The optimization is accomplished on the basis of methods used for checking statistical hypotheses. Two possible methods for processing information from γ-ray detectors are examined: setting a threshold according to a general likelihood ratio including all combinations of detectors or separate combinations of detectors. In the second case, all possible combinations of detectors must be sorted when the measurements are analyzed. Calculations for a specific setup with six detectors show that sorting detector combinations permits detection of smaller quantities of explosives than can be done with a general likelihood ratio. A sequential analysis instead of sorting detector combinations permits identifying explosives more quickly than can be done with a general likelihood ratio.Neutron-radiation analysis is one method for detecting exlosives in transportation hubs and in companies [1][2][3][4]. The method is based on the capture of thermal neutrons by nitrogen isotopes followed by the emission of γ rays, which are detected by a detector. Most explosives contain from 16 to 40% nitrogen (25% on the average) while ordinary materials in objects which are checked contain up to 28% nitrogen (10% on the average) [5]. The most informative part of the γ-ray spectrum in detecting nitrogen corresponds to the range 10-11 MeV [1,3]. Since an explosive can be found at any location of an object being checked, several detectors are used to detect γ rays. This makes it possible to indicate the relative location of an explosive and to estimate its quantity. The observable random quantities are the sums of the numbers of detector count n ik over N successive time intervals with duration ∆t:where k is the number of the successive time interval; i is the number of the detector, i = 1, 2, ..., Q; and Q is the number of detectors. The measurement time is N∆t. When analyzing measurements, the indications of each detector can be examined separately or the indications of several detectors can be summed. It is useful to divide the space of the measurement chamber into sections according to the number of detectors used. An explosive can be present in one or several of these sections. Thus, when measurements are analyzed, the relative configuration of the detectors and the explosive must be taken into account. The present paper analyzes methods of information processing that can be used to detect the smallest mass of explosives.Since γ-ray detection is of a random character, a judgement as to the presence or absence of an explosive on the basis of measurements must be regarded as a check of statistical hypotheses [6,7]. Two alternative hypotheses are checked: an explosive is present in one or several sections of the measurement chamber (hypothesis 1) and there is no explosive (hypothesis 0). An indicator that an effect is present (in this case an explosive) is that a selected threshold for the number K n i k i k N = = ∑ 1 ,

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The calibration of the energy scale of a device which is a spectrometer and is to be used for detecting explosives in various objects (baggage of airline passengers, mail, briefcases, cases, and others) is examined. The work is based on the method of neutron-radiation analysis. In the present case the calibration is of fundmental importance because the nitrogen sensitivity of the device is low. A brief description of a working model, the basic characteristics, the background spectrum of capture radiation with a sample of nitrogen-containing substance, and an example of a calibration curve are presented. The method of check sums and its advantages are examined. It is shown that it can be used in setups for detecting explosives.Today there are various methods for detecting explosives. Operational systems have been developed in our country and abroad on the basis of these methods [4][5][6][7]. Specifically, neutron-radiation analysis is used to detect explosives according to the elemental composition. This method is well known and is used successfully in various branches of science and technology [1-3], including searching for explosives. Analysis of the operation of the setups using various methods of detection [6][7][8] shows that in most cases it is difficult to satisfy all requirements which a real setup must satisfy. We note that from the standpoint of use in practice, irrespective of the method of detection, the reliability of the setup, simplicity of operation, and accessibility for repair are important. Application of the Method of Neutron-Radiation Analysis for Detecting Explosives.It is well known that the method of neutron-radiation analysis is based on irradiation of an object by a flux of thermal neutrons and detecting the spectrum of the capture γ radiation using spectrometric detectors. Since the nitrogen content in most explosives widely used today is 25% [7], the detection of a high nitrogen concentration in an object being inspected could indicate the presence of explosives in it. The difference of the spectrum of capture radiation of nitrogen from the spectra of other elements is that nitrogen contains a 10.83 MeV γ-ray line [1], which makes it possible to avoid the difficulties associated with complete interpretation of the spectrum of the object being inspected. The main requirement for the setup is detection with a prescribed probability of a definite amount of explosive in the shortest possible time time. The procedure should be conducted automatically to avoid any influence of a subjective factor on decision making. Given the presence of modern personal computers, the time required to process the information and make a decision is negligible compared with the total inspection time. Consequently, complicating the algorithm in exchange for increasing the size of the instrumental part of the system is justified, since doing so does not increase the inspection time and, aside from decreasing the cost of the system, makes it possible to satisfy the requirement of higher reliability.

