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I read on the wikipedia page for cross-section, that cross-section is related to the reciprocal of a material's density. This seems entirely counter-intuitive. Is there an intuitive reason for this?

Or am I misunderstanding this? From Wikipedia

For a given event, the cross section σ is given by $$σ=\frac μn$$ where

  • $σ$ is the cross section of this event (SI units: $m^2$),
  • $μ$ is the attenuation coefficient due to the occurrence of this event (SI units: $m^{-1}$), and
  • $n$ is the number density of the target particles (SI units: $m^{-3}$)"
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    Might be easier to think of it in terms of mean free path: $\lambda\approx1/n\sigma$. The more particles ($n$), the shorter the mean free path. It happens that elsewhen, $\mu=1/\lambda$ was defined. – Kyle Kanos Nov 11 '15 at 21:18

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I read on the wikipedia page for cross-section, that cross-section is related to the reciprocal of a material's density. This seems entirely counter-intuitive.

If you have a sphere of mass $m$ made of aluminium then the cross section is $\pi R_{Al}^2$ where $R$ is the radius of the sphere that you can calculate knowing $m$ and $\rho_{Al}$.

Now, you have a sphere, of the same mass $m$, made of lead this time. Its radius will be smaller because $\rho_{Pb} > \rho_{Al}$ and in consequence the cross section, $\pi R_{Pb}^2$, will be also smaller.

In conclusion, the denser the sphere of mass $m$, the smaller its radius and cross section.

Energizer777
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