Effective cross section, absorption removal

The subscripts /, s, c, and 6 refer, respectively, to the fast flux, slow flux, core region, and blanket region D is the diffusion coefficient is the neutron flux 2/ refers to the effective cross section for removing neutrons from the fast group and 2, refers to the thermal absorption cross section. Other symbols have the same meaning given previously, with k calculated on the basis that (ep)fuei= 1. 

The attenuation coefficient for a beam of gamma rays is related to the number of gamma rays removed from the beam, either by absorption or scattering. For the Compton effect, the absorption cross section is determined by the energy absorbed by the electron, which is the total collision energy minus the average scattered photon... 

Conservation of energy requires that the light removed from the incident beam by the particle is accounted for by scattering in all directions and absorption in the particle. The combined effect of scattering and absorption is referred to as extinction, and an extinction cross section (Cext) can be defined by... 

Absorption of Neutrons. All materials within the neutron-generating volume of the vessel will remove excess neutrons by non fission capture or absorption. The degree of effectiveness of removing neutrons is a fundamental property of the atom and is measured in terms of a cross section. Tables listing absorption cross sections for all the elements can be found in general reference books listed in the References for this chapter. 

The scattering length R may also be determined from direct measurements of the total cross section in thick material. In this case, the neutrons with energies corresponding to the resonance energies are removed by absorption and the measured transmission depends mainly on those neutrons whose energies lies between resonances. These neutrons are attenuated effectively only by potential scattering. 

Coherent two-photon spectroscopy is a well-known technique that eliminates the Doppler effect, but suffers from the low cross sections o/g for the coherent absorption of two photons of equal frequency. For quasiresonant two-step excitation the overall absorption cross section is considerably larger, but the Doppler effect is only partially removed. For example, a residual Doppler width (FWHM)... 

This quantity may be called an effective-removal cross section and is related to the actual-removal (total) cross section by the addition to of a time-absorption term a/v. If solutions of the form (7.244) exist, then we have succeeded in reducing the time-dependent problem to an equivalent steady-state problem which describes the neutron economy in a system with total-removal cross section 2 and a source term identical to that of the actual system. 

Losses in shielding efficiency may occur as a result of environmental conditions. Effects that should be taken into account are those due to the interactions of neutron and gamma rays with the shielding (e.g. the burnup of radionuclides that have a high neutron absorption cross-section, radiolysis and embrittlement), those due to reactions with other materials (e.g. erosion and corrosion by the coolant), and temperature effects (e.g. the removal of hydrogen and/or water from concrete). 

Essentially, Cgcat and Cabs represent the electromagnetic powers removed from the incident wave as a result of scattering and absorption of the incident radiation, while Cext gives the total electromagnetic power removed from the incident wave by the combined effect of scattering and absorption. The optical cross-sections have the dimension of area and depend on the direction and polarization state of the incident wave as well on the size, optical properties and orientation of the particle. The efficiencies (or efficiency factors) for extinction, scattering and absorption are defined as... 

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