Two methods of setting the threshold for determining the difference of one γ-ray spectrum from another in the case where these differences are related with the presence of explosives are compared. In the first method, the threshold is set according to a general likelihood function corresponding to the energy channels of the spectrum. In this method, to improve the detection characteristics the number of counts in the channels must be multiplied by weighting factors. In the second method, the threshold is set according to the channel combinations. Here it is necessary to sort through the channel combinations. The calculations of the detection characteristics are performed for two setups: a neutron-activation channel is used in one and inelastic neutron scattering is used in the other. It is established that in this case the threshold setting according to the channel combinations gives better detection characteristics than threshold setting according to a likelihood function. Detection quality increases as the number of processing channels increases.To detect explosives by means of neutron-radiation analysis of inelastic neutron scattering, the background spectrum must be distinguished from the spectrum due to the presence of explosives. Since the nitrogen content in explosives is higher than in ordinary materials, neutron-radiation analysis is performed at γ-ray energies 10-11 MeV [1, 2]. To detect explosives by using inelastic fast-neutron scattering, it is desirable to use as indicators the contents of nitrogen, oxygen, and carbon. The nitrogen and oxygen content in explosives is higher than in ordinary materials and the carbon content is lower. In this case, the γ-ray spectrum is analyzed in a wider energy range 2-7.5 MeV [3,4].The theory of checking statistical hypotheses is used to process the γ-ray spectra; this permits determining on the basis of the measurements the presence or absence of the effect with a prescribed probability of false alarms α and correct detection 1 -β. These quantities depend on, specifically, the chosen threshold, for example, the number of detector counts. An excursion above threshold attests to the presence of the effect. The detection system with an method of analysis of the measurements is characterized by the mass G of the explosive, determined with a prescribed probability of false alarms and correct detection.The optimization of the processing of information coming from many detectors with different threshold setting methods is examined in [5]. In the present work, the considerations used in [5] are applied to optimal processing of γ-ray spectra.The random quantity in detection is the number of detector counts n ik over N successive time intervals with duration Δt. The total number of counts in the ith channel over the entire measurement time is K n i k i k N = = ∑ 1 ,

The concept of the rate of transport of exchange and non-exchange forms of radionuclides over river catchment is introduced. On this basis, a differential transport equation is proposed for finding the radionuclide content in soil and radionuclide flow into a river with nonuniform contamination of the catchment area. The time dependence of the radionuclide wash-off time constant is determined from the measurements. It is found that transport is slow, so that radionuclide decay plays a large role. A large fraction of the radionuclides, aside from the long-lived transuranium nuclides, decays within the catchment area and does not enter the river. The flow into the river is largely determined by the radionuclide content near river edge. Examples of calculations of radionuclide flow into a river and bukhta are presented.To study the transport of radionuclides in a river and its basin, the wash-off from the catchment must be taken into account. This process affects their concentration in the water and soil of the catchment. Balance equation can be used to analyze transport in the catchment. Data from many measurements have been generalized for this purpose [1][2][3][4][5][6][7].The following problems are examined in the present article: 1) the determination of the radionuclide wash-off time constant at a given location in the basin; 2) analysis of the radionuclide content in rivers in the zone of the Chernobyl nuclear power plant, Siberia, Italy, France, and Finland to find the wash-off time constant and its time dependence;3) formulation of the transport equation for a radionuclide in a catchment with a constant wash-off time; and 4) determination of the wash-off characteristics for radionuclides in a river and bukhta using the transport equations, including with nonuniform contamination of the catchment.As a result of the radioactive contamination of catchment due to the operation of a nuclear power plant, enterprises reprocessing nuclear fuel, storage facilities for spent nuclear fuel, and bases for re-fueling reactors and salvaging submarines, radionuclides are transported by surface wash-off to a river (bukhta, lake). During this process, some radionuclides decay and only a fraction reaches a river. The shorter the half-life and the slower transport, the smaller this fraction is.It is assumed in this article that a radionuclide migrates toward a river at a certain rate. This parameter makes it possible to formulate the balance equation for the contamination density of the catchment. The solution of this equation determines the radionuclide flux into the river and the contamination density for known dependence of its flow onto unit surface area of the catchment.Determination of the Wash-Off Time Constant and Transport Rate of a Radionuclide in a Catchment. The transport rate determined from the expressions for the activity per unit area per unit time of the exchange and non-exchange forms

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