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               vn   v n   neutron velocity VN = VN N = nuclear velocity v = relative velocity


The relative speed v, is then defined as


        v       =  n- VN, where v = V2n m         (2.2)
          i n           ->N              n  n

Collision processes are related to the relative speed through the neutron flux = n(r,v, ,t)v, and the energy dependent microscopic cross sections, a(E), where n(rv, ,t) is the neutron density. For a neutron of speed vn and a nucleus of speed VN, the collision processes of (2.1) must now be integrated over all nuclear speeds VN and directions

  * The expressions for these collision processes become:


        Neutrons removed by absorption and scattering =

        f dVN .Nd NN(-r,VNN     a)t(v)n f  J  ')(>,vn, nt)v
        VNN


        Neutrons gained by fission =


X(v) f dVrN     N    V dv'n f , d (v'n)N(' ,VN,r N,t)af(v)
       N      N      n        n

          x× ~ n  v n',t v v n