Double-slit interference in H$_2^{\,+}$ subjected to ultrashort x-ray radiation

Extending our earlier work~[1], we consider the double-slit interference effect [2,3] in the H$_2^{\,+}$ ion irradiated by intense short x-ray laser pulses with central photon energies from $200$-$500$ eV. The time-dependent Schr\"odinger equation in prolate spheroidