are similar to the ones already discussed but differ in their application. The choice of a particular detector, which must be considered separately from the various ways of reducing the background, will depend upon the specific activity of the material to be counted. When the specific activity is low, as in radiocarbon dating, there is no point in considering a method which will not permit introducing a large sample and counting with high efficiency. The beta-particle energy is also involved in the choice of a detector, since absorption effects in the sample and counter window are extremely acute for beta-particle energies below about 200 kev. On the other hand, absorption is a relatively minor consideration for high-energy beta particles. The most difficult counting situation is encountered when the samples of interest combine a low specific activity with a low beta-particle energy. Typical samples of tritium (H3) and C14 fall in this category. The usual techniques for low-level counting of these nuclides are gas counting and liquid scintil- lation counting. The general problem of low-level counting has been reviewed 04 qc. of. qf. by Arnold, Kulp, and DeVoe. The report by DeVoe7 is especially valuable because of the wealth of information it contains about the radioactive contamination of materials needed by workers attempting to detect minimal amounts of radioactivity. 2. Apparatus A. Large-Volume Counters. A typical arrangement of a low- background large-volume counter is shown in Fig. 51(a). The detector is situated at the center of a steel shield; lead is usually avoided because of its associated radioactivity. The mercury shield around the detector is to stop any radiation produced in the walls of the tubes comprising the anticoinci- dence mantle. The most important single feature is the anticoincidence mantle. This device, although shown in the figure as a ring of Geiger tubes, may also be a hollow cylinder of scintillator, 112
ANTICOINCIDENCE MANTLE (GEIGER TUBES) GUARD COUNTER ( + HV) GAS INLET GAS OUTLET METALLIZED INTERIOR SURFACES (-HV) METALLIZED PLASTIC FILM WINDOW .DETECTOR /(+HV) PLASTIC Fig. 51. Low-background counters. (a) Typical arrangement for obtaining very low backgrounds. (b) Low-background pro- portional counter covered by an anticoincidence, or guard counter. 113