Energy threshold in multiple ionization by electron or positron impact

The energy threshold for the formation of highly charged ions is experimentally well-known and measured. For single ionization, it is the binding energy of the outermost electrons. For multiple ionization, the ionization begins at impact energies much larger than the theoretically expected ones. In this contribution we present a simple expression for the energy threshold for multiple ionization by electron or positron impact. It was obtained as the mean value of the energy transferred to each ionized electron by using Thompson classical approximation. Present results reproduce quite well the experimental thresholds. Moreover, the inclusion of these values in the theoretical multiple ionization cross sections allows describing rather well the experimental data for single up to sextuple ionization of rare gases