Dead-Time Measurement for Radiation Counters by Variance-to-Mean

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1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 33, No. 11, p (November 1996) TECHNICAL REPORT Dead-Time Measurement for Radiation Counters by Variance-to-Mean Method Kengo HASHIMOTOt, Kei OHYAtt, Atomic Energy Research Institute, Kinki University* Yoshihiro YAMANE Department of Nuclear Engineering, School of Engineering, Nagoya University** (Received July 8, 1996) The variance-to-mean ratios of counts accumulated during a time-gate were measured as a function of gate width for several Geiger-Mueller(GM) and neutron proportional counters. The measured ratios asymptotically decreased with an increase in gate width. The ratio for a GM counter was saturated in about 400ms of gate width, while that for a neutron counter was done in about 40ms. Applying the first- and second-order formulae derived from the Muller's expression for the variance-to-mean ratio, the dead times of these counters were inferred from these saturated ratios. In the count-rate range above 1,000cps for the GM counter and above 12,000cps for the neutron counter, the dead times obtained by the first-order formula apparently depended on count rate. On the contrary, the application of the second-order formula sufficiently reduced the count-rate dependence. The dead times obtained by the second-order formula were consistent with those by the previous two-source or reactor-power variational methods. KEYWORDS: dead time, time measurement, variance-to-mean ratio, Geiger-Mueller counters, neutron proportional counter, correlation measurement, nonparalysable model, BF3 counter, herium-3 counter, sensitivity, counting rates I. INTRODUCTION For any gas counter such as Geiger-Mueller (GM) or proportional counter, there exists a minimum time interval required to register consecutive detection events as separate counts. This resolution time is called the dead time. The important effect due to the dead time is the reduction of the count rate. The fraction of the loss of signal pulses increases with an increase in count rate. Under a high count-rate condition, the count rate measured must be corrected for the loss. The dead time of a counter should be previously determined for the correction. As the techniques for the dead-time measurement, the two-source method and decaying source method have been frequently employed(1). In our experiences, the reproducibility of the results evaluated by the former method was always poor. In particular, the measurement for a proportional counter was difficult, since its short dead time of a few ms makes it difficult to * Kowakae, Higashi-Osaka-shi 577. ** Furoh -cho, Chikusa-ku, Nagoya Corresponding author, Tel , t Fax Present tt address: Department of Nuclear Engineering, Osaka University, Yamada-oka, Suita-shi 565. provide the proper measurement setup including strong sources. Moreover, the latter method is inapplicable to the counter with such a short dead time. The main objectives of this report are to propose a correlation technique for the dead-time measurement, and to demonstrate the applicability of the technique. The present technique never requires special apparatus and skillful operations. The principle of the technique is very simple as described below. The Poisson distribution of the incoming particles or photons is distorted by the dead time of a counter. The distortion is enhanced with an increase in count rate and dead time. Formulating the counting probability distribution depending on these parameters, we can infer the dead time of the counter from the degree of the distortion and the count rate measured. In this study, the variance-to-mean ratio of counts accumulated during a time-gate is employed as a measure of the distortion. The formulation of the above ratio is simplified on the basis of two assumptions that the gate width specified is much longer than the dead time and that the count rate obtained is smaller than the reciprocal of the dead time. The other objective is to clarify the gate-width and count-rate range in which the simplified formulation is applicable. To achieve these goals, the variance-to-mean ratios were 863

