Thermal-neutron region

This simple method for calculating reaction rates in a mixed thermal-epithermal spectrum is called the Hogdahl convention (Hogdahl, 1965). It assumes that in the thermal neutron region the activation cross section varies with neutron energy as the 1/v law. This is... 

The assumption that the activation cross section varies with neutron energy as 1/v in the thermal neutron region is valid for most (n,y) reactions. The two reactions that deviate the most from the 1/v assumption are Lu(n,y) Lu (typically +0.4%/K) and Eu(n,y) Eu (typically —0.1%/K). The reaction rates for these two reactions, relative to a monitor reaction like Au(n,y) Au, will depend on the thermal neutron temperature in the irradiation channel used. A new set of equations, the Westcott formalism (Westcott 1955), was developed to account for these cases and used the Westcott g T ) factor, which is a measure of the variation of the effective thermal neutron activation cross-section relative to that of a 1/v reaction. In the modified Westcott formalism, the following differences are also included the Qo(a) value of the Hogdahl formalism is replaced by the So(< ) value, and the thermal to epithermal flux ratio, f, is replaced by the modified spectral index, r a) TJTo). To use this formalism with the kg method (De Corte et al. 1994), it is necessary to measure the neutron temperature, r , for each irradiation and a Lu temperature monitor should be irradiated. The Westcott formalism needs to be implemented only when analyzing for Lu and Eu. There are several other non-1/v nuclides Rh, In, Dy, Ir, and Ir, but for these the error... 

The cross sections for (n,y) reactions common in reactor thermal neutron activation generally decrease with increasing neutron energy with the exception of resonance-capture cross section peaks at specific energies. This reaction is, therefore, not important in most 14 MeV activation determinations. However, some thermalization of the 14 MeV flux may always be expected due to the presence of low Z elements in the construction materials of the pneumatic tubes, sample supports, sample vial, or the sample itself (particularly when the sample is present in aqueous solution). The elements Al, Mn, V, Sn, Dy, In, Gd, and Co, in particular, have high thermal neutron capture cross sections and thermal capture products have been observed in the 14 MeV neutron irradiation of these elements in spite of care taken to reduce the amount of low Z moderating materials in the region of the sample irradiation position 25>. 

A systematic diffraction study was made with both neutrons and x-rays of metal- hydride systems in the composition range of 2 to 66.5 atomic % hydrogen of hafnium, titanium, and zirconium, and a nuclear null-matrix consisting of 62 atomic % titanium and 38 atomic % zirconium, with emphasis on the metal-rich regions. A nuclear null-matrix as defined here consists of two or more types of nuclei in which some of the nuclei scatter thermal neutrons 180° out of phase with others, such that the resultant structure factor is zero. 

The physical process of resonance neutron scattering is through the formation of a compound nucleus . Cd, and Gd belong to the small class of nuclei which exhibit a resonance in the thermal energy region. In the case of Cd the compound nucleus Cd will either eject a neutron in an (n, n) process or emit y-rays in an (n, y) process the latter being inelastic. Unlike in X-ray anomalous dispersion, in the present case both the elastic (n, n) and inelastic (n, y) processes contribute to b"(0) ... 

In the fission of a heavy nucleus, many products are formed in detectable amounts throughout the mass region 72 to 161. In general, thermal neutron fission results in two unequal mass fragments which fly apart with a total kinetic energy of about 170 Mev. The most probable heavy mass is around 139 and the most probable light mass is around 95. 

The preceding considerations permit to draw some reasonably well founded conclusions for the prospects of a chain reaction in a lattice arrangement. In such an arrangement, for the same ratio iVu of U and slowing down molecules, the loss caused by the absorption of the latter is larger, the loss caused by the radiative capture is smaller. In both the thermal and the non-thermal region, the inner part of the U sphere is protected from the neutrons by the outer portions. This has a favorable effect as far as the radiative capture absorption is concerned but an unfavorable as far as the absorption of thermal neutrons is considered. 

To compute the thermal utilization from the thermal neutron densities in the three regions, we must first compute the total slowing down powers, Pq and P2 of the water and the graphite. Taking the effective hydrogen scattering cross section to be 15 X 10 (which underestimates the scattering power of the water), we have... 

The physical interpretation of (15) is quite simple. If the neutrons did not diffuse while in the thermal region but all the diffusion took place in the fast neutron region evidently Uf would be continuous and likewise the product of the derivative of n/ with the diffusion constant. On the other hand, if all the neutron diffusion took place while the neutrons are thermal, rtt would be continuous and so would the thermal diffusion constant times the derivative of rtf. If the diffusion takes place for both thermal and fast neutrons one must expect that a linear combination of the above quantities will be continuous with coefficients which are proportional to the amount of diffusion in the corresponding regions. This is exactly what the above equations show. 

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