Universal relations between range and damage profile parameters

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Abstract
A critical review of the numerous results on range profiles obtained with our Monte Carlo code TRIM (in its latest version) showed that there exist several, as yet unknown, universal relations between the moments of range and damage profiles. In combination with the well-known PRAL algorithm or other recently developed analytical formulae for the energy-range relation, one may use these relations to obtain improved range and damage profile predictions with a pocket calculator. For dominant nuclear and dominant electronic interactions mostly different relations are found. The influence of the surface on the moments is smaller than commonly assumed. As the relations derived here from theoretical results are intended essentially to help experimenters in their work, we find it appropriate to give the reader a feeling for the accuracy of experimentally obtainable range profile parameters to compare with the theoretical predictions. Therefore, the influence of various effects on the range parameters is additionally demonstrated for some test measurements.
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