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Title: Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime

We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities from $${10}^{7}\,{\rm{t}}{\rm{o}}\,{10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$$ and ions with positive charge $$q\lt 8$$. Non-resonant cross sections tend to have a velocity peak at collision velocities $$v\lesssim 1\ {\rm{a}}{\rm{u}}$$ with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m, is proportional to the energy defect of the collision, $${\rm{\Delta }}E$$, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T, and inversely proportional to v m. For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters $${v}_{{\rm{m}}},{I}_{{\rm{T}}},{Z}_{{\rm{T}}},\mathrm{and}\ {Z}_{{\rm{P}}}$$, where the $${Z}_{{\rm{T}},{\rm{P}}}$$ are the target and projectile atomic numbers. In conclusion, for the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.
 [1] ;  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0953-4075
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Physics. B, Atomic, Molecular and Optical Physics
Additional Journal Information:
Journal Volume: 50; Journal Issue: 11; Journal ID: ISSN 0953-4075
IOP Publishing
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
74 ATOMIC AND MOLECULAR PHYSICS; scaling law; charge exchange; electron capture; charge transfer; energy defect; cross section; collision
OSTI Identifier: