Question 2.12: A 5.0 cm thick layer of purely absorbing material is found t......
A 5.0 cm thick layer of purely absorbing material is found to absorb 99.90 percent of a neutron beam. The material is known to have a density of 4.0x 10^{22} nuclei/cm³. Determine:
a. the macroscopic cross section,
b. the mean free path,
c. the microscopic cross section.
d. Is the cross section as big as a barn?
a. From Eqs. (2.4) & (2.5): 0.001 = exp (-\Sigma\cdot5.0)\;. Thus the macroscopic cross section is \Sigma=\ln(\mathrm{0.001})/\,5.0=1.38~c m^{-1}\,.
b From Eq. (2.7) the mean free path is \lambda=1/\sum=1/1.38=0.724{\mathrm{~}}\mathrm{~}\mathrm{cm}
c \sigma=\Sigma\,/N=1.38\,/(4.0\cdot10^{22})=0.345\cdot10^{-22}c m^{2}
d Since one barn = 10^{-24}cm^{2}\ \sigma=0.345\cdot10^{-22}c m^{2}\cdot10^{24}b/c m^{2}=34.5b Definitely bigger than a barn.