Absolute-cross-section measurements for electron-impact ionization of triply charged inert-gas ions: ${\mathrm{Ne}}^{3+}$, ${\mathrm{Ar}}^{3+}$, ${\mathrm{Kr}}^{3+}$, and ${\mathrm{Xe}}^{3+}$

Electron-ion crossed beams have been employed to obtain absolute cross sections for single ionization of ${\mathrm{Ne}}^{3+}$, ${\mathrm{Ar}}^{3+}$, ${\mathrm{Kr}}^{3+}$, and ${\mathrm{Xe}}^{3+}$. These data reveal a steady progression from excellent agreement with theory and semiempirical formulas for ${\mathrm{Ne}}^{3+}$ to significant departures from any simple models for ${\mathrm{Xe}}^{3+}$. For ${\mathrm{Ar}}^{3+}$ some small departure from the models is apparent and the measurements agree with previous experimental results of Müller et al. For ${\mathrm{Kr}}^{3+}$ and ${\mathrm{Xe}}^{3+}$ the measured cross sections in the energy range below four threshold units exhibit complex structure and exceed estimates of direct ionization by roughly factors of 2 and 3, respectively. These features are attributed to indirect ionization processes involving excitation of inner-shell electrons, and the observed cross-section shapes imply that the excitation-autoionization features cannot be simply attributed to dipole-allowed excitation transitions. Ionization rates for Maxwellian electron-temperature distributions are calculated from the data.