Slowing-down density definition

Here, r = ln(JB/ thermai) has a somewhat different definition from the usual one it is zero for neutrons, the energy E of which is thermal, (t t) is the transport cross section which may depend on the energy but does not depend on the position thermal neutrons the average logarithmic energy loss (independent of position) <7, the absorption cross section for thermal neutrons which depends on the position. q(r) is the density of fast neutrons per unit r (it is not Fermi s slowing down density Q), multiplied with the velocity, n the density of thermal neutrons times their velocity, /(r) dr is the number of fission neutrons per slow neutron captured in U, for which r is between r and r + dr. Finally pi is the chance of escaping resonance absorption and p2 the thermal utilization. The multiplication constant here... 

Note that condition (3) follows immediately from the definition of Q as the slowing-down density in the absorber-free medium. The actual slowing-down density is obtained from the relations... 

The presence of 2 instead of S, in (6.47) results from the particular choice of the relationship between the slowing-down density and the flux made in (6.6). It should be remembered that this relationship is justifiable only in a medium of light absorption, that is, one in which 2 2, [see (4.112) and related discussion]. Thus in most cases in which the present theory is expected to be useful, the two choices of r give nearly the same result however, for consistency, the definition (6.47) will be used here and in the remainder of this work. 

Note that with these definitions one can also obtain (6.100) directly by physical arguments. Thus to find the slowing-down density past u, we compute first the increment dq arising from the neutrons bom in du about u which slow down successfully as far as w without being captured or escaping from the system (see Fig. 6.5) ... 

With these definitions we write the total collision density in Ff as consisting of two parts one due to fast neutrons in Vp w hich slow down into the unit lethargy interval about w, and another due to the net transport of neutrons of lethargy u through the surface Ap from the moderator thus,... 

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