Neutron cross section, average

Bound neutron scattering lengths and neutron cross sections averaged over a Maxwellian spectrum at 30 keV for astrophysical applications are also presented. A list of the major references used is given below. The literature cutoff date is January 2003. Uncertainties are given in parentheses. Parentheses with two or more numbers indicate values to the excited state(s) and to the ground state of the product nucleus. 

Neutron cross sections themselves follow no trend. Moreover, as was shown above, quite different values are foimd for different isotopes of the same element. This is extensively exploited in dif action studies of liquid solutions [4]. Occasionally, when isotopes of the same element have scattering lengths of opposite sign, the average coherent cross section can be reduced to zero by making a sample with the correct proportions of each isotope. Such null-scattering samples produce only incoherent signals. 

Figures 2-6 present some important results from the models by Leya et al. (2000a) and Masarik et al. (2001). Figure 2 shows that both models do reproduce the measured Ne depth profile in Knyahinya well, and hence can be expected to reliably predict nuclide production in meteorites of a wide range of sizes. Remarkably, secondary neutrons contribute about two thirds to the total Ne production at the surface and this fraction increases to 85% near the center. This illustrates the importance of reliable neutron cross section data. Figures 3 and 4 show the He and Ne production rates, respectively, in the two most abundant meteorite classes, the H and L chondrites, as a function of depth and size. As noted above, for average-sized meteorites (R < 40 cm), production rates vary within only about a factor of 1.5. On the other hand, for the Gold Basin chondrite with its preatmospheric radius of perhaps 3 m, nuclide concentrations vary by more than an order of magnitude (Kring et al. 2001 Wieler et al. 2000b). This meteorite is almost represented by the lines denoting an infinite radius (2ti).

Astrophysical Cross Sections, averaged over a stellar neutron maxwellian spectrum characterized by a thermal energy of 30 keV, expressed in barns (10 cm ), millibarns (mb) or microbarns (pb). 

As mentioned earlier, fission or fast neutrons five rise to threshold reactions of the type (n,p), (n,a), and (n,2n). With Z = atomic number, the first and the second lead to the production of respectively, Z-1 and Z-2 radionuclides, e.g., Fe(n,p) Mn, Cu(n,p) Ni, P(n,a) AI, or Fe(n,a) Cr. Although the cross sections (average fast neutron cross sections or of) for these reactions are low compared to those for thermal neutron activation, serious interferences may ensue. 

Fig. 31. Curve prepared by E. Vogt, report BNL 331 (c-21), comparing the variation of i qq vs.. 4 predicted using the two indicated forms for the shape of the strength function in the. intermediate coupling theory to the experimental values deduced from ANL—yn 1]. Here i oo is related to the shift in the average value of the R matrix for neutron scattering from the value it would have for the uniform model. The average behavior near individual nuclear levels is E — /e cot [nEJD) + i oo where = distance from nearest level. The cross section averaged over levels is d — 4n[ a — R(X)) +XR9], where a = nuclear radius.

It has been found that a reactor with 1.35 kilograms of U235 disposed in a rectangular core 51 centimeters X 11 centimeters X 66 centimeters with a thirty-centimeter beryllium reflector constructed with aluminum structural proximately twice the ratio of the neutron scattering cross 35 material and water moderated, the volume ratio of alumi-section to neutron absorption cross section averaged over mini to v/ater being 0.65, is critical and exhibits the... 

The corresponding neutron cross-section is readily obtained. Assuming that the neutron beam is unpolarised, the average of over neutron spin states is... 

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. 

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. 

W. R. COBB, 123-Group Neutron Cross Section Data Generated from ENDF/B-II Data for Use in the XSDRN Discrete Ordinates Spectral Averaging Code, DCL-16, Radiation Shielding Information Center (1971). 

The nuclear reaction (b) is chiefly induced by thermal neutrons and shows a cross section of 6 10 cm (Maxwell spectrum, T=575 K). Reaction (c) on the other hand is induced by fast neutrons with an effective threshold energy of 2.4 MeV the cross section averaged over the flux of neutrons with energies beyond this threshold value amounts to 8.5 10 cm . Using this data and assuming a lithium concentration of 2 ppm (99.99% Li), which is held constant... 

The material of the infinite medium is characterized by neutron cross sections Sa( ), 2,(J ), and / E)y and v is the average number of neutrons per fission. We define... 

The cosin function describes the modulation with a period h over the cylinder of length L = 2Nh. c is the average amphtude of the modulation. Unfortunately Eq. 32 and the following caimot not be solved analytically. Nevertheless, a numerical solution can describe the sahent features of the neutron cross-section, from an ensemble of cylinders of radius a and length L, which are randomly oriented and display a modulated density along the axis. 

The preceding theory is a special case of a general quantum-mechanical treatment of neutron cross sections. With high neutron-flux sources (reactors), and the development of velocity selectors (choppers, spectrometers) which permit measurements at chosen velocities, the cross-section values obtained are more accurate, but the methods much more complex. The above theory shows how the first cross-section measurements were made. The presentation of this simple method is further justified by the fact that many cross sections have been measured as averages in the same way, and for some materials this simple method is still very useful. 

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