Electron scattering from the molecular hydrogen ion and its isotopologues

We have extended the $ab$ $initio$ convergent close-coupling method to electron scattering from the vibrationally excited molecular hydrogen ion and its isotopologues. Calculations have been performed within the adiabatic-nuclei approximation. Results are presented for dissociative excitation and ionization as a function of the initial vibrational state of the molecules. Comparison with experiment is excellent across the energy range from near threshold to 1 keV.

Figure 1

Normalized Franck-Condon (FC) factors of ${\mathrm{H}}_2(X{}^1{\Sigma }_g,0,0)\to$ ${\mathrm{H}}_2{}^{+}(1s{\sigma }_g,v,0)$, ${\mathrm{D}}_2(X{}^1{\Sigma }_g,0,0)\to$ ${\mathrm{D}}_2{}^{+}(1s{\sigma }_g,v,0)$ and ${\mathrm{T}}_2(X{}^1{\Sigma }_g,0,0)\to$ ${\mathrm{T}}_2{}^{+}(1s{\sigma }_g,v,0)$.

Figure 2

Total ionization cross sections (TICS) of electron scattering from the electronic ground state of ${\mathrm{He}}^{+}$. The molecular CCC united atom ($R=0$ $a_0$) calculations are compared with the atomic CCC code calculations [63] and the measurements of Peart et al. [64].

Figure 3

351- and 289-state CCC results of proton production (PP) and dissociative ionization (DI) cross sections of electron scattering from ${{\mathrm{H}}_2}^{+}$ at a fixed-nuclear distance of $R=2.0$ $a_0$.

Figure 4

Franck-Condon (FC) and von Busch and Dunn [15] (BD) vibrationally weighted proton production (PP) cross sections for electron scattering from the electronic ground, vibrationally excited states of ${{\mathrm{H}}_2}^{+}$. Results are compared with the present $R=2.0$ $a_0$ calculations, vibrationally weighted total inelastic (TI) Born calculations of Peek [20], the TI measurements of Peart and Dolder [8], and the PP experiments of El Ghazaly et al. [7], Dunn et al. [3, 4], and Dance et al. [5].

Figure 5

Franck-Condon (FC) and von Busch and Dunn [15] (BD) vibrationally weighted dissociative ionization (DI) cross sections for electron scattering from the electronic ground, vibrationally excited states of ${{\mathrm{H}}_2}^{+}$. Results are compared with the present $R=2.0$ $a_0$ results, the $R=2.0$ $a_0$ configuration-average distorted-wave (CADW) method [33], the $R=2.0$ $a_0$ time-dependent close-coupling (TDCC) method [32], and measurements of Peart and Dolder [14] and El Ghazaly et al. [7].

Figure 6

Dissociative excitation (DE) and dissociative ionization (DI) cross sections for electron scattering from ${{\mathrm{H}}_2}^{+}$ in the electronic ground, vibrational state $v_i$.

Figure 7

Franck-Condon (FC) weighted deuteron production (DP) cross sections for electron scattering from the electronic ground, vibrationally excited states of ${{\mathrm{D}}_2}^{+}$. Results are compared with the experiments of El Ghazaly et al. [7] and Dunn and Van Zyl [4].

Figure 8

Franck-Condon (FC) weighted dissociative ionization (DI) cross sections for electron scattering from the electronic ground, vibrationally excited states of ${{\mathrm{D}}_2}^{+}$. Results are compared with the experiment of El Ghazaly et al. [7].

Figure 9

Dissociative excitation (DE) and dissociative ionization (DI) cross sections for electron scattering from ${{\mathrm{D}}_2}^{+}$ in the electronic ground, vibrational state $v_i$.

Figure 10

Proton production (PP), deuteron production (DP), and triton production (TP) cross sections for electron scattering from vibrationally excited ${{\mathrm{H}}_2}^{+}$, ${{\mathrm{D}}_2}^{+}$, or ${{\mathrm{T}}_2}^{+}$, respectively. Vibrational cross sections are weighted according to the Franck-Condon (FC) factors.

Figure 11

Proton production (PP), deuteron production (DP), and triton production (TP) cross sections for 20 and 100 eV electron scattering from ${{\mathrm{H}}_2}^{+}$, ${{\mathrm{D}}_2}^{+}$, or ${{\mathrm{T}}_2}^{+}$, respectively. The molecular ions are in the electronic ground, vibrational state $v_i$. Cross sections are weighted according to their Franck-Condon factors.

Figure 12

Dissociative ionization (DI) cross sections for 100 eV electron's scattering from ${{\mathrm{H}}_2}^{+}$, ${{\mathrm{D}}_2}^{+}$, or ${{\mathrm{T}}_2}^{+}$, respectively. The molecular ions are in the electronic ground, vibrational state $v_i$. Cross sections are weighted according to their Franck-Condon factors.

Figure 13

Dissociative excitation (DE) and dissociative ionization (DI) cross sections for electron scattering from ${{\mathrm{T}}_2}^{+}$ in the electronic ground, vibrational state $v_i$.

Figure 14

Dissociative excitation (DE) and dissociative ionization (DI) cross sections for electron scattering from ${\mathrm{HD}}^{+}$ in the electronic ground, vibrational state $v_i$. DE results of ${\mathrm{HD}}^{+}$ in the vibrational ground state are compared with the experiment of Andersen et al. [13].

Figure 15

Dissociative excitation (DE) and dissociative ionisation (DI) cross sections for electron scattering from ${\mathrm{HT}}^{+}$ in the electronic ground, vibrational state $v_i$.

Figure 16

Dissociative excitation (DE) and dissociative ionization (DI) cross sections for electron scattering from ${\mathrm{DT}}^{+}$ in the electronic ground, vibrational state $v_i$.