$R$-matrix calculation of electron collisions with electronically excited ${\mathrm{O}}_2$ molecules

Low-energy electron collisions with ${\mathrm{O}}_2$ molecules are studied using the fixed-bond $R$-matrix method. In addition to the ${\mathrm{O}}_2$ $X{}^3\Sigma _g^{-}$ ground state, integrated cross sections are calculated for electron collisions with the $a{}^1\Delta _g$ and $b{}^1\Sigma _g^{+}$ excited states of ${\mathrm{O}}_2$ molecules. Thirteen target electronic states of ${\mathrm{O}}_2$ are included in the model within a valence configuration interaction representations of the target states. Elastic cross sections for the $a{}^1\Delta _g$ and $b{}^1\Sigma _g^{+}$ excited states are similar to the cross sections for the $X{}^3\Sigma _g^{-}$ ground state. As in case of excitation from the $X{}^3\Sigma _g^{-}$ state, the ${\mathrm{O}}_2^{-}$ ${\Pi }_u$ resonance makes the dominant contribution to excitation cross sections from the $a{}^1\Delta _g$ and $b{}^1\Sigma _g^{+}$ states. The magnitude of excitation cross sections from the $a{}^1\Delta _g$ state to the $b{}^1\Sigma _g^{+}$ state is about ten times larger than the corresponding cross sections from the $X{}^3\Sigma _g^{-}$ to the $b{}^1\Sigma _g^{+}$ state. For this $a{}^1\Delta _g\to b{}^1\Sigma _g^{+}$ transition, our cross section at $4.5\mathrm{eV}$ agrees well with the available experimental value. These results should be important for models of plasma discharge chemistry which often requires cross sections between the excited electronic states of ${\mathrm{O}}_2$.

Figure 1

Potential energy curves of the ${\mathrm{O}}_2$ electronic states. The equilibrium distance of the $X{}^3\Sigma _g^{-}$ state, $R=2.3a_0$ is used in our $R$-matrix calculations.

Figure 2

The elastic cross sections of the ${\mathrm{O}}_2$ $X{}^3\Sigma _g^{-}$ state. The thick full line represents cross sections obtained by 13 target states calculation including $1{}^{1,3}\Pi _{g,u}$ target states. The thick dotted line is the cross sections including nine target states without $1{}^{1,3}\Pi _{g,u}$ target states. The partial cross sections from the 13 target states calculation are represented by thin full lines marked with open symbols. Symmetries with minor contributions are not shown in the figure. For comparisons, we also include the previous $R$-matrix results of Noble and Burke (see Ref. 18), the experimental cross sections of Trajmar et al. (see Ref. 39), Kanik et al. (see Ref. 40), Shyn and Sharp (see Ref. 41), Sullivan et al. (see Ref. 42), and Linert et al. (see Ref. 43).

Figure 3

The excitation cross section from the ${\mathrm{O}}_2$ $X{}^3\Sigma _g^{-}$ state to the $a{}^1\Delta _g$ state. Our results are shown in thick full and dotted lines as in Fig. 2. The partial cross sections of ${}^2\Pi _{g,u}$ symmetries are also shown as thin full lines marked with open symbols. For comparison, we include the previous $R$-matrix results of Noble and Burke (see Ref. 18), the ERT calculations of Teillet-Billy et al. (see Ref. 12), the experimental cross sections of Doering (see Ref. 44), Shyn and Sweeney (see Ref. 45), and Middleton et al. (see Ref. 13).

Figure 4

The excitation cross section from the ${\mathrm{O}}_2$ $X{}^3\Sigma _g^{-}$ state to the $b{}^1\Sigma _g^{+}$ state. Our results are shown in thick full and dotted lines as in Fig. 2. We include the previous theoretical results of Noble and Burke (see Ref. 18), Teillet-Billy et al. (see Ref. 12) and the experimental cross sections of Shyn and Sweeney (see Ref. 45) and Middleton et al. (see Ref. 13).

Figure 5

The excitation cross sections from the ${\mathrm{O}}_2$ $X{}^3\Sigma _g^{-}$ state to the $6\mathrm{eV}$ states which consist of the ${\mathrm{O}}_2$ $c{}^1\Sigma _u^{-}$, $A^{\prime }{}^3\Delta _u$, and $A{}^3\Sigma _u^{+}$ states. The total cross sections shown here are the sum of the individual cross sections of these three states. Our results for the total cross sections are shown in thick full and dotted lines as in Fig. 2. The individual excitation cross sections from 13 states calculations are shown as thin full lines marked with open symbols. We include the total cross sections from the previous $R$-matrix results of Noble and Burke (see Ref. 18), the ERT calculations of Gauyacq et al. (see Ref. 37), the experimental results of Teillet-Billy et al. (see Ref. 46) and Green et al. (see Ref. 38).

Figure 6

The elastic cross sections for the ${\mathrm{O}}_2$ $a{}^1\Delta _g$ state. The thick full line represents the cross sections obtained by 13 target states calculation including $1{}^{1,3}\Pi _{g,u}$ target states. The contributions of the ${}^2\Delta _g$ and ${}^2\Delta _u$ total symmetries are also shown.

Figure 7

Excitation cross section from the ${\mathrm{O}}_2$ $a{}^1\Delta _g$ state to the $b{}^1\Sigma _g^{+}$ state. Our results are shown in the thick full line with the contributions of ${}^2\Sigma _g^{+}$ and ${}^2\Pi _u$ symmetries in thin lines as in Fig. 6. The experimental cross section of Hall and Trajmar (see Ref. 8) is also included for comparison.

Figure 8

Excitation cross sections from the ${\mathrm{O}}_2$ $a{}^1\Delta _g$ state to the $6\mathrm{eV}$ states of the ${\mathrm{O}}_2$ $c{}^1\Sigma _u^{-}$, $A^{\prime }{}^3\Delta _u$, and $A{}^3\Sigma _u^{+}$ states. The cross sections for excitation to the individual state are shown in the thin lines. The thick full line represents the sum of these cross sections.

Figure 9

Elastic cross section for the ${\mathrm{O}}_2$ $b{}^1\Sigma _g^{+}$ state. The results are shown in the thick full line with the contributions of ${}^2\Sigma _g^{+}$, ${}^2\Pi _u$, and ${}^2\Sigma _u^{-}$ symmetries in the thin lines as in Fig. 6.

Figure 10

Excitation cross sections from the ${\mathrm{O}}_2$ $b{}^1\Sigma _g^{+}$ state to the $6\mathrm{eV}$ states of the ${\mathrm{O}}_2$ $c{}^1\Sigma _u^{-}$, $A^{\prime }{}^3\Delta _u$, and $A{}^3\Sigma _u^{+}$ states. The cross sections for excitation to the individual state are shown in the thin lines. The thick full line represents the sum of these cross sections.