- 33 -


                            CO CO CO

a(E) =       a               f (Er)P(VNfdVN = I (a(Er)P(VN)dVxdV dz
          VN                 - 0 _ 00

                                                  (2.25)


where Oa(Er) is given by equation (2.12), E r by (2.23) and P(VN) by (2.24).

        Equation (2.25) is the plasma fuel equivalent of

the solid fuel cross section given by (2.18). An analytical evaluation of (2.25) was investigated by expanding the integrand in a three-variable Taylor's series about the most probable velocities (Vxp, Vyp, V zp) = (kT, kT, kT). The advantages of this approximate analytic approach do not justify the difficulty involved in obtaining sufficient accuracy. A more direct method of computing the effective cross section is based on the use of the energy dependent form of the Maxwellian distribution. Expressed in terms of the kinetic energy, EN, of the nucleus, the distribution is



        P(EN)dE  -    2        e-EN/kT            (2.26)
           N) N    (7kT) 3/2 N


Since all directions of motion of the absorbing nuclei are equally probable, EX= E    E where Ei     MV2      E
                     x  y    z       i   2   1     EN;
i = x, y, z. The velocity component of the nucleus parallel to the direction of travel of the neutron is