Ab initio calculation of charge transfer in proton collisions with N${}_2$

Total and partial charge transfer cross sections are calculated in collisions of protons with the nitrogen molecule at energies between $0.1$ and 10 keV. Ab initio potential energy curves and nonadiabatic couplings have been obtained for a number of N${}_2$ bond lengths using a multireference configuration interaction method. The influence of the anisotropy of the target molecule is investigated. Results are compared with previous experimental and theoretical data.

Figure 1

Internal nuclear coordinates and displacements used in the description of the (HN${}_2{)}^{+}$ system.

Figure 2

Potential energy curves obtained at $\theta ={45}^{\circ }$ for several N-N bond distances as indicated in the panels. The solid lines correspond to H${}^{+}$+N${}_2$ channels, while dashed lines are H $+$ N${}_2^{+}$ channels (see Table ). The symbols are obtained from the experimental excitation energies of [34]. The inset shows the energy differences $E_2-E_1$ and $E_3-E_1$ for $\rho =2.1$ $a_0$.

Figure 3

Same as in Fig. 2, with $\rho =2.1$ $a_0$ and $\theta$ values indicated in the panels.

Figure 4

Potential energy curve of the electronic ground state of N${}_2$ and the vibrational probability densities $|{\chi }_i{|}^2$ of the first five vibrational states. The bullets are displayed at the five values of $\rho$ used in the vibrational sudden calculation of the CT cross sections.

Figure 5

Radial $\langle {\phi }_i|\partial /\partial Z|{\phi }_j\rangle$ and rotational $\langle {\phi }_i|\partial /\partial X|{\phi }_j\rangle$ couplings corrected with $v$-terms translation factors in H${}^{+}$+N${}_2$($X{}^1{\Sigma }_g^{+}$) collisions along the projectile-target distance $R$ and for a geometrical configuration given by $\rho =2.1$ $a_0$ and $\theta ={45}^{\circ }$ (see Fig. 1). The lines are labeled indicating ${\phi }_i$-${\phi }_j$ pairs of states, with the state number assigned in increasing energy order (see Table ).

Figure 6

Opacity functions $b{P}_{1,j}^{\mathrm{iso}}(b,v;\rho =2.1a_0,\theta ={45}^{\circ })$ for transitions to the first three CT channels (solid lines) at three impact velocities (indicated in the panels) in H${}^{+}$+N${}_2$($X{}^1{\Sigma }_g^{+}$) collisions. The dashed lines are the opacities for the total CT, and the dot-dashed lines are the nonoscillatory component of the probabilities obtained with the Demkov model [see Eq. (17)].

Figure 7

State-resolved CT cross sections ${\sigma }_f^{\mathrm{iso}}(v,\rho =2.1a_0,\theta ={45}^{\circ })$ in H${}^{+}$+N${}_2$($X{}^1{\Sigma }_g^{+}$) collisions. CT channels are displayed as solid lines, while dashed lines correspond to excitation channels, as indicated in the figure.

Figure 8

Total CT cross sections as functions of the impact energy in H${}^{+}$+N${}_2$($X{}^1{\Sigma }_g^{+}$) collisions. The lines are the present results with a fixed $\theta ={45}^{\circ }$ for different values of $\rho$, indicated in the figure, and the vibrational-sudden result of Eq. (9). The solid symbols are experimental data of Stier and Barnett [14], Rudd et al. [15] (CT and ionization), and Gao et al. [16], while the empty symbols correspond to the calculations of Cabrera-Trujillo et al. [19].

Figure 9

Same as Fig. 8 but, in this case, $\rho =2.1$ $a_0$ and CT cross sections are presented for various values of $\theta$, as indicated in the figure, along with the orientation-averaged one obtained with Eq. (13).