Quantum-mechanical calculations of charge transfer in collisions of ${\text{O}}^{3+}$ with He

Charge transfer due to collisions of ground-state ${\text{O}}^{3+}\left(2s^{2}2p{}^{2}P\right)$ ions with He is investigated using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method. The ab initio adiabatic potentials and radial couplings utilized in the QMOCC calculations are obtained from the multireference single- and double-excitation configuration interaction approach. State-selective and total charge-transfer cross sections are calculated for collision energies from 0.01 eV/u to 1 keV/u. Comparison with existing data reveals that the present QMOCC calculations are in good harmony with the measured total single-electron charge-transfer cross sections. Excellent agreement with the available experimental data is also found for state-selective cross sections at the measured energy region.

Figure 1

Adiabatic (solid lines) and diabatic potentials (dashed lines) of ${\left[\text{OHe}\right]}^{3+}$ ${{}^2\Sigma }^{+}$ states as a function of internuclear distance. The curves denote ${\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\left(3{{}^2\Sigma }^{+}\right)$, ${\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}P}^{\text{o}}\right)+{\text{He}}^{2+}\left(4{{}^2\Sigma }^{+}\right)$, ${\text{O}}^{2+}\left(2s2p^3{{}^{1}P}^{\text{o}}\right)+{\text{He}}^{+}$ $\left(1s{}^{2}S\right)$ $\left(5{{}^2\Sigma }^{+}\right)$, and ${\text{O}}^{3+}\left(2s^{2}2p{{}^{2}P}^{\text{o}}\right)+\text{He}\left(1s^2{}^{1}S\right)$ $\left(6{{}^2\Sigma }^{+}\right)$ states from bottom to top for both adiabatic and diabatic states.

Figure 2

Adiabatic (solid lines) and diabatic potentials (dashed lines) of ${\left[\text{OHe}\right]}^{3+}$ ${}^2\Pi$ states as a function of internuclear distance. The curves denote ${\text{O}}^{2+}\left(2s2p^3{{}^{3}D}^{\text{o}}\right)+{\text{He}}^{+}$ $\left(1s{}^{2}S\right)$ $\left(3{}^2\Pi \right)$, ${\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)$ $\left(4{}^2\Pi \right)$, ${\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}D}^{\text{o}}\right)+{\text{He}}^{2+}\left(5{}^2\Pi \right)$, ${\text{O}}^{2+}\left(2s2p^3{{}^{1}D}^{\text{o}}\right)+{\text{He}}^{+}$ $\left(1s{}^{2}S\right)$ $\left(6{}^2\Pi \right)$, ${\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}P}^{\text{o}}\right)+{\text{He}}^{2+}\left(7{}^2\Pi \right)$, ${\text{O}}^{2+}\left(2s2p^3{{}^{1}P}^{\text{o}}\right)+{\text{He}}^{+}$ $\left(1s{}^{2}S\right)$ $\left(8{}^2\Pi \right)$, and ${\text{O}}^{3+}\left(2s^{2}2p{{}^{2}P}^{\text{o}}\right)+\text{He}\left(1s^2{}^{1}S\right)$ $\left(9{}^2\Pi \right)$ states from bottom to top for both adiabatic and diabatic states.

Figure 3

Nonadiabatic radial couplings of ${\left[\text{OHe}\right]}^{3+}$ as a function of internuclear distance. Upper figures: couplings between ${{}^2\Sigma }^{+}$ states; lower figures: couplings between ${}^2\Pi$ states. Note that different height and width scales are used for the various plots.

Figure 4

Diabatic radial couplings of ${\left[\text{OHe}\right]}^{3+}$ ${{}^2\Sigma }^{+}$ states as a function of internuclear distance. Solid line, $3{{}^2\Sigma }^{+}-4{{}^2\Sigma }^{+}$; dashed line, $3{{}^2\Sigma }^{+}-5{{}^2\Sigma }^{+}$; dotted line, $3{{}^2\Sigma }^{+}-6{{}^2\Sigma }^{+}$; dash-dotted line, $4{{}^2\Sigma }^{+}-5{{}^2\Sigma }^{+}$; dash-dot dotted line, $4{{}^2\Sigma }^{+}-6{{}^2\Sigma }^{+}$; short-dashed line, $5{{}^2\Sigma }^{+}-6{{}^2\Sigma }^{+}$.

