Charge-transfer processes in ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ collisions and the reverse process at low-keV energies

Theoretical investigations on single charge-transfer processes in collisions of ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ and its reverse process have been carried out at collision energies from $20\mathrm{eV}∕\mathrm{u}\text{to}10\mathrm{keV}∕\mathrm{u}$. The molecular orbital expansion method within the semiclassical impact parameter formalism has been employed for the scattering dynamics, while the ab initio multireference single- and double-excitation configuration interaction (MRD-CI) method was adopted for determination of molecular electronic states. The initial channels correspond to the quintet and triplet states for the corresponding collision processes, respectively. Four molecular states in the quintet manifold and eight molecular states in the triplet manifold were coupled. In the quintet manifold, the charge-transfer cross sections for ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ range from $1.3\times {10}^{-22}{\mathrm{cm}}^2$ at $20\mathrm{eV}∕\mathrm{u}\text{to}2.5\times {10}^{-15}{\mathrm{cm}}^2$ at $10\mathrm{keV}∕\mathrm{u}$. The cross sections of the reverse process, ${\mathrm{F}}^{+}+{\mathrm{H}}^{+}\to {\mathrm{F}}^{2+}+\mathrm{H}$, range from $3.0\times {10}^{-22}{\mathrm{cm}}^2\text{to}2.3\times {10}^{-15}{\mathrm{cm}}^2$ in the same energy range. In the triplet states, the charge-transfer cross sections for ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ range from $1.1\times {10}^{-18}{\mathrm{cm}}^2\text{to}2.5\times {10}^{-16}{\mathrm{cm}}^2$, and its reverse process gives charge-transfer cross sections ranging from $1.7\times {10}^{-24}{\mathrm{cm}}^2\text{to}1.5\times {10}^{-17}{\mathrm{cm}}^2$.

Figure 1

The relative energy levels of the $\mathrm{F}{\mathrm{H}}^{2+}$ molecule in the quintet manifold. The solid lines are from the bottom $1{}^5\Sigma ^{-}$, $2{}^5\Sigma ^{-}$, and $3{}^5\Sigma ^{-}$, respectively, and the dotted line is $1{}^5\Pi$.

Figure 2

Radial coupling matrix elements in the quintet manifold. (a) $1{}^5\Sigma ^{-}–2{}^5\Sigma ^{-}$, (b) $1{}^5\Sigma ^{-}–3{}^5\Sigma ^{-}$, and (c) $1{}^5\Sigma ^{-}–4{}^5\Sigma ^{-}$.

Figure 3

Rotational coupling matrix elements in the quintet manifold. (a) $1{}^5\Sigma ^{-}–1{}^5\Pi$, (b) $2{}^5\Sigma ^{-}–1{}^5\Pi$, and (c) $3{}^5\Sigma ^{-}–1{}^5\Pi$, respectively.

Figure 4

${\mathrm{F}}^{2+}+\mathrm{H}$ collision in the quintet manifold. The partial cross sections are long dash for $2{}^5\Sigma ^{-}$, chain for $1{}^5\Pi$, and dotted line for $3{}^5\Sigma ^{-}$, respectively. The total transfer cross sections, shown with a solid line with circles, are the sum of these partial cross sections.

Figure 5

${\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ collision in the quintet manifold. The partial cross sections are a full line for $1{}^5\Sigma ^{-}$, dotted line for $3{}^5\Sigma ^{-}$, and chain for $1{}^5\Pi$. The total charge-transfer cross sections: full line; the excitation cross sections: dashed line.

Figure 6

(a) Adiabatic potentials of the ${}^3\Sigma$ states. Full lines from the bottom correspond to $1{}^3\Sigma ^{-}$, $2{}^3\Sigma ^{-}$, and $3{}^3\Sigma ^{-}$. The dot-dashed line is for $1{}^3\Sigma ^{+}$, and the long dashed line represents $4{}^3\Sigma ^{-}$. (b) Adiabatic potentials of the ${}^3\Pi$ states. The full lines are from the bottom $1{}^3\Pi$, and $2{}^3\Pi$. The long dashed line is $3{}^3\Pi$.

Figure 7

Radial coupling matrix elements in the triplet manifold: full line, $2{}^3\Pi –3{}^3\Pi$; dotted line, $1{}^3\Sigma ^{-}–2{}^3\Sigma ^{-}$; dash line, $3{}^3\Sigma ^{-}–4{}^3\Sigma ^{-}$; chain, $2{}^3\Sigma ^{-}–4{}^3\Sigma ^{-}$.

Figure 8

Rotational coupling matrix elements in the triplet manifold. Solid line, $3{}^3\Sigma ^{-}–2{}^3\Pi$; dotted line, $2{}^3\Sigma ^{-}–3{}^3\Pi$, chain, $2{}^3\Sigma ^{+}–2{}^3\Pi$; long dashed line, $2{}^3\Sigma ^{-}–1{}^3\Sigma ^{+}$; and the upper dashed line, $1{}^3\Sigma ^{-}1{}^3\Pi$ that are degenerated.

Figure 9

Partial cross sections for each outgoing channel in ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ in the triplet manifold. (a) $1{}^3\Sigma ^{-}$, (b) $3{}^3\Sigma ^{-}$, (c) $4{}^3\Sigma ^{-}$, (d) $1{}^3\Pi$, (e) $2{}^3\Pi$, (f) $3{}^3\Pi ^{-}$, and (g) $1{}^3\Sigma ^{+}$, respectively.

Figure 10

Charge transfer and excitation cross sections for ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ in the triplet manifold. Solid line with circles, charge-transfer, and solid line, excitation, respectively.

Figure 11

Charge transfer (solid line) and excitation (dotted line) cross sections in ${\mathrm{F}}^{+}+{\mathrm{H}}^{+}\to {\mathrm{F}}^{2+}+\mathrm{H}$ (a) for the incoming channel of $1{}^3\Sigma ^{-}$, and (b) for $1{}^3\Pi$, respectively.

Figure 12

${\mathrm{F}}^{+}+{\mathrm{H}}^{+}\to {\mathrm{F}}^{2+}+\mathrm{H}$ in the triplet manifold. Charge transfer cross sections (solid line), and excitation cross sections (dotted line). The cross sections are the averaged ones for the incoming channel of $1{}^3\Sigma ^{-}$ and $1{}^3\Pi$ shown in Fig. 11.