The Neutron Flux

The neutron flux is a scalar quantity that is used for the calculation of neutron reaction rates. In most practical cases, the neutron source does not consist of a parallel beam of neutrons hitting a target. Instead, neutrons travel in all directions and have an energy (or speed) distribution. A case in point is the neutron environment inside the core of a nuclear reactor. Neutron reaction rates are calculated as follows in such cases. 

Consider a medium that contains neutrons of the same speed v, but moving in all directions. Assume that at some point in space the neutron density is n (neutrons/m ). If a target is placed at that point, the interaction rate R [reactions/(m s)] will be equal to 

I distance traveled by all / probability of interaction per unit neutrons in 1 m / distance traveled by one neutron 

The product nv, which has the units of neutrons/(m s) and represents the total pathlength traveled per second by all the neutrons in 1 m, is called the neutron flux /  

Although the units of neutron flux are /(m s), the value of the flux (r) at a particular point r does not represent the number of neutrons that would 

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The RCCA s (32 to 52 assemblies in the core), regulate the neutron flux in the reactor, and are used for emergency shutdown of the reactor activity. In normal working conditions, the RCCA s are suspended above the fuel elements. 

Account must be taken in design and operation of the requirements for the production and consumption of xenon-135 [14995-12-17, Xe, the daughter of iodine-135 [14834-68-5] Xenon-135 has an enormous thermal neutron cross section, around 2.7 x 10 cm (2.7 x 10 bams). Its reactivity effect is constant when a reactor is operating steadily, but if the reactor shuts down and the neutron flux is reduced, xenon-135 builds up and may prevent immediate restart of the reactor. 

Production in Target Elements. Tritium is produced on a large scale by neutron irradiation of Li. The principal U.S. site of production is the Savaimah River plant near Aiken, South Carolina where tritium is produced in large heavy-water moderated, uranium-fueled reactors. The tritium may be produced either as a primary product by placing target elements of Li—A1 alloy in the reactor, or as a secondary product by using Li—A1 elements as an absorber for control of the neutron flux. 

NAA is a quantitative method. Quantification can be performed by comparison to standards or by computation from basic principles (parametric analysis). A certified reference material specifically for trace impurities in silicon is not currently available. Since neutron and y rays are penetrating radiations (free from absorption problems, such as those found in X-ray fluorescence), matrix matching between the sample and the comparator standard is not critical. Biological trace impurities standards (e.g., the National Institute of Standards and Technology Standard Rference Material, SRM 1572 Citrus Leaves) can be used as reference materials. For the parametric analysis many instrumental fiictors, such as the neutron flux density and the efficiency of the detector, must be well known. The activation equation can be used to determine concentrations ... 

A scram causes the control rods to drop into the core, absorb neutrons and stop the chain reaction. Some rods perform both controlling and scram functions. The control rods are raised to increase the neutron flux (and power) or lowered to reduce it by magnetic jacks (W and CE) or a magnetic "clamshell" screw (B W). The chemical volume and control system (CVCS - not siiown) controls the water quality, removes radioactivity, and varies the reactivity by controUing the amount of a boron compound that is dissolved in the water - called a "poison." Thus, a PWR coiiirols reactivity two ways by the amount of poison in the water and by moving the control rods. 

Since the amount of fissile material in the fuel assemblies is only about 3 percent of the uranium present, it is obvious that there cannot be a large amount of radioactive material in the SNF after fission. The neutron flux produces some newly radioactive material in the form of uranium and plutonium isotopes. The amount of this other newly radioactive material is small compared to the volume of the fuel assembly. These facts prompt some to argue that SNF should be chemically processed and the various components separated into nonradioac-tive material, material that will be radioactive for a long time, and material that could be refabricated into new reactor fuel. Reprocessing the fuel to isolate the plutonium is seen as a reason not to proceed with this technology in the United States. 

This NAA technique is based on the nuclear reactions 23Na(n,7)24Na and 41K(n/y)42K. Half-lives of the activated products are 15.0 hrs and 12.4 hrs, respectively. For Na analysis, the samples were irradiated in a specially designed thermal column to suppress the fast neutron reaction of 27Al(n,a)24Na which interferes with the reaction for Na. For K analysis, the proplnt samples were irradiated at a standard irradiation position of the reactor. For the Na irradiations, the neutron flux in the thermal column was in the order of 1010, whereas for the K assays it was approx 1012 neutrons/cm2-sec... 

In practice the assumption of the uniform heat release per unit length of the rod is not valid since the neutron flux, and hence the heat generation rate varies along its length. In the simplest case where the neutron flux may be taken as zero at the ends of the fuel element, the heat flux may be represented by a sinusoidal function, and the conditions become as shown in Figure 9.20. 

Since the heat generated is proportional to the neutron flux, the heat dQ developed per unit time in a differential element of the fuel rod of length dx may be written as ... 

Because the path of the s process is blocked by isotopes that undergo rapid beta decay, it cannot produce neutron-rich isotopes or elements beyond Bi, the heaviest stable element. These elements can be created by the r process, which is believed to occur in cataclysmic stellar explosions such as supemovae. In the r process the neutron flux is so high that the interaction hme between nuclei and neutrons is shorter that the beta decay lifetime of the isotopes of interest. The s process chain stops at the first unstable isotope of an element because there is time for the isotope to decay, forming a new element. In the r process, the reaction rate with neutrons is shorter than beta decay times and very neutron-rich and highly unstable isotopes are created that ultimately beta decay to form stable elements. The paths of the r process are shown in Fig. 2-3. The r process can produce neutron-rich isotopes such as Xe and Xe that cannot be reached in the s process chain (Fig. 2-3). 

The wire is inserted directly into the core and becomes activated by the neutron flux. 

Intermediate-range nuclear instrumentation consists of a minimum of two redundant channels. Each of these channels is made up of a boron-lined or boron gas-filled compensated ion chamber and associated signal measuring equipment of which the output is a steady current produced by the neutron flux. 

The neutron beam is larger than the dimensions of the sample to be doped hence the neutron flux impinging onto the crystal is uniform. 

The values of E(t) so computed are listed in Table 4. The correction for fractionation of carbon dioxide at the sea surface is a serious one. It makes the interpretation of 13C/12C variations in wood difficult and militates against the use of the isotope ratio of carbon as a thermometer. This correction, when applied to variations of carbon-14 in wood, is able to explain the Suess radiocarbon "wiggles" of about 100 years duration each, without the need to invoke changes in the neutron flux from the sun [54]. 

The sensitivity of the method depends upon the neutron flux, the ability of an element to capture neutrons (the neutron capture cross-section) and the half-life of the induced activity (Ewing 1985 458). This can be expressed as ... 

Although quantification of the elements present in the y spectrum can in theory be achieved from first principles using the equation given above, in practice uncertainties in the neutron capture cross-section and variations in the neutron flux within the reactor mean that it is better to use standards. These standards must be included in each batch of samples irradiated in order to account for variations in neutron flux inside the reactor. For analysis of minor and trace elements calibration is easier than with other analytical methods provided that the major element composition remains reasonably constant, as the y ray intensity is proportional to concentration over a very wide range of concentrations. However, for analysis of major elements, e.g., silver in silver coins, the relationship between intensity and concentration is more complex, due to progressive absorption of neutrons as they pass through the specimen. In such cases y ray intensity will also depend on the thickness of the sample and therefore specialized calibration methods are required (Tite 1972 277). 

Dead time considerations in the alpha particle detection limit the count rate, and hence limit the neutron flux that can be used with this approach. This means that large scan times will probably be required with most implementations of this approach. 

Each temperature step of the stepped heating procedure of the 40Ar-39Ar method yields a date. To calculate this date, one must determine how many 39K atoms in the sample are represented by the measured number of 39Ar atoms. To determine this number, a sample of known age is included as a monitor of the neutron flux. From measurements of this monitor, a parameter J can be calculated (see Appendix). The date for each step of the 40Ar-39Ar measurement can then be calculated from... 

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