Detecting Electron Motion in Atoms and Molecules

The detection of spatial and temporal electronic motion by scattering of subfemtosecond pulses of 10 keV electrons from coherent superpositions of electronic states of both H and $T_2^{+}$ is investigated. For the H atom, we predict changes in the diffraction images that reflect the time-dependent effective radius of the electronic charge density. For an aligned $T_2^{+}$ molecule, the diffraction image changes reflect the time-dependent localization or delocalization of the electronic charge density.

Figure 1

Proposed H atom experiment. The red arrow indicates the polarization of the pump laser. For future reference, the coordinates and the angles are defined in the figure.

Figure 2

Populations of $np$ states of the H atom as a function of the duration of a laser pulse with peak intensity $I=1\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$, $\omega =12.45\mathrm{eV}$, and $\varphi =0$ [cf. Eq. (1)].

Figure 3

Right column: Differential cross sections in the $y\mathrm{\text{−}}z$ plane (cf. Fig. 1) for scattering of a 110 as, 10 keV electron pulse from the coherent state ${\mathrm{H}}^{*}(3p+4p)$ (whose beat period is $\mathsf{T}=6.3\mathrm{fs}$). Left column: Charge density of the state ${\mathrm{H}}^{*}(3p+4p)$. The three rows correspond to pump-probe time delays of $0\mathsf{T}$, $\mathsf{T}/4$, and $\mathsf{T}/2$. Owing to symmetry, we show only the upper half of each diffraction image.

Figure 4

Left column: Elastic DSCSs as a function of the azimuthal angle $\phi$ for two different polar angles $\theta$ (cf. Fig. 1); each panel shows results for three pump-probe time delays. Right column: Comparison of the elastic DSCS and the most important inelastic one (for deexcitation to the $3s$ state) plotted vs the polar scattering angle $\theta$.

Figure 5

Charge density of the $T_2^{+}$ state in Eq. (9) (with $c_g=c_u$, $R=6$) in the $y\mathrm{\text{−}}z$ plane and the corresponding averaged elastic DSCS for three delay times.

Figure 6

Left column: Averaged elastic DSCS (from the right column of Fig. 5) plotted vs azimuthal angle $\phi$ for two polar angles $\theta$. Right column: The corresponding temporal asymmetry parameter $A(t=\mathsf{T}/4;\phi ,\theta )$ [cf. Eq. (11)].