The Application Of Padé Approximents In Sputtering Transport Theory

Based on both analytical and numerical methods,the authors have investigated a theory proposed by Glazov in 1994 for finding the depth distributions of energy and momentum by atomic particles in elastic collisions.It has been shown that the integro-differential equations derived by Glazov is incorrect.The traditional Boltzmann transport equation of the depth distributions of energy and momentum cannot be equivalent to Glazov's equation.Therefore,the "singularity" of distributions at the target surface originated from the "nonequivalent".In fact,all of the results derived based on Glazov's equation turned out to be questionable.On the other hand, the author used the same computation method and accuracy(the moments n=300 with 28-decimal-digits precision)published by Glazov has been repeated in this work.The author found that the Fourier transform of energy and momentum depth distribution functions f(k,η)and f_L(k)diverges when k≥37.Rising the calculation accuracy up to the moments n=1200 with 600-decimal-digits precision can not remove about mentioned diverge,so this diverge is intrinsic.This has showed that the Glazov's computation method is not tenable.In order to conquer this difficulty,the author has to introduce Padéapproximants.In this work,the author used Padéapproximants and the extremely high accuracy (the moments n=1200 with 600-decimal-digits precision)to compute some of the depth distributions of energy and momentum,obtained unprecedented calculation results,and found some new phenomenon.This new phenomenon needs further research,and the results will be published elsewhere.