Neutron distribution knowledge

Even if the full details of the dynamics of moderator atom motion were known, it would not be possible to incorporate all this information into neutron thermalization calculations for reactors. Therefore, it is necessary to work with somewhat simplified models. Especially in the absence of a complete knowledge of the appropriate differential cross sections, it is necessary to compare calculations using these models with clean experimental information on the neutron distribution in position and energy for configurations of interest in reactor physics. 

The radial distribution function plays an important role in the study of liquid systems. In the first place, g(r) is a physical quantity that can be determined experimentally by a number of techniques, for instance X-ray and neutron scattering (for atomic and molecular fluids), light scattering and imaging techniques (in the case of colloidal liquids and other complex fluids). Second, g(r) can also be determined from theoretical approximations and from computer simulations if the pair interparticle potential is known. Third, from the knowledge of g(r) and of the interparticle interactions, the thermodynamic properties of the system can be obtained. These three aspects are discussed in more detail in the following sections. In addition, let us mention that the static structure is also important in determining physical quantities such as the dynamic an other transport properties. Some theoretical approaches for those quantities use as an input precisely this structural information of the system [15-17,30,31]. 

The use of difference methods offers a means whereby a detailed picture of ionic hydration can be obtained 22). For neutron diffraction, the first-order isotopic difference method (see Section III,A) provides information on ionic hydration in terms of a linear combination of weighted ion-water and ion-ion pair distribution functions. Since the ion-water terms dominate this combination, the first-order difference method offers a direct way of establishing the structure of the aquaion. In cases for which counterion effects are known to occur, as, for example, in aqueous solutions of Cu + or Zn +, it is necessary to proceed to a second difference to obtain, for example, gMX and thereby possess a detailed knowledge of both the aquaion-water and the aquaion-coun-terion structure. 

Taking into account that development of a comprehensive model is not feasible given the current state of knowledge, a simple kinetic model Actranf has been elaborated by Harper et al. (1992). In this model, the primary circuit is divided into three main sections the coolant, the in-core surfaces and the out-of-core surfaces. Cobalt is introduced into the system by release from circuit materials, either as Co from any point in the circuit or as Co from activated materials in the neutron field. Both isotopes are removed from the coolant to the purification system by a first-order process, and are also removed from the circuit when they have been deposited on fuel assembUes that are withdrawn from the reactor in the course of refuelling. Co is converted to Co by neutron activation when it is deposited on fuel surfaces or when it is contained in the internals of the reactor pressure vessel. Thus, unlike the models described above, Actranf considers both possible Co sources the calculations showed that activation of Co which is temporarily deposited in the reactor core is only a small contributor when compared with the direct release of Co from in-core sources, in particular in plants equipped with Stellites inside the reactor pressure vessel. Distribution of cobalt isotopes around the surfaces of the primary circuit proceeds by exchange of dissolved species with the coolant deposition and re-release are assumed to be first-order processes. The first applications of the model to operating plants with and without Stellite materials in the primary circuit have yielded encouraging results. 

Therefore, knowledge of these scattCTing and spectroscopic methods applied to ionic solutions is quite useful for clay-water-ion interface simulations. They discussed the utility of the computational results directly comparable to the scattering and spectroscopic methods. These includes radial distribution function comparison (MD or MC with X-ray or neutron diffraction methods), angular distribution of water molecules around ions (MD or MC with neutron diffraction measurements), self-diffusion coefficient of water and ions (MD with quasi-elastic neutron scattering and NMR measurements), and intramolecular vibrations (flexible potential MD with IR or Raman spectroscopic data). 

The detailed features of the chain reaction are determined by the various nuclear processes which can occur between the free neutrons and the materials of the reactor system. As in chemical chain reactions, the rates of the reactions involved in the chain are directly dependent upon the density of the chain carrier, in the present case the neutrons. Thus in order to determine the various properties of a reactor, such as the power-production rate and the radiation-shielding requirements, it is necessary to obtain the fission reaction rate throughout the system and, therefore, the neutron-density distribution. In fact, all the basic nuclear and engineering features of a reactor may be traced back ultimately to a knowledge of these distribution functions. 

The subject of reactor analysis is the study of the analytical methods and models used to obtain neutron-density-distribution functions. Since these functions are intimately related to various neutron-induced nuclear reactions, a knowledge of at least the basic concepts of nuclear physics is essential to a thorough understanding of reactor analysis. 

Much of the attention in reactor analysis is devoted to the calculation of the fractions/a, / , etc., defined above. A knowledge of these quantities forms the basis for determining the neutron-density distributions in the reactor. We will later derive suitable procedures for computing these quantities, not only as a function of the spatial coordinates, but also in terms of other independent variables of interest, such as the neutron energies. 

The frequency function can be computed from our knowledge of the distribution of absorption reactions throughout the entire medium. Now qo is the total number of absorptions per unit time in this system and Sa (r) dr the absorptions per unit time in dr at r. Thus the probability of a neutron being absorbed in dr at r, namely, the function /(r) dr, is simply... 

A measurement of the quantity A soo is obtained from a knowledge of the actual flux distribution in the test specimen. The usual experimental procedure is to obtain a measure of the relative flux at various stations along the axis of the parallelepiped by means of metallic foils. The activation of these foils due to neutron captures is directly proportional to the flux level at the foil. Thus a plot of the foil activities as a function of position along the axis will yield a curve having the spatial form of the axial thermal flux. Moreover, if this curve is drawn on semilog paper, it will display a linear behavior in the intermediate range AS, as shown in Fig. 5.266. The slope of this curve yields the quantity fcaoo. But, from (5.243) we have that... 

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