2 864 K. HASHIMOTO et al. measured as functions of gate width and count rate for several GM and neutron proportional counters. In this report, Chap.II presents the analysis method of the technique proposed and Chap.III shows experimental setups and the specification of counters employed. In Chap.IV, the discussion on the results is given. II. DETERMINATION METHOD Consider a counting problem where a counter registers the number k of events in a fixed counting interval t and the intrinsic counting process is Poissonian with constant count rate r. The dead-time characteristic of counter is assumed to be non-paralysable (nonextended). The registration of a pulse is followed by a dead time t, in which every further registration is inhibited. After the time t fixed, the counter can register the first input pulse. Muller et al.(2) derived rigorous and asymptotic (in the sense that t/t->oo) formulae for the expectation and the variance of k. The exact expectation and the asymptotic variance can be described as follows: E(k,t)=lrt, (1) s2(k,t)=l3{rt+x2l(1+2/3x+-1/6x2)} (2) where x=lt, (3) l =1/(1+x). (4) Dividing Eq.(2) by Eq.(1), the variance-to-mean ratio V is given by V=s2(k,t)/E(k,t) =l2+xl3(t/t)(1+2/3x+1/ 6x2) =1-2x+3x2+(t/t)x (1-3x+6x2)(1+2/3x+1/6x2) =1-2lx+l2x2+(t/t)x(1-7/3x), (5) where the higher-order terms over the third are neglected. Neglecting the fourth term in Eq.(5) in the limiting case t ât, we obtain the following second-order formula: on t, and that x is so small that the higher-order terms can be neglected. In this report, therefore, the counting interval range holding the asymptotic ratio should be experimentally clarified, and the validity of the neglect of the higher-order terms should be examined. These examinations will be given in Chap.IV. III. EXPERIMENTAL APPARATUS The measurements of the variance-to-mean ratios for various GM and neutron proportional counters were carried out. As radiation source for GM counters b-ray sources(u3o8, 90Sr) for calibration were employed, while neutron proportional counters were irradiated by Pu- Be neutron source (1.2x106n/s). The neutron counters were surrounded by paraffin blocks to thermalize source neutrons. GM counters were connected to a conventional scaler system (Aloka TDC-105), which consisted of a detector bias supply, an amplifier, a discriminator and a scaler modules. Logic pulses from the discriminator were fed to the 8192 multi-channel scaler (Labo- MCS4L). In the measurements for neutron proportional counters, these counters were connected to a conventional nuclear instrumentation. The system consisted of a detector bias supply, a spectroscopy amplifier, a single channel analyzer (SCA) and a scaler modules. Logic pulses from the SCA were also fed to the multi-channel scaler. These schematic diagrams are shown in Fig. 1. The specifications of GM and neutron counters employed are given in Table 1, where the dead times previously obtained by the two-source and the reactor-power variational methods are included. The dead times of GM counters were determined by two-source method. In general, the reproducibility of the results by this method is poor. Therefore the measurements were carefully repeated 20 times. The average values are given in this table. On the other hand, the dead times of neutron counters were determined on the basis of the reactorpower variational technique(3). Utilizing the multi-channel scaler (MCS), the counts V=1-2Rt+R2t2, (6) where R represents the measured count rate lr. In the case x á1, the above equation may be reduced to the first-order formula: V=1-2Rt. (7) Equations (6) and (7) indicate that the dead time t can be evaluated by the measurement of the varianceto-mean ratio V. As mentioned above, however, these equations are based on the assumptions that counting interval t is much larger than the dead time T so that the ratio V converges into an asymptotic value independent Fig. 1 Illustrative block diagram of the experiment JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

3 Dead-Time Measurement for Radiation Counters by Variance-to-Mean Method 865 Table 1 Specification of radiation counters t1 Used in GM mode 2 Determined by t two -source method 3 Determined by reactor -power t variational technique of a counter can be continuously registered during a certain time interval, namely gate width. By a channel advance in the MCS, 8192 samples per a sweep can be obtained. The sweep was repeated 5-30 times to obtain 40, ,760 samples. These data were transfered to a personal computer and rapidly analyzed to obtain the variance-to-mean ratio V. To observe the ratio as a function of the counting-interval, the gate width of the MCS was varied in the range from 1ms to 100ms.IV. RESULTS AND DISCUSSION 1. GM Counter Measurement Figure 2 shows the variance-to-mean ratio measured with Aloka-GM2503B tube, when count rate R is about 600cps. In the range below 50ms, the measured ratio rigorouly follows the expression shown by Muller(4): V=1-Rt, for t át. (8) In the range from 50 to 200ms, the convergence into an asymptotic value can be observed. It is expected that the dead time of the GM counter may exist in this time range. In the region above 400ms, the gate-width dependence can be hardly observed within experimental error limits. The estimation of these statistical errors was based on the formula derived by Szeless and Ruby(5). The ratio V over the gate-width of 400ms should be measured to obtain the dead time of the GM counter in terms of Eqs. (6) and (7). Figure 3 shows the variance-to-mean ratio for Aloka-GM2503B tube as a function of count rate, where gate width specified is 10ms. First, the least-squarefitting of Eq. (6) to all data (ranging in count rate from 300 to 2,000cps) was made. The fitted curve and the inferred dead time are also shown in this figure. The fitting of the second-order formula is satisfactory. On the contrary, from the fitting of Eq. (7) the shorter dead time of ms was inferred. Next the fitting of Eq. (7) to the data ranging in count rate below 1,000cps was done. As shown in Fig. 3, the dead time obtained by this fitting agrees very closely with that by the secondorder fitting. When the first-order fitting was done over the wider count-rate range, inconsistent dead times were obtained. This feature indicates that first-order formula Eq. (7) is applicable in the count-rate range below about 1,000cps. In the range above the count rate, however, Eq.(6) should be applied to obtain the consistent dead time of the GM counter. The results for three GM counters are summarized in Table 2. The count-rate dependence of the dead time obtained for Aloka-GM2503B tube is also shown in this table. The count-rate dependence of the dead time obtained by the second-order formula Eq. (6) cannot Fig. 2 Gate-width dependence of variance-to-mean ratio measured for GM counter (Aloka-GM2503B) VOL. 33, NO. 11, NOVEMBER 1996

