Neutron flux definition

Neutron flux density is the number of neutrons that enter a sphere of unit cross-sectional area per unit of time. This quantity is sometimes defined in terms of a unidirectional beam of neutrons incident perpendicularly upon a unit area, but this definition is less general. It is also sometimes called neutron current density. 

Vector analysis. The author learnt vector analysis in a 1950 postgraduate course, based on the German book of 1932, Classical Electricity and Magnetism, by M. Abraham and R. Becker, published by Blackie and Sons, Glasgow. The book was written so that its definitions of scalar flux (flow in all directions) and of vector current (flow in one direction) fitted both hydrodynamics and electromagnetism. The same definitions were carried over unmodified into the scalar neutron fluxes and vector neutron currents of the nuclear power reactor. In electrochemistry, however, the term exchange current attaches to what is more properly described (see above) as a local, somewhat anisotropic, scalar flux. 

How do you find the distance between the hydrogens in these structures to determine if they are dihydrogen or hydride complexes The definitive method is neutron diffraction from a large crystal. Our structures were determined by Tom Koetzle and co-workers at Brookhaven at the high neutron flux reactor. There are only a few places left in the world to do this now that the Brookhaven National Laboratory facility has been closed. Typically dihydrogen ligands have large ther-... 

It is generally agreed that neutron activation analysis has shown great sensitivity for many elements. Absolute sensitivities of detection depend on the atomic weight of the element, the fractional abundance of the target nuclide, and its cross section for thermal neutrons (which are fixed values) as well as on the available neutron flux, the irradiation time, the decay period, and the counting efficiency of the detector (which are variable parameters). The formulae described under Fundamentals (vide supra) will make it clear that, unless conditions are exactly specified, published values cannot easily be compared especially as the definitions for sensitivity chosen by the investigators may be different. Experimental sensitivities may be idealized because of matrix problems, difficulties in radiochemical separations, and other analytical problems associated with the analysis of complex, real samples. 

The location of the capsule is important because the flux profile varies both axially and vertically in the vessel. Rgure 4.4 shows the typical placement of surveillance capsules in the reactor vessel. The capsule will experience a higher neutron flux than the reactor vessel wall, depending on how close to the core the capsule is positioned.The term used to characterize the difference in flux is lead factor, usually defined as the ratio of the neutron flux E> MeV) at the location of the capsule specimens to the peak neutron flux E> MeV) at the RPV inside surface. Sometimes, lead factor is expressed as the ratio of the capsule flux to the flux in the vessel wall at the 1/4-thickness (1/4-T) position (not at the inside wall), so it is important to specify which definition is used in order to avoid confusion. 

Heterogeneous assemblies. In heterogeneous systems the situation is obviously much more complicated, since the neutron flux depends strongly on position. In order to have a definite picture, we assume a cell structure with volumes Fo of the absorber and Fi of moderator. 

Thus, Ij. is the contribution to the effective group cross section for group / due to process x from all resonances of sequence (i). It is shown in Section IV that, if < ( ), the energy-dependent neutron flux, is known exactly, then, as is well known, this definition of the multigroup cross sections leads to exactly the same value of the multiplication constant as the continuous energy diffusion theory. 

The neutron flux above 0.5 eV is characterized by an l/Elaw. This also appears in Fig. 57.3 showing that the product of neutron flux and energy is constant from 10 eV up to 10 eV ( thermal reactor ). This dependence allows for a convenient definition of a nominal flux of epithermal neutrons and the corresponding reaction cross sections (resonance integrals). 

The thermophysical state of a material may be defined as the end result of prior thermal treatment and its interaction with mechanical deformation introduced in the final fabrication process. All of these conditions can have an effect on corrosion emd must be characterized for definitive analysis. Surface condition of a specimen may also have an important influence on corrosion rate. The thermophysical condition of a material under test may be affected by the exposure environment. For example, if the intended application for a given metal or alloy is as a component in a nuclear reactor, then care should be exercised to ensure that high neutron fluxes do not significantly alter predicted corrosion behavior. Radiation can enhance nucleation reactions, and this may result in precipitation at lower than normal temperatures, or precipitation of normally unstable phases. In addition, radiation can dramatically affect the defect structure of a material and, therefore, significantly... 

