Interaction muons with Iron I would like to know why $\mu^+$ muons can easily penetrate a solid metal such as Fe with negligible interactions while $\pi^+$ mesons lose their energy a lot faster when traveling through the metal. Is it because the interaction between electrons and muons is forbidden or should I somehow see it from the crossection?
 A: It actually depends on the energy of the particles.
As a charged particle passes through a metal, it is basically pushing/pulling sea electrons near its path, due to Coulomb repulsion/attraction. That is, the particle is doing work on the electrons in the material, and so it loses energy. The rate of energy loss is given (approximately) by the Bethe formula:
$$
-\frac{dE}{dx}=\frac{4\pi}{m_e c^2}\frac{n z^2}{\beta^2}\left(\frac{e^2}{4\pi\epsilon_0}\right)^2\left[ln\left(\frac{2m_e c^2 \beta^2}{I(1-\beta^2)}\right) - \beta^2 \right]
$$
where $\beta$ and $z$ are the velocity and charge of the particle, respectively. The other quantities are properties of the material. Note that $m_e$ and $n$, the electron mass and number density, repsectively, appear in the equation.
So, to answer your question specifically, we find that for a given fixed velocity, the muon and pion would loose energy at the same rate in matter. But, at a fixed energy, they will loose energy at different rates, since the two particles have different masses.
A: Pions in the GeV range also interact hadronically via the strong force.
Therefore in iron blocks with a thickness of the order of the hadronic interaction length they will loose energy a lot faster than muons. The dE/dx piece is almost the same but due to the hadronic interactions, e.g. 6 GeV pions in iron of few 10 of cm will loose about twice the energy.
