Photon-momentum transfer in diatomic molecules: An ab initio study

For a molecule, the two-center interference and the molecular scattering phase of the electron are important for almost all the processes that may occur in a laser field. In this study, we investigate their effects in the transfer of linear photon momentum to the ionized electron by absorbing a single photon. The time-dependent Schrödinger equation of ${{\text{H}}_2}^{+}$ is numerically solved in the multipolar gauge in which the electric quadrupole term and the magnetic dipole term are explicitly expressed. This allows us to separate the contributions of the two terms in the momentum transfer. For different configurations of the molecular and the laser orientation, the transferred momentum to the electron is evaluated at different internuclear distances with various photon energies and two-center interferences are identified in the whole region. At small electron energies and small internuclear distances, we find significant deviations from the prediction of the classical double-slit model due to the strong mediation of the Coulomb potential. Finally, even for a large internuclear distance, our results show that a varying molecular scattering phase is important at all electron energies, which is beyond the simple prediction of the linear combination of the atomical orbitals.

Figure 1

The 2D photoelectron momentum distributions in the polarization-propagation plane of ${{\text{H}}_2}^{+}$ by a linearly polarized laser in: (a) the $zx$, (b) the $xz$, and (c) the $yx$ configuration, respectively. The laser is polarized along the vertical axis and the wave vector is along the horizontal axis. (d) The average momentum transfer of the photoelectron along the laser propagation direction ($q_k$) as a function of the electron energy, ionized from ${{\mathrm{H}}_2}^{+}1s{\sigma }_g$ state for the three typical configurations: the $zx$ (dot-dashed blue line), the $xz$ (solid yellow line), and the $yx$ (dashed green line), respectively. The result for H atom (red dotted line) is also plotted for comparison.

Figure 2

The ratio between the average momentum transfer ($q_k$) from ${{\text{H}}_2}^{+}$ to that from H atom in the $(E,R)$ plane, plotted in a double logarithmic scale. White straight lines with a slope equal to $-1/2$ are plotted for reference.

Figure 3

The ratio between the average momentum transfer for $1s{\sigma }_g$ (yellow solid line) and $2p{\sigma }_u$ (green dashed line) of ${{\text{H}}_2}^{+}$ with internuclear distance $R=10$ a.u., calculated by TDSE. The prediction by the independent atom model for $1s{\sigma }_g$ (blue dot-dashed line) is also shown, together with a horizontal line with $F=1$ to guide one's eyes.

Figure 4

The ratio between the contribution by electric-quadrupole term to the average momentum transfer and that by the magnetic dipole term, with different internuclear distances: (a) $2\mathrm{a}.\mathrm{u}.$, (b) $5\mathrm{a}.\mathrm{u}.$, (c) $10\mathrm{a}.\mathrm{u}.$. For each frame, results are, respectively, presented for the $zx$ (dot-dashed blue line), the $xz$ (solid yellow line), and the $yx$ (dashed green line) configuration.