Role of ionization-excitation processes in the cross section for direct ionization of heavy atomic ions by electron impact

The contribution to the ionization cross section of ionization-excitation processes by electron impact is usually negligibly small for low- and medium-$Z$ elements. We demonstrate here, however, that for heavy atomic ions with the outermost shell being $nd$ $\left(n=4,5\right)$ the ionization-excitation processes play an evident role in the ionization cross section. For the $4s^{2}4p^{6}4d^{10}$ ground level of ${\mathrm{Gd}}^{18+}$, the ionization-excitation cross section due to the excitation of levels in the $4s^{2}4p^{6}4d^{8}4f$ configuration is comparable to the direct $4p$ and $4s$ ionization cross sections of ${\left(4s^{2}4p^{5}4d^{10}\right)}_{1/2}$ and ${\left(4s4p^{6}4d^{10}\right)}_{1/2}$. The total ionization cross section will be underestimated by 15% without including the contribution from ionization-excitation processes. This is a general conclusion for heavy atomic ions, which is verified by taking Pd-like ions of ${\mathrm{Sn}}^{4+},{\mathrm{Ba}}^{10+},{\mathrm{Nd}}^{14+},{\mathrm{Tb}}^{19+},{\mathrm{Yb}}^{24+}$, and ${\mathrm{W}}^{28+}$ as examples. The role of ionization-excitation processes can be understood from the overlapping of the wave functions between the $4d$ and $4f$ orbitals.

Figure 1

Level-to-level direct ionization and ionization-excitation cross section (1 Mb = $10{}^{-18}$ ${\mathrm{cm}}^2)$ of the $4s^{2}4p^{6}4d^{10}$ ground level of ${\mathrm{Gd}}^{18+}$. The numbers for each line are defined in Table 1. The lines corresponding to 1–5, 1–6, 1–7, 1–9, and 1–11 represent the ionization-excitation cross section.

Figure 2

Ionization cross section of the ground level of ${\mathrm{Gd}}^{18+}$ with and without contributions from the ionization-excitation processes.

Figure 3

Ionization cross section with and without contributions from the ionization-excitation processes for Pd-like ions of ${\mathrm{Sn}}^{4+},{\mathrm{Ba}}^{10+},{\mathrm{Nd}}^{14+},{\mathrm{Tb}}^{19+},{\mathrm{Yb}}^{24+}$, and ${\mathrm{W}}^{28+}$.

Figure 4

Square of the radial wave functions of orbitals $4d,4f$, and $5f$ for (a) ${\mathrm{Sn}}^{4+}$, (b) ${\mathrm{Gd}}^{18+}$ and (c) ${\mathrm{W}}^{28+}$.