title: Technical Note: On the proton range and nuclear interactions in compounds and mixtures.
abstract: OBJECTIVE
  Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures.
  
  
  METHODS
  Benefiting from the Bragg-Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive.
  
  
  RESULTS
  The examination of the formula presented shows that the authors' method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials.
  
  
  CONCLUSIONS
  The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematically easy to handle and valid for desired compounds or mixtures composed of an arbitrary number of constituent elements, including materials of interest for proton radiotherapy purposes.
authors.affiliation: Department of Physics, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran 15418-49611, Iran.
authors.forename: Fatemeh S
authors.initials: FS
authors.lastname: Rasouli
authors.affiliation: Department of Physics, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran 15418-49611, Iran.
authors.forename: S Farhad
authors.initials: SF
authors.lastname: Masoudi
authors.affiliation: ICT Radiotherapy Services, Livingston, New Jersey 07039.
authors.forename: David
authors.initials: D
authors.lastname: Jette
mesh_terms: D045424:Complex Mixtures / Q000528:radiation effects*; D008962:Models, Theoretical; D011336:Probability; D011522:Protons
chemical_list: D045424:Complex Mixtures; D011522:Protons