Abstract
It is well known that cross sections for ionization of atoms by fast charged particles and by photons are related by the Bethe-Born theory. We employ this relationship to derive a corresponding relation for the ratio R of double to single ionization including the first two terms of the Bethe expansion. For sufficiently fast charged particles, where the second term can be ignored, the ratios as a function of \ensuremath{\Delta}E---the energies transferred to the atom by the projectile---for ionization by charged particles ${\mathit{R}}_{\mathit{z}}$(\ensuremath{\Delta}E) and by photons ${\mathit{R}}_{\ensuremath{\gamma}}$(\ensuremath{\Delta}E) are equal: ${\mathit{R}}_{\mathit{z}}$(\ensuremath{\Delta}E)=${\mathit{R}}_{\ensuremath{\gamma}}$(\ensuremath{\Delta}E). In addition, a relation for the ratio of total charged-particle impact ionization cross sections to the photon ratio is derived. The results are compared with recent experimental data and various discrepancies are found and discussed.
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