Based on both analytical and numerical methods

the authors have investigated a theory proposed by Glazov in 1994 for finding the depth distributions of momentum deposition by atomic particles in elastic collisions. It is shown that the integro-differential equations derived by Glazov are incorrect because of the “entanglement” of two original independent variables. The “singularity” of the distributions at the target surface originated from the “entanglement”. The traditional Boltzmann transport equation of the depth distributions of momentum deposition cannot be equivalent to the Glazov’s equation. Therefore

all of the results derived from the Glazov’s equation turned out to be questionable. On the other hand

the numerical calculations with high accuracy (usually the moments were found up to n=300 with 28-decimal-digits precision) published by Glazov at the same time were repeated in this work

and it was shown that the Glazov’s numerical results were not accurate enough to reproduce most of figs in his work. In this work

the Padé approximation has been used with higher accuracy (the moments found up to n=980 with 500-decimal-digits precision) to compute the Fourier transform of the momentum deposition depth distribution functions f(k

η) and fL(k). Our numerical results show that the Padé approximation is a powerful tool to research these depth distribution functions.