Infinite Homogeneous Multiplying Media

Equation (4.145) is an immediate extension of (4.106) and states that any change in g(u) must be due to the combined effect of the removals 

2a(u) l (u) and of the source S(u), Equation (4.112) is taken from the analysis of Sec. 4.4b and therefore applies to the asymptotic range and to media with slight absorption. These relations replace the more general form (4.104). Equations (4.112) and (4.145) are to be used with the initial conditions 

The physical statement of (4.147) is that the number of neutrons slowing past lethargy u (in an infinite medium, per unit volume per unit time) is given by the number of neutrons produced at u, S(w ) du multiplied by the probability p(w w ) that a neutron at w will reach u without being absorbed and the product integrated over all w w [for which jS(w ) has a nonzero value]. 

The slowing-down density in this system is obtained by the direct substitution of (4.149) into the general result (4.147). The solution is 

Thus (u) is the normalized fission spectrum in lethargy. Note that j(u) du gives the fraction of neutrons which appear from fission with lethargies in du about u. It is sometimes more convenient to work with the corresponding function in energy space z E), which may also be 

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As an example of the application of these concepts, consider the analysis of the slowing-down problem in an infinite, homogeneous multiplying medium which is at steady state, i.e., critical. Let the distribution of fission neutrons be given by the normalized spectrum 3(w) defined in Eq. (4.152), and let 2a(w), S/(m), S (r), and 2,(w) denote the nuclear constants of the medium. The total collision density for this system is given by... 

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