Slowing-down density in pure scatterer

As previously mentioned, the symbol 0 denotes neutron flux and the argument following indicates the variable in terms of which it is defined. 

Properly, the functions (E) and 4 v) should be given distinct symbols, but this practice has been discarded here in the interests of simplicity in notation. Equation (4.54) states that, if the intervals dE and dv correspond, then the neutron flux described by either coordinate system (E or v) must be identical. 

A similar relationship may be written in terms of the lethargy. If we define 

The neutron densities may also be related by equations of this type [see Eq. (3.42)]. Throughout this work we will use all three independent variables , u, and v freely and transfer from one to the other as the need arises. For completeness we list below the various collision densities in terms of the new variable u  

It is important to recognize that, whereas the neutron fluxes (or densities) are related by expressions of the type (4.54) and (4.57) which require a 

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