NUmber Density

tony.almeda

if fuel coposition as follow : 75 wt% Tho2- 25 wt% uo2, were the U enrichment 19.5 w% ... how can i caculate the number density (Atoms/barn-cm) for the comopsition ?

statphys

If I recall correctly number density of a nuclide is just the number of atoms per unit volume as given by;

N = (Rho * NA) / A

Where; Rho = density (in g/cm^3)
NA = Avagadro number
A = Atomic weight in g

To find the composite for the mixture just weight by the relative proportions of the nuclides in the mixture.

i.e [0.75*N(Thorium)] + [0.25*0.195*N(U-235)] + [0.25*(1-0.195)*N(U-238)]

From your query I wonder if you are really after the macroscopic cross-section which is simply the number density multiplied by the microscopic cross-section (as measured in barns).