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By National Council on Radiation Protection and Measurements
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Extra info for Conceptual Basis for Calculations of Absorbed-Dose Distributions (N C R P Report 108)
10) Finally, the conservation equation for neutrons can be handled the same way as for photons. But, when neutron scattering is symmetrical in the center-of-mass system, the ratio of the neutron energies before and after the scattering is independent of the initial energy. 6) by ln(E) rather than E and integrating. 6). This has been done in the study of the slowing down of electrons, because their secondary particles are also electrons, indistinguishable from the primaries. 7), by adding to its right-hand side another source term that represents the generation of secondary electrons by other electrons in the medium, as shown in Equation.
Fortunately, the complete array of cross sections may be required only in the most detailed types of calculations. Many other transport methods are based on approximations that reduce the cross-section requirements. For example, in the treatment of neutron diffusion, the simplifying assumption is often made that elastic scattering is isotropic in the center-of-mass system. In the treatment of the penetration and diffusion of charged particles, the continuous-slowing-down approximation is often used, in which the kinetic energy of the charged particles is assumed to decrease continuously along the particle tracks a t a rate given by the stopping power (mean energy loss per unit pathlength).
For photons and neutrons, this is certainly not an adequate approximation. Nevertheless, the CSDA can be applied and the results used as a rough guide. 10). With E substituted for hv, this equation also applies to neutrons. But, particularly below about 1MeV, neutrons tend to lose a constant average fraction of their energy per collision, regardless of their energy; as a consequence, a better solution is obtained using the average logarithmic decrement. 12). 61, requires different methods for the different types of particles.