Strong-field approximation for ionization of a diatomic molecule by a strong laser field. II. The role of electron rescattering off the molecular centers

The strong-field approximation for ionization of diatomic molecules by a strong laser field [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. A 74, 063404 (2006)] is generalized to include rescattering of the ionized electron wave packet off the molecular centers (the electron's parent ion or the second atom). There are four rescattering contributions to the ionization rate, which are responsible for the high-energy plateau in the electron spectra and which interfere in a complicated manner. The spectra are even more complicated due to the different symmetry properties of the atomic orbitals of which a particular molecular orbital consists. Nevertheless, a comparatively simple condition emerges for the destructive interference of all these contributions, which yields a curve in the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane. Here $\ensuremath{\theta}$ is the electron emission angle and ${E}_{{\mathbf{p}}_{f}}$ is the electron kinetic energy. The resulting suppression of the rescattering plateau can be strong and affect a large area of the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane, depending on the orientation of the molecule. We illustrate this using the examples of the $3{\ensuremath{\sigma}}_{g}$ molecular orbital of ${\mathrm{N}}_{2}$ and the $1{\ensuremath{\pi}}_{g}$ molecular orbital of ${\mathrm{O}}_{2}$ for various orientations of these molecules with respect to the laser polarization axis. For ${\mathrm{N}}_{2}$, for perpendicular orientation and the equilibrium internuclear distance ${R}_{0}$, we find that the minima of the ionization rate form the curve ${E}_{{\mathbf{p}}_{f}}\phantom{\rule{0.2em}{0ex}}{\mathrm{cos}}^{2}\phantom{\rule{0.2em}{0ex}}\ensuremath{\theta}={\ensuremath{\pi}}^{2}∕(2{R}_{0}^{2})$ in the $({E}_{{\mathbf{p}}_{f}},\ensuremath{\theta})$ plane. For ${\mathrm{O}}_{2}$ the rescattering plateau is absent for perpendicular orientation.