The term ‘cross section’ is a physicists term that we will be using throughout the quarter to describe the interaction of radiation with matter. This term comes from the notion that when particles interact, the strength of their interaction can be represented by the collision of two hard spheres with the radius of the ‘cross section’. The cross section is defined for one particle, and thus when a particle strikes an absorber, the cross section is multiplied by the number density of the absorber. So…the absorption coefficient is then defined as:
L = 1/ n*sigma,
Where n is the L is the absorption coefficient, n is the number density, and sigma is the cross section for the interaction. Knowing this, the fact that the cross section removes particles from a beam (Beer’s law) (and any other facts you can get from your modern physics text: you may have to use dimensional analysis):
A beam of neutrons of kinetic energy 0.29 eV, intensity 105 /s traverses an absorber of 92U235 of mass thickness 10-1 kg/m2. The collision can result in the following events:
a) Elastic, billiard ball scattering Sigmaf = 2 X 10-30 m2
b) Capture of the neutron followed by emission of a gamma-ray Sigmae = 7 X 10-27 m2
c) Capture of the neutron followed by nuclear fission f = 2 X 10-26 m2
Calculate:
a) Attenuation of the neutron beam by the absorber
b) Number of fission reactions occurring per second
c) The flux of elastically scattered neutrons at a point 10 m from the absorber and out of the main beam, assuming that the elastic scattering is isotropic.