Figure 5

Diabatic radial couplings of ${\left[\text{OHe}\right]}^{3+}$ $\left({}^2\Pi \right)$ as a function of internuclear distance. The upper figure: solid line, $3{}^2\Pi -4{}^2\Pi$; dashed line, $4{}^2\Pi -5{}^2\Pi$; dotted line, $5{}^2\Pi -6{}^2\Pi$; dash-dotted line, $6{}^2\Pi -7{}^2\Pi$; dash-dot dotted line, $7{}^2\Pi -8{}^2\Pi$; short-dashed line, $8{}^2\Pi -9{}^2\Pi$; The lower figure: solid line, $3{}^2\Pi -9{}^2\Pi$; dashed line, $4{}^2\Pi -9{}^2\Pi$; dotted line, $5{}^2\Pi -9{}^2\Pi$; dash-dotted line, $6{}^2\Pi -9{}^2\Pi$; dash-dot dotted line, $7{}^2\Pi -9{}^2\Pi$; short-dashed line, $8{}^2\Pi -9{}^2\Pi$.

Figure 6

Total SEC and DEC cross sections for ${\text{O}}^{3+}+\text{He}$ collisions. Calculations: current QMOCC SEC (solid line) and DEC (dashed line), MCLZ SEC [13] (dash-dotted line), COB [13] SEC (dotted line), and DEC (short dotted line). SEC experiments: Ref. [12] (unfilled triangles), Ref. [13] (filled squares), and Ref. [14] (unfilled squares). DEC experiments: Ref. [13] (filled circles).

Figure 7

State-selective QMOCC SEC and DEC cross sections for ${\text{O}}^{3+}+\text{He}$. Solid line with filled circles: SEC to $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{3}D}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; solid line with unfilled circles: SEC to $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; solid line with filled squares: DEC to $\left[{\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}P}^{\text{o}}\right)+{\text{He}}^{2+}\right]$; solid line with unfilled squares: SEC to $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{1}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; solid line with filled triangles: DEC to $\left[{\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}D}^{\text{o}}\right)+{\text{He}}^{2+}\right]$; solid line with unfilled triangles: SEC to $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{1}D}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$.

Figure 8

Oscillations in the state-selective charge-transfer cross sections for ${\text{O}}^{3+}+\text{He}$. (a) State-selective cross section for ${{}^2\Sigma }^{+}$ channels; (b) state-selective cross section for ${}^2\Pi$ channels. Solid line: electron captured to $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; dashed line: $\left[{\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}P}^{\text{o}}\right)+{\text{He}}^{2+}\right]$; dotted line: $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{1}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; dash-dotted line: $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$; short-dashed line: $\left[{\text{O}}^{+}\left(2s^{2}2p^3{{}^{2}D}^{\text{o}}\right)+{\text{He}}^{2+}\right]$; short-dotted: $\left[{\text{O}}^{2+}\left(2s2p^3{{}^{1}D}^{\text{o}}\right)+{\text{He}}^{+}\left(1s{}^{2}S\right)\right]$.

Figure 9

The state-selective SEC cross-section ratios for capture to the triplet states ${\text{O}}^{2+}\left(2s2p^3{{}^{3}P}^{\text{o}},{{}^{3}D}^{\text{o}}\right)$ and singlet states ${\text{O}}^{2+}\left(2s2p^3{{}^{1}P}^{\text{o}},{{}^{1}D}^{\text{o}}\right)$. Solid line: the present QMOCC results with the contribution of DEC ${{}^{2}P}^{\text{o}}$ included in the ${{}^{1}P}^{\text{o}}+{{}^{1}D}^{\text{o}}$ cross section; dashed line: present QMOCC results with the contributions of DEC ${{}^{2}P}^{\text{o}}$ and ${{}^{2}D}^{\text{o}}$ included in ${{}^{1}P}^{\text{o}}+{{}^{1}D}^{\text{o}}$ cross section; dotted line: present QMOCC results without the contributions of DEC included in ${{}^{1}P}^{\text{o}}+{{}^{1}D}^{\text{o}}$ cross section; filled circles: results of the experiment of Bangsgaard et al. [12].

Figure 10

Total SEC cross sections for ${\text{O}}^{3+}+\text{He}$ collisions. Solid line: the present QMOCC results; dashed line: the scaled SEC cross sections from the QMOCC SEC of ${\text{O}}^{3+}+\text{H}$ [31]; dotted line: the scaled SEC cross sections from the QMOCC SEC of ${\text{O}}^{3+}+{\text{H}}_2$ [31]. Noted that the I in $Y$ axis represents the ionization potential of H and ${\text{H}}_2$, respectively.

Figure 11

Total SEC and state-selective rate coefficients in charge transfer of ${\text{O}}^{3+}\left({{}^{2}P}^{\text{o}}\right)$ with He as a function of temperature. (a) Total rate coefficients: solid line with filled squares: present results; solid line with filled circles: results of Butler and Dalgarno [15]; (b) present QMOCC state-selective rate coefficients.