Scattering of Particles in Air Showers

The radial distribution of singly scattered particles in air showers is discussed. The probability $\mathcal{P}\left(x^{\prime }\right)d{x}^{\prime }$ that a singly scattered particle is found in the annular ring between $x^{\prime }$ and $x^{\prime }+d{x}^{\prime }$ is $\mathcal{P}\left(x^{\prime }\right)d{x}^{\prime }=0.16\left(\frac{d{x}^{\prime }}{x^{\prime 3}}\right)$, where $x^{\prime }$ is the "Moliere unit." In the deduction of this formula Belenky's expression for the mean square length of a shower, which remains valid below the critical energy, is evaluated. The main process contributing to particles at large distances from the shower axis involves the radiation, and subsequent rematerialization, of electrons below the critical energy.