Cross Section Energy Dependence

We begin our description of the energy dependence of cross sections with hydrogen; since it consists of a single proton, its cross section is easiest to describe. Hydrogen has only elastic scattering and absorption cross sections. Since it has no internal structure, hydrogen is incapable of scattering neutrons inelastically. Figure 2.3a is a plot of hydrogen’s elastic scattering cross section. The capture cross section, shown in Fig. 2.3b, is inversely proportional to under root of E, and since energy is proportional to the square of the speed, it is referred to as a 1/v or ‘‘one-over-v’’ cross section. Hydrogen’s capture cross section—which is the same as absorption since there is no fission—is only large enough to be of importance in the thermal energy range. The absorption cross section is written as

Conventionally, the energy is evaluated at Eo ¼ kT, in combination with the standard room temperature of T=293.61 K. Thus

Eo =0.0253 eV. For most purposes we may ignore the low- and highenergy tails in the scattering cross section. The total cross section may then be approximated as

Hydrogen-2, or deuterium, cross sections have an analogous
behavior, except that the scattering cross section is moderately
larger, and the absorption cross section much smaller.
Like hydrogen, other nuclei have elastic scattering cross sections,
whichmay be equated to simple billiard ball collisions in which kinetic
energy is conserved. These are referred to as potential scattering cross
sections because the neutron scatters from the surface of the nucleus,
rather than entering its interior to form a compound nucleus. Potential
scattering cross sections are energy independent except at very low or
high energies. Their magnitude is directly proportional to the crosssectional
area of the nucleus, where the radius of the nucleus may be
given in terms of the atomic weight as R=1.25x10^-13A^1/3 cm. Further
understanding of neutron cross sections, however, requires that we
examine reactions resulting from the formation of compound nuclei.