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I am really confused about the difference between flux and scalar flux. I have a specific question:

If we have a parallel neutron beam of strength $\phi_0$ given in neutrons/cm$^2$s, incident on a finite slab of thickness $L$, consisting of a purely absorbing material with cross section $\Sigma_a (x)$ and the neutrons only travel from left to right in the slab, how do I find the scalar flux? Do I merely divide $\phi_0/\Sigma_a$? That would give me a result in neutrons per second, right? I think this might have to do something with the neutron attenuation, but can't seem to get on the right track with this problem.

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  • $\begingroup$ $\phi/\Sigma_a$ does not seem a thing. Normally you multiply $\phi/Sigma_a$ to get number of events occurring, depending on what type of event $\Sigma_a$ represents. $\endgroup$
    – rmhleo
    Oct 14, 2014 at 0:26

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The difference is that angular momentum flux $\psi$ depends on the direction and scalar momentum flux does not, because is integrated over all directions: $\phi = \int_{4\pi} \psi d\Omega$.

For the rest, they exhibit the same dependence on Energy. So $\psi$ gives the amount of neutrons that at a certain position $\bf r$ and at energy $E$ are moving in the direction $\hat \Omega$. While $\phi$ reflects the amount of neutrons that at a certain position $\bf r$ and at energy $E$ are moving in any direction.

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