Cross section thermal

A possible influence of electric fields on cross sections has in the past perhaps been emphasized more in connection with thermal cross sections than with optical ones. However, as pointed out, for instance, by Monemar and Samuelson (1978), Pantelides and Grimmeiss (1980), and Szawelska et al. (1981), it can also influence optical ones. Figure 18 (Fig. 3 of Monemar and Samuelson, 1978) compares the hole cross section for GaP(0) in the bulk and in a space-charge region. Thus, measurements in bulk appear preferable. The alternate approach of calculating this influence of a held has not yet, to our knowledge, been carried out. 

This velocity, 2200 m/s, is taken as the characteristic velocity of thermal neutrons, and cross sections for neutrons of velocity 2200 m/s (En= 1/ 2mv2 = 0.0253 eV) are referred to as thermal cross sections. 

We are limited in this modeling process by the accuracy with which measurements can be made and by the accuracy of the fission yields and neutron reaction cross sections which are used to interpret the results. As an example consider the Nd- Nd fission product pair, which has been used as an indicator of thermal neutron fluence because the capture cross section for the former is large and for the latter is small. The thermal cross section for l53Nd has recently been listed as 325 ( 10) barns (20), and more recently as 266 barns (11). Using the 325-barn value we deduce an age of about 2 to 27T billion years from neodymium to uranium ratios in the Oklo reactors, while an age of about 1.8 billion years is obtained using the 266-barn figure. 

S. F. Mughabghab, M. Divadeenam and N. E. Holden, Neutron Cross Sections, Vol. 1, Neutron Resonance Parameters and Thermal Cross Sections, Part A (Z = 1—60), Academic Press, New York, 1981. 

The temperature dependencies of the thermal cross sections (reaction constants (k) can be obtained by taking the Boltzmann average of these over velocities. These are... 

The Westcott g and s factors can also be used to determine the effective thermal cross section a, such that when multiplied by the integrated Maxwell-Boltzmann thermal flux the proper reaction rate with a nuclide is obtained, as already defined by Eq. (2.55). From Eqs. (2.55) and (2.62), a is related to a by... 

Also shown in Table 8.2 are the effective thermal cross sections for the individual nuclides, calculated for the neutron spectrum of a typical PWR and including the contributions from resonance absorption. The cross sections are multiplied by the atoms per fission-product pair to obtain the effective cross sections per fission-product pair listed in Table 8.2. Although the total effective cross section of 89.2 b/fission-product pair is calculated for the mixture of radionuclides existing 150 days after fuel discharge, it is a good approximation for the effective... 

NucUde Half-life (S = stable) Atoms per fission-product pair Effective thermal cross sections, b Neutron absorption, bams per fission-product pair... 

Effective thermal cross sections for a typical neutron spectrum of a PWR, including contributions from nonthermal resonance absorption. 

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3,4,82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for the energy dependence of the effective reaction cross section. They often form the basis for the interpretation of the temperature dependence of thermal cross sections. Figure A3.4.5 illustrates several cross section models. 

A. L. Pope and J. S. Story, Minigal Output from UK Nuclear Data Library—NDLI Thermal Cross-sections, Resonance Integrals and Fission Spectrum Averages, AEEW-M1191 (1973). 

A possible resolution of this problem lies in the twin facts that, firstly, Fraites and Winicur obtained the thermal cross-section by extrapolation from the measured range of collision energies, 60—133 meV (5.8—13kJmol" ), and... 

The elementary methods of reactivity calculation, together with the known thermal cross sections and age, yield ... 

The ratio of the thermal cross section to the resonance integral... 

Tabulated values of thermal cross sections, resonance integrals, fission-averaged cross sections, and 14 MeV neutron cross sections are available in the literature (Mughabghab et al. 1981 Mughabghab 1984 IAEA 1987 OECD 1994). Recommended data for the most important nuclides can be found in the Appendix of this volume. 

Mughabghab SF, Divadeenam M, Holden NE (1981) Neutron cross sections, vol 1 neutron resonance parameters and thermal cross sections, part A, Z = 1-60. Academic, New York... 

The table of thermal cross sections typically includes values for monoenergetic neutrons, 0.0253 eV (velocity of2,200 m s ) rather than cross sections averaged over the entire Maxwell distribution. In practice, however, thermal cross sections are measured or used, not for a single velocity, but for the entire Maxwell distribution of velocities present in a nuclear reactor. In the design of nuclear reactors, for example, neutron flux and cross sections appropriate for the entire Maxwell distribution are of course essential, whereas the monoenergetic neutron flux (o) and the corresponding cross sections are most useful in computations of production rates of radionuclides in nuclear reactors. 

The (ast-fisslon factor was determined from the ratio of the activities of a depleted and an enriched uranium foil, the resulting value being 1.0214 0.0021. Thebuclcllng was obtained from the critical size of the assemblies and the extrapolation distance. The latter, which was determined by least-squares fitting the flux distribution, was found to be 2.64 0.3 cm. The average buckling was 6.642 x 10 cm . The thermal-diffusion area, calculated from thermal cross sections, was 1,87 cm . The delayed-neutron age to thermal was calculated by O. G. Sullivan using a Monte Carlo moments-method calculation. The value was 15.6 cm . 

---