Calculation of energy loss spectra through very thin layers

The extreme asymmetry of energy loss spectra through very thin layers means that their shape and behaviour with thickness are not reflected solely by the knowledge of their two first moments. We show that for protons traversing very thin films or gas strippers the FWHM of the energy loss spectrum varies as the thickness x, even though the standard deviation varies as √x, and the dependence of the most probable energy loss on x is far from linear. This peculiar behaviour is similar to predictions of the well-known Landau theory for electron energy loss. The consequences of these observations are discussed, in particular with respect to the energy spread of beams produced by tandem accelerators. (orig.)