A statement of the neutron-balance condition involves the collision densities of the various possible neutron-nucleus reactions. The collision densities, in turn, may be described in terms of the neutron densities and the appropriate cross sections [cf. Eq. (3.5)]. Although the neutron density n is the fundamental quantity which describes the neutron population, it is frequently more convenient in reactor calculations to work with another function, called the neutron flux. The neutron flux 0 is related to the neutron density through the definition (y = neutron speed)... 

It should be recognized that if it is desired to use the relation (4.132) in an actual computation, instead of the simpler form (4.134), it is necessary to carry out an iterative procedure. This complication arises from the definition of y(u) which involves the neutron flux [see Eq. (4.131)]. This difficulty may be overcome by following the procedure outlined below As a first approximation use Eq. (4.134), and call the corresponding expression for the flux i(m) thus,... 

Consider an infinite medium in which there is a spatially constant neutron flux introduce a spherical cavity of radius 72 and use the theorem stated above, along wdth the definition of neutron flux (i.e., the flux is the neutron track length per unit volume per unit lime), to show that the first term in the expression for the partial current in terms of the flux is 0/4. 

In view of the maturity of the SANS technique it is surprising that data are still published in arbitrary units that are functions of the timescale of the experiment and/or the sample dimensions (e.g. thickness). Conversion to an absolute scale may be accomplished by multiplying by a calibration constant and, as explained in Section 7.1.2, the absolute cross section dS/dS2(0) is defined [116] as the ratio of the number of neutrons scattered per second into unit solid angle divided by the incident neutron flux (neutrons cm s ) and thus has the dimensions of area (cm ). On normalizing with respect to unit sample volume, dS/df2(2) has units of cm From the above definition, the relationship between the cross section and the measured count rate I(Q) (counts s ) in a detector element with area Aa and counting efficiency s, situated normal to the scattered beam at a distance r from the sample, is given by... 

The units of neutron flux are neutrons per cm per second. The description of the situation at any point in a reactor requires an extension of the simple definition given above to take account of the fact that the neutrons there have a wide range of energies and may be traveling in any direction. The most general description of the neutron distribution throughout the reactor will be by a function of the form... 

Fig. 3.7. Definition of linear extrapolation distance d. This is obtained by a linear extrapolation of the neutron flux into the region outside the reactor, using the flux gradient at the boundary.

If the sample containing the element to be determined is placed in a homogeneous flux of neutrons, some may be captured by the target nuclei to produce radioactive isotopes. These compound nuclei are unstable, having a definite probability of decay, and some will disintegrate during the bombardment. As a result, concentration of the radioactive species... 

If the neutron density is given as a function of space, speed, and time, then the flux is similarly specified thus, if we use the definition (3.3), the flux is... 

It is sometimes more convenient to describe the neutron population in terms of the neutron kinetic energy instead of the speed. In this event, the neutron density and the flux are defined per unit of energy. In order to show the relationship between the speed and the energy definitions, let us consider the function... 

The distinction arises from the definition of these two types of functions. The fluxes and densities are defined per unit energy (or lethargy, or speed) and therefore require that the width of the interval in question be specified. The cross sections, on the other hand, specify the interaction characteristics between nuclei and neutrons of a particular energy. Figure 4.9 shows a typical cross-section curve given as a function of neutron energy. Note that all three cross sections [Pg.86]

The function Pfi(r r ) defined here will be the kernel in the integral-equation formulation of the neutron-balance equation note that it is independent of energy in this particular model in which the cross sections are energy independent. It should be noted that this definition differs from that given the function K r P) used in the preceding section. Whereas the kernel K represented the flux at r due to a unit source at r the kernel Pb implies a function of the type K multiplied by 2r. This relationship may be seen more clearly if we consider, for example, the quantity 2rif(r r ) dr, a physical interpretation of which is... 

In order to progress from Eq. (8.398) when confronted with the unknown variation of the neutron cross sections and the flux with lethargy, the following definitions are made ... 

Figure 28.8 shows that this idealized method assumes that no neutron below the effective energy contributes to the reaction and that all the neutrons above Egf are assumed to have the same cross section, Oq. The reaction rate is held constant with area A being made equivalent to area B. If a fission spectrum is definitely present and the detector cross section for the reaction has the proper shape, the accuracy of the measurement will depend on the determinations of the detector activity. The fast flux above 2.9 MeV for the sulfur detector will be expressed as... 

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