Study on the angular dependence of the average energy loss for ions in solids

By using the transport theory, we have derived a general expression which connects $\Delta E\left(\theta \right)$, the average energy loss measured at different $\theta$ emergence angles, and $Q\left(\theta \right)$, the average elastic and inelastic energy loss in a single scattering as a function of the scattering angle $\theta$, for ions transmitted through thin films. In this way, the effect of multiple scattering on the angular dependence of the energy loss is properly taken into account. By means of this procedure the average energy-loss function $Q$ is retrieved from experimental $\Delta E\left(\theta \right)$ data, as we show for the cases of 50-200-keV ${\mathrm{H}}^{+}$ on C and A1 foils.