4 866 K. HASHIMOTO et al. Fig. 3 Count-rate dependence of variance-to-mean ratio measured for GM counter (ALOKA-GM2503B) Table 2 Dead time of GM counterst2 be observed within error limits. On the contrary, the dead time by the first-order formula Eq.(7) apparently decreases with an increase in count rate. This result indicates the failure of the first-order formula under high count-rate condition. The present dead times of three counters obtained by the second-order formula agree with those by two-source method within error limits (see Table 1). The poor reproducibility was responsible for the large errors of the two-source method, while the dead times by the present method was reproducible within statistical errors. 2. Neutron Proportional Counter Measurement Figure 4 shows the variance-to-mean ratio measured for LND-2524 tube, when count rate R is about 9,200 cps. In the range below 5ms, the measured data follows Eq.(8). In the time region above 40ms, the gate-width dependence cannot be observed within error limits. The ratio V over the gate-width of 40ms should be measured to obtain the dead time of the neutron counter. The gate width having the saturated ratio is one-tenth of that observed in GM counter, because of the shorter dead time Fig. 4 Gate-width dependence of variance-to-mean ratio measured for 3He counter (LND-2524) JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

5 Dead-Time Measurement for Radiation Counters by Variance-to-Mean Method 867 of the neutron counter. In the intermediate range from 5 to 40ms, the dead time of the neutron counter is expected to exist. Figure 5 shows the variance-to-mean ratio for LND tube as a function of count rate, where gate width specified is 10ms. The least-square-fitting of Eqs.(6) and (7) to these data were made in the same manner as preceding section. As shown in this figure, the dead time obtained by the first-order fitting to the data ranging in count rate below 12,000cps agrees very closely with that by the second-order fitting. When the first-order fitting was done over the wider count-rate range, inconsistent dead times were obtained. The first-order formula Eq.(7) is applicable in the count-rate range below about 12,000cps, while the second-order formula Eq. (6) should be applied in the range above the count rate to obtain the consistent dead time. The results for three neutron counters are summarized in Table 3. The count-rate dependence of the dead time obtained by Eq.(6) can be hardly observed, while the dead time by Eq.(7) apparently decreases with an increase in count rate. This dependence indicates the failure of the first-order formula. The above tendencies are the same as those of GM counter. The dead times of three neutron counters obtaind by the second-order formula are fair agreement with those by the reactor-power variational method (see Table 1). V. CONCLUSION The following conclusions can be drawn from the present studies: (1) The first- and second-order formulae for the asymptotic variance-to-mean ratio of counts could be derived to determine the dead time of a gas counter. (2) The variance-to-mean ratio measured for a GM was saturated in about 400ms of gate width, while the ratio for a neutron proportional counter was done in about 40ms. These gate widths are about five times the dead times of the counters. In the range above these gate widths, the present formulae are applicable. (3) The dead times of some GM and neutron counters were inferred from the saturated ratios. In the count-rate range above 1,000cps for GM counter and above 12,000cps for neutron counter, dead time obtained by the first-order formula apparently depended on count rate. These upper limits for the first-order formula may be described as 0.1/t. On the contrary, the application of the second-order formula sufficiently reduced the count-rate dependence. The dead time obtained by the second-order formula agree with those by the previous methods. Fig. 5 Count-rate dependence of variance-to-mean ratio measured for 3He counter (LND-2524) Table 3 Dead time of neutron counterst1 t1 Gate width was specified to 10ms. 2 Obtained by Eq.(7), t3 Obtained t by Eq.(6) VOL. 33, NO. 11, NOVEMBER 1996

6 868 K. HASHIMOTO et al. ACKNOWLEDGEMENTS The present work was performed as a joint research program of the UTR-KINKI at the Kinki University Atomic Energy Research Institute under the support and cooperation by the Section of Kinki University Cooperation Use, Faculty of Engineering, Osaka University. The authors express their gratitude to Drs. T. Koga and H. Morishima of Kinki University for useful discussion and assistance in the measurement. This work was supported by the science research promotion fund from Japan Private School Promotion Foundation. -REFERENCES- (1) Knoll, C.F.: "Radiation Detection and Measurement", Chap.4, John Wiley & Sons, (1989). (2) Muller, J.W., et al.: Nucl. Instrum. Methods, 112, 47( 1973). (3) Hashimoto, K., Ohsawa, T.: Nihon-Genshiryoku- Gakkai Shi (J. At. Energy Soc. Jpn.), 36[3], 227 (1994), [in Japanese]. (4) Muller, J.W.: Nucl. Instrum. 1974). Methods, 117, 401( (5) Szeless, A., Ruby, L.: Trans. Am. Nucl. Soc., 12[2], 739 (1969). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY