Incorporation of the electron energy-loss straggling into the Fermi- Eyges equation

A modified Fermi-Eyges equation has been derived from the linear Boltzmann equation by including a term for describing electron energy-loss straggling. The solution has been obtained by the use of a generalized Eyges' method, yielding the electron energy distribution expressed with moments method in addition to Eyges' original solution. The first- and second-order approximations of the spectrum give the well-known continuous-slowing-down approximation (CSDA) and Gaussian distribution, respectively. Inclusion of the third-order moment in the spectrum yields the Vavilov distribution approximated with the Airy function. The higher order approximations can be evaluated numerically.