Statistical fluctuations of the ionisation yield of low-energy electrons in He, Ne and Ar

Using the Monte-Carlo method the statistical fluctuations of the ionisation yield produced during the degradation of low-energy electrons in the three noble gases He, Ne and Ar were studied. To do this, the probability P(T 0 , j) for exact j ionisations generated upon the complete slowing down of electrons of initial energy T 0 was calculated in the energy range 20 eV<or=T 0 <or=5 keV. The probability distributions in the number of ionisations produced were then used to determine moments M nu and central moments m nu up to the order nu =5 related to such well known quantities as the mean energy expended per ion pair formed, the Fano factor, and the generalised Fano factors introduced by Inokuti et al. (1980), all of which are able to characterise a special property of the ionisation number distribution, as for instance its variance, its asymmetry and its flatness near the centre.