The difference between microscopic and macroscopic cross sections.

[CaptainMayhem]

Hello there folks. So I'm doing some homework, and one of the questions asks for a comparison of the microscopic absorption cross sections of B, Cd, Gd, and Hf with the fission cross section of U-235. I've found the fission cross section in my trusty 17th edition of Nuclides and Isotopes, but the next part of the question confused me. It then asks for the macroscopic cross sections assuming density is derived from the periodic table.

I'm not sure how to figure out the micro/macroscopic cross sections. There is only one given value per nuclide. Help?!

 

[Astronuc]

Microscopic cross-sections (σ) are given for each nuclide usually in units of barns, where 1 b = 1 x 10^-24 cm². It is essentially the effective area for the particular reaction.

The macroscopic cross-section (Σ) has units of cm^-1 is derived from the microscopic section according to

Σ = N σ, where N is the atomic density of a particular nuclide.

The reaction rate for a give interaction = Σ Φ, where Φ is the neutron flux.

These forumla work well for average or thermal neutron energies. If a wide enough energy spectrum is considered then one has to use integrals over the appropriate energy range.