$R$-matrix calculation of integral and differential cross sections for low-energy electron-impact excitations of the ${\mathrm{N}}_2$ molecule

Low-energy electron-impact excitations of ${\mathrm{N}}_2$ molecules are studied using the fixed-bond $R$-matrix method based on state-averaged complete active-space self-consistent-field orbitals. Thirteen target electronic states of ${\mathrm{N}}_2$ are included in the model within a valence configuration interaction representation of the target states. Integrated as well as differential cross sections of the $A{}^3\Sigma _u^{+}$, $B{}^3\Pi _g$, $W{}^3\Delta _u$, $B^{\prime }{}^3\Sigma _u^{-}$, $a^{\prime }{}^1\Sigma _u^{-}$, $a{}^1\Pi _g$, $w{}^1\Delta _u$, and $C{}^3\Pi _u$ states are calculated and compared with the previous experimental measurements. These excitations, especially of the higher four states, have not been studied enough theoretically in the previous literature. In general, good agreements are observed both in the integrated and differential cross sections. However, some discrepancies are seen in the integrated cross sections of the $A^3{\Sigma }_u^{+}$ and $C{}^3\Pi _u$ states, especially around a peak structure.

Figure 1

Potential energy curves of the ${\mathrm{N}}_2$ electronic states. The equilibrium distance of the $X{}^1\Sigma _g^{+}$ state, $R=2.068a_0$, is used in our $R$-matrix calculations.

Figure 2

Integral excitation cross sections of the $A{}^3\Sigma _u^{+}$ [panel (a)], $B{}^3\Pi _g$ [panel (b)], $W{}^3\Delta _u$ [panel (c)], and $B^{\prime }{}^3\Sigma _u^{-}$ [panel (d)] states. Our results are shown as thick solid lines. For comparison, we include the previous $R$-matrix results of Gillan et al. [21], Schwinger multichannel results of da Costa and Lima [35], and the experimental cross sections of Cartwright et al. [11], Campbell et al. [13], and Johnson et al. [3].

Figure 3

Integral excitation cross sections of the $a^{\prime }{}^1\Sigma _u^{-}$ [panel (a)], $a{}^1\Pi _g$ [panel (b)], $w{}^1\Delta _u$ [panel (c)], and $C{}^3\Pi _u$ [panel (d)] states. Our results are shown as thick solid lines. In addition to the experimental ICS’s in Fig. 2, we include the results of Ajello and Shemansky [5], Zetner and Trajmar [10], Mason and Newell [6], Poparic et al. [7], Zubek [8], and Zubek and King [9].

Figure 4

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $A{}^3\Sigma _u^{+}$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. The solid line represents our result. For comparison, we include the previous theoretical cross sections of Gillan et al. [21] and experimental results of Khakoo et al. [2], Brunger and Teubner [12], Cartwright et al. [11], Zetner and Trajmar [10], and LeClair and Trajmar [37].

Figure 5

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $B{}^3\Pi _g$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. The results of Schwinger multichannel calculations by da Costa and Lima [35] are also shown in the panels. Other details are the same as in Fig. 4.

Figure 6

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $W{}^3\Delta _u$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. Other details are the same as in Fig. 4.

Figure 7

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $B^{\prime }{}^3\Sigma _u^{-}$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. Other details are the same as in Fig. 4.

Figure 8

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $a^{\prime }{}^1\Sigma _u^{-}$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. Other details are the same as in Fig. 4.

Figure 9

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $a{}^1\Pi _g$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. Note that the DCS’s are shown in logarithmic scale. Other details are the same as in Fig. 4.

Figure 10

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $w{}^1\Delta _u$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. Other details are the same as in Fig. 4.

Figure 11

Differential cross sections for electron-impact excitation from the ${\mathrm{N}}_2$ $X{}^1\Sigma _g^{+}$ state to the $C{}^3\Pi _u$ state. Electron-impact energy of (a) $12.5\mathrm{eV}$, (b) $15\mathrm{eV}$, and (c) $17.5\mathrm{eV}$. The experimental DCS’s of Zubek and King [9] are added. Other details are the same as in Fig. 4.