A relation is proposed to compare data for the ratio R of cross sections for double ionization (or ionization excitation) (${\mathrm{\sigma }}^2$) to that for single ionization (${\mathrm{\sigma }}^1$) caused by charged particles (Z), photoannihilation (PE), and Compton (C) scattering. The relation is ${\mathit{R}}_{\mathit{Z}}$(ε)=${\mathit{f}}_{\mathit{Z},\mathit{d}}$(ε)${\mathit{R}}_{\mathrm{PE}}$+[1-${\mathit{f}}_{\mathit{Z},\mathit{d}}$(ε)]${\mathit{R}}_{\mathit{C}}$( ε). Here, R(ε)=(d${\mathrm{\sigma }}^2$/dε)/(d${\mathrm{\sigma }}^1$/dε), R=${\mathrm{\sigma }}^2$/${\mathrm{\sigma }}^1$, and ${\mathit{R}}_{\mathit{C}}$(ε) is the ratio of cross sections for Compton scattering; ε is the energy transferred to the system by the projectile; and ${\mathit{f}}_{\mathit{Z},\mathit{d}}$(ε) is the dipole fraction of the energy distribution ${\mathrm{\rho }}_{\mathit{Z}}$(ε)=(d${\mathrm{\sigma }}_{\mathit{Z}}^1$/dε)/${\mathrm{\sigma }}_{\mathit{Z}}^1$ for single ionization. We have evaluated ${\mathit{f}}_{\mathit{Z},\mathit{d}}$(ε) so that only ratios of cross sections at high energies need be observed experimentally to test this relation. © 1996 The American Physical Society.

• Received 19 March 1996

DOI:https://doi.org/10.1103/PhysRevA.54.3668