Effective neutron temperature

Values of the epithermal spectrum index, r, and ffie effective neutron temperature, Tn. wei deduced from fa-to-Mn and Lu-177-to-Mn acttvation ratios using the technique of Chidley et aL modified to allow for the variation of the g-value of fa with neutron temperature. 

One way in which this shift in the neutron density may be taken into account is by introducing an effective neutron temperature Tn. Thus we define some fictitious temperature Tn which, when used in the function m of (4.196), gives a new Gaussian that yields a better fit to the distorted density distribution arising from the presence of the absorber. The determination of this parameter is deferred until a later section. For the present, all we require is that such a number can be specified for a given system. 

A useful measure of the flux distortion is provided by the concept of the effective neutron temperature Tn- We define this temperature as that number which when used in (4.197) gives the best least-squares fit of a Maxwell-Boltzmann distribution to the computed flux (solid-line curve) in the range 0 < x < 35. The ratio of the effective neutron temperature to the moderator temperature Tn/Ts is indicated in the figure for the first two cases. The ratio has been omitted from the last case (A = 9, = 2 ) because the flux was so severely distorted from a... 

Maxwell-Boltzmann distribution that the concept of an effective neutron temperature was meaningless. It was found that the linear relation... 

Effective neutron temperature Tn, /f,of Maxwell Boltzmann Distribution F lti. 4.30 f factors for fission and absorption cross sections. 

Thus our model replaces the actual neutron distribution by a slowing-down distribution plus a thermal group. The thermal group consists of neutrons of one speed, this speed to be defined by the effective neutron temperature Tn- The actual thermal distribution, which was approximated by the Maxwell-Boltzmann relation (4.200), is replaced then by a spike or group at E = (see Fig. 4.32). The selection of this thermal energy E i, is discussed shortly. 

The next step in the calculation is the determination of the thermal-group properties of the core constituents based on the effective neutron temperature T [see Eq. (4.211)]. An estimate of this temperature requires, however, a value of the parameter k which involves the absorption cross section of the mixture. 

At this point we interrupt the calculation to check our assumed value for the effective neutron temperature, using the absorption cross sections computed above. The expression for k required for this calculation is given by... 

We compute next the macroscopic cross sections of the core constituents. These calculations are based on the microscopic cross-section data of Table 2.2. In the usual way we estimate first the effective neutron temperature from Eq. (4.211). It can be shown that this temperature is 330°K. We use this figure to compute the macroscopic absorption cross sections for the D2O and the aluminum based on the assumption of a l/v dependence for (Ta. We obtain from Eqs. (2.54) and (4.245)... 

The first group in a rather arbitrary ordering of the experiments is devoted to studies of the behavior of neutrons from fission or source energy to thermalization. Moderation and diffusion properties, diffusion length, and Fermi age are measured in a water tank facility at a reactor. Distribution of thermalized neutrons can be measured in several uraniumbearing exponential facilities in which neutron multiplication occurs and from which material buckling and critical reactor size can be inferred. In another exercise, the effective neutron temperature in two of the critical training reactors is measured by several methods. 

In the first part of this experiment the diffraction of neutrons by a single crystal is demonstrated and neutron wave properties experimentally verified. To do this, a crystal spectrometer is aligned in a beam of neutrons and a rocking curve is measured. The resolution of the spectrometer is calculated. The energy spectrum of neutrons coming out of the reactor beam hole is then measured and compared with the calculated theoretical distribution. The approximately Maxwellian shape of the beam spectrum is thus shown. The use of the experimental spectrum plot as a direct method for obtaining the effective neutron temperature is demonstrated. 

Early studies, which did not include many high-order reflections, revealed systematic differences between spherical-atom X-ray- and neutron-temperature factors (Coppens 1968). Though the spherical-atom approximation of the X-ray treatment is an important contributor to such discrepancies, differences in data-collection temperature (for studies at nonambient temperatures) and systematic errors due to other effects cannot be ignored. For instance, thermal diffuse scattering (TDS) is different for neutrons and X-rays. As the effect of TDS on the Bragg intensities can be mimicked by adjustment of the thermal parameters, systematic differences may occur. Furthermore, since neutron samples must be... 

The X-N technique is sensitive to systematic errors in either data set. As discussed in chapter 4, thermal parameters from X-ray and neutron diffraction frequently differ by more than can be accounted for by inadequacies in the X-ray scattering model. In particular, in room-temperature studies of molecular crystals, differences in thermal diffuse scattering can lead to artificial discrepancies between the X-ray and neutron temperature parameters. Since the neutron parameters tend to be systematically lower, lack of correction for the effect leads to sharper atoms being subtracted, and therefore to larger holes at the atoms, but increases in peak height elsewhere in the X-N deformation maps (Scheringer et al. 1978). 

The effect of temperature on the bulk structure can be studied by free energy calculations and by crystal dynamics simulations. Infra-red and Raman spectra, and certain inelastic neutron scattering spectra directly reflect aspects of the lattice dsmamics. Infra-red spectra can be simulated firom the force constant matrix, based on interatomic potential models [94-97]. The matching of simulated mode fiequencies with those measured in Raman or IR spectra can indeed be used to develop, validate or improve the form and parameterization of the interatomic potential functions [97]. 

Figure 5 Effects of temperature and Gu HCl concentration on the surface concentration of p-casein at the air/liquid interface. The surface concentration was calculated by fitting a two-layer model to the neutron reflectivity spectra obtained after 8 hours adsorptionfrom a 100 mgjL fi-casein solution. (O), 10°C ( ), 20°C...

Figure 3.16 is a cutaway view of this reactor. The reactor vessel is a cylinder 13 ft in diameter with an ellipsoidal bottom. The top of the vessel is closed with a flanged and bolted ellipsoidal head, which is removed for refueling. When in operation the reactor is filled with water at a pressure of 155 bar (15.5 MPa). The water enters the inlet nozzle at the left at a temperature of 282 C and leaves the outlet nozzle at the right at 317 C. The effective average temperature of the water is 301.6 C, which will be taken as the temperature of the Maxwell-Boltzmann component of the neutron flux. 

In the determination of the number of fissions in an irradiated sample by the use of flux monitors, account must be taken of the flux depression in the sample due to self-shielding to obtain an effective flux. Also, the capture cross sections of the monitors and the fission cross sections of the sample are neutron energy dependent. It is, therefore, necessary to know the eneigy distribution of the neutrons or the neutron temperature and to determine effective cross sections (Section IV). This can be done by using two monitors such as cobalt and samarium, the one monitor being used to determine the neutron temperature corresponding to the neutron distribution as described by Fritze et al. (35). 

For example, at low neutron fluxes Kr (with a half-life of 10.8 years), completely decays before it can capture another neutron and thus Kr is bypassed while at higher neutron densities Kr is produced. Hence the effective neutron density is recorded in the observed Kr/ Kr ratio. Similarly there is a branching at unstable Se, and because the half-life of this nuclide is sensitive to stellar temperature, both neutron density and temperature are recorded in the °Kr/ Kr ratio. 

Ferrand M, Dianoux AJ, Petty W, G. Zaccai G Thermal motions and function of bacteriorhodopsin in purple membranes effects of temperature and hydration studied by neutron scattering. Proc. Natl. Acad Sci. U. S. A 1993, 90 9668-9672. 

Effects 1 and 2 are functions of the bulk temperature of the plates and HjO,respectively. Effect 3 is a function only of the neutron tenq>erature. To determine the neutron temperature from the H O temperature is not easy it is supposed that the two are equal. ... 

E.Creutz, H. Jupnik, and E.P.Wigner, Effect of Temperature on Total Resonance Absorption of Neutrons by Spheres of Uranium Oxide , J. Appl. Phys. 26, 276 (1955). 

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