Constant and Neutron Flux

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. 

To determine the expressions for the optimised counting times, we write the expressions (10) and (11) in terms of count-rates and times (count rates are constant quantities for each Bragg reflection). We assume that the incident neutron flux is constant during a flipping ratio measurement, and that no dead-time correction is needed. In these conditions, we have the relations ... 

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). 

As given in Equation (5.7), the neutron production rate can be expressed as a function of U content. From the production rate, we can calculate the neutron flux (X) with the relation fn = v x n, where v denotes the mean velocity of neutrons and n is an equilibrium concentration of neutrons. The latter quantity is related to the neutron production rate (pn) as n = (pjt) where T denotes the time constant for the neutron absorption in the medium (-2500 s1). Andrew et al. (1986) estimated the average neutron flux in the Stripa granite to be 5.5 x 10 4 neutrons cm 2s, which is in good agreement with the measured flux of 4.7 x 10 4 neutrons cm 2s 1 in the borehole in the granite. 

In the correlation method the neutron flux density of the specified region is determined from the ratio of pulse measmement channel count rate to detector sensitivity s(E). If we assume that the neutron spectrum in the area of neutron detector location does not depend on the type of SRP being stored in the pit, then for all the measurements s(E) is a constant value. In the next calculations it can be assumed as 1 and thus, the coimt rate being measured can be assumed equal to the value of proportional neutron flux density. 

Pulsed research reactors, such as reactors of the Triga type, are especially designed for production and investigation of short-lived radionuclides. In these reactors the neutron flux is increased for about 10 ms to about 10 cm s by taking out the control rods (section 11.5). Due to the negative temperature coefficient of the zirconium hydride moderator, the outburst of power causes a sudden decrease of the moderator properties and shutting off of the reactor. After several minutes the effects have vanished and a new pulse can be started. The activities of radionuclides of various half-lives obtained with pulsed reactors are compared in Table 12.2 with those produced at constant neutron flux densities. The table shows that pulsed reactors are useful for production and investigation of radionuclides with half-lives < 10 s. 

The D2O ice samples investigated in this context were prepared inside vanadium sample cans inside an Orange Cryostat on the constant wavelength neutron powder diffractometers D2B (wavelength 1.6 A) and (wavelength 2.4 A), based at the high-flux reactor of... 

The homogeneity has been checked at three occasions once prior to the intercomparison work and the first part of the certification, once after the ampouling prior to the second part of the certification, and once at the stage of the F and Cl certification. The first series of tests were carried out by instrumental neutron analysis (INAA). Samples were irradiated with thermal neutrons in a tube container for 10 min, or for 40 h when mounted on a turntable. In the first case the neutron flux was kept constant. 

When analysing the results of a neutron experiment we shall need to relate the number of neutrons seen in a detector of small area, dA, as it is positioned at different scattering angles around the sample, see Fig. 2.1. The detector subtends a small solid angle, di2, at the sample. The number of neutrons per unit time, or flux, scattered to the detector, Jf, is directly proportional to the incident neutron flux, Ji. It is also proportional to the size of the detector but inversely proportional to the square of the distance, d, between the sample and the detector, also df2= 6A / d. The differential cross section, dcr/d/2, is the constant of proportionality. 

The assumption of a constant speed, c , implies that the reactor flux will be proportional to the neutron density, n. The fission rate of the reactor per m of fuel, F, is given by the product of the neutron flux and the total cross-sectional area for fission ... 

To specify completely the neutron activity and to choose the proper cross sections for calculating the reaction rate constant, it is necessary to know the distribution of neutron concentration, or neutron flux, with respect to energy. In a thermal reactor the distribution of neutrons in thermal equilibrium with nuclei at an absolute temperature T is similar to the distribution of gas molecules in thermal equilibrium and can be approximated by the Maxwell-Boltzmann distribution... 

In reactor control problems and in reactor neutron balances, the quantity of interest is the poisoning ratio r, which is the ratio of neutrons absorbed by the poison to neutrons absorbed in fission. Assuming for simplicity that the neutron flux is constant throughout the reactor, the xenon poisoning ratio at steady state is... 

For irradiation in a constant neutron flux, the activity of any fission-product nuclide can be evaluated from the equations in Chap. 2. When fissions occur at a constant rate and when neutron-absorption reactions in the fission product and its precursors can be neglected, the activity of a nuclide with relatively short-lived precursors can be evaluated by applying Eq. 

Consider an emitter with an average neutron absorption cross section a exposed to a total neutron flux (f), and upon absorption of a neutron becoming radioactive with a half-life T [or decay constant A = (In2)/T]. The number of radioactive atoms NU) present after exposure for time t is (see Eq. 14.16)... 

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