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

TL;DR

This paper investigates how relativistic effects influence the energy distribution of electrons emitted by ultrarelativistic lead ions penetrating thin foils, revealing narrower spectra due to ion excitation effects and comparing different target materials.

Contribution

It demonstrates that relativistic time dilation significantly narrows electron energy spectra and compares effects across aluminum and gold foils for 33 TeV lead ions.

Findings

Narrower electron energy distributions due to ion excitation effects.

Similar spectral shapes observed in different target materials.

Insights into historical experimental observations of narrow spectra.

Abstract

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.