It's a question about neutron absorption in the nucleon. When more than one isotope exists and given the mass ration or abundance, is there a formula for obtaining the total micro absorption cross-section?
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1 Answer
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If you know the abundances of each isotope ($f_i$), the "effective" absorption cross section is $$\sigma_a = \sum_i f_i \sigma_{ai}$$ where $i$ is the isotope and $\sigma_{ai}$ is the microscopic absorption cross section in units of cm$^2$ (or barns where one barn=$10^{-24}$ cm$^2$.
However, if you are dealing with multiple isotopes, you usually want the macroscopic cross section of the mixture. The macroscopic cross section is the product of the number density times the microscopic cross sections. For a mixture, you can add the individual macroscopic cross sections together. $$\Sigma_a = \sum_i N_i \sigma_{ai}$$ where $N_i$ is the number density of isotope $i$ in units of atoms/cm$^3$
