Relativistic time dilatation and the spectrum of electrons emitted by 33 TeV lead ions penetrating thin foils

We study the energy distribution of ultrarelativistic electrons produced when a beam of 33 TeV Pb${}^{81+}$(1s) ions penetrates a thin Al foil. We show that, because of a prominent role of the excitations of the ions inside the foil which becomes possible due to the relativistic time dilatation, the width of this distribution can be much narrower compared to the case when the ions interact with rarefied gaseous targets. We also show that a very similar shape of the energy distribution may arise when 33 TeV Pb${}^{82+}$ ions penetrate a thin Au foil. These results shed some light on the origin of the very narrow electron energy distributions observed experimentally about a decade ago.