Neutron absorbers macroscopic cross-sections

One sees in Heitler s book that the absorption coefficient of water for 7-rays of about 5 MeV (which are hardest to absorb) is. 03. A shield of 110 cm gives a 6 = 3 for (2), permitting an about 6.5 cm decrease of the thickness of the Pb to be used. On the other hand, the lead shield also guards against neutrons. According to Friedman s report (C-99), the total cross section of Pb is about 6 X 10 cm for fast neutrons, of which 3.6 is due to inelastic scattering. This gives. 19 for the macroscopic absorption coefficient of lead for fast neutrons and the presence of 13.5 cm lead should permit one to decrease the thickness of the water layer to 105 cm. 

The fraction of these thermal neutrons which is absorbed in the fuel is known as the thermal utilization, /. It is given in terms of the macroscopic absorption cross section of the fuel, and of the combined fuel-moderator... 

The average spatial thermal flux is actually the total neutron density times 2200 m/sec. This is true because the absolute thermal flux is measured with l/v-absorber, using its cross section at this standard velocity. The macroscopic fission cross section of U is that for the same velocity. Actually, since this cross section does not have a l/v-dependence, a correction can be made to make it an equivalent l/v-cross section, which will give the correct fission rate in Eq. (4). This correction is based on a Maxwellian neutron distribution and is a function of the neutron temperature. The temperature of the neutrons in the AGN-201 core is approximately 350 K, which corresponds to a correction factor of 0.98. 

If 0 is the flux in neutrons per cm per second at a distance z from the plane source, then the rate at which neutrons will be absorbed in the medium will be equal to 2 0 per centimeter cubed per second, where is the macroscopic absorption cross section of the medium. In an element of area A, and thickness dz at a distance z from the plane source, the number of neutrons captured per second will be 2g 0A dz. This is a measure of the probability that a neutron will be absorbed within the element. Therefore, the mean square distance that a neutron travels from its source to where it is absorbed is given by... 

For X rays ft is analogous to the macroscopic absorption cross section 2a for neutrons. The only difference is that ft represents the fraction of energy removed from the beam of X rays per cm length, whereas 2. represents the fraction of neutrons absorbed per unit length. 

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