Molecular-frame electron-scattering experiment on the dipole-forbidden $2{\sigma }_g\to 1{\pi }_g$ transition of ${\mathrm{N}}_2$

We report molecular-frame electron-scattering cross sections of ${\mathrm{N}}_2$, obtained using an electron-ion coincidence technique. Vector correlation between the scattered electron and the fragment ion has been measured at incident electron energy of 1.4 keV for the dipole-forbidden $2{\sigma }_g\to 1{\pi }_g$ transition of ${\mathrm{N}}_2$ as well as for the inner-valence ionization. The generalized oscillator strength thus obtained exhibits characteristic molecular-orientation dependence due to anisotropic shapes of the molecular orbitals participating in the transition. The present method enables one to explore stereodynamics of dipole-forbidden transitions to autoionization states, which are inaccessible by photoabsorption experiments.

Figure 1

A schematic representation of the experimental setup for molecular-frame EELS experiments.

Figure 2

Left-hand panel: (a) partial ion yield spectra for $\theta =2.2^{\circ }$ and $8.2^{\circ }$ constructed from the electron-${\mathrm{N}}^{+}$ coincident data. The solid line represents the result of the photoionization experiment [18]. (b) Partial ion yield spectra for ${\mathrm{N}}^{+}$ with $\mathrm{KE}<0.45\mathrm{eV}$. (c) Partial ion yield spectra for ${\mathrm{N}}^{+}$ with $0.9<\mathrm{KE}<1.4\mathrm{eV}$. Upper right-hand panel depicts theoretical potential energy curves of the $C{}^2{\mathrm{\Sigma }}_u^{+}$ and $F{}^2{\mathrm{\Sigma }}_g^{+}$ states digitalized from Ref. [20]. The dotted lines running vertically indicate the Frank-Condon region. Shown in the lower right-hand panel is the kinetic energy distribution of ${\mathrm{N}}^{+}$ at $\theta =2.2^{\circ }$ .

Figure 3

(a) Experimental GOSs in a molecular frame for the 32 eV band $(E=30-33\mathrm{eV})$ and ionization continuum $(E=35-38\mathrm{eV})$. For comparison in shape the angular distributions are normalized at ${\varphi }_{\mathit{K}}={85}^{\circ }$. (b) TDDFT calculations for the $2{\sigma }_g\to 1{\pi }_g$ and $2{\sigma }_g\to 4{\sigma }_g$ excitations. For ease of comparison, the latter is multiplied by a factor of 5. The inserted figures are the theoretical contour plots of the $1{\pi }_g$ and $4{\sigma }_g$ orbitals.