Macroscopic Cross Sections and Physical Properties

Thus 2 is directly proportional to the nuclear density and to the target area presented by a given nucleus. 

Of course, the picture of nuclei as hard billiard ballsis not really allowable a more valid calculation might proceed as follows  

as the neutron moves an infinitesimal distance ds, it spends a time ds/v at a distance r from all nuclei in the spherical shell r to r + dr whose center is at the neutron (see Fig. 2.5). Thus in this formulation the parameter X is given by 

In the last step in (2.39) the integral of the weighted probability function over all space is designated by the symbol Equation (2.37) may also be written in this form with a particular choice for the function h r). 

quite generally, the expected number of collisions per unit distance traveled X is proportional to the nuclear density through a proportionality constant which has the units of length squared and plays the role of an effective target area per nucleus. This proportionality constant will be designated by the symbol r and referred to as the croscopic cross section for neutron-nucleus collision throughout this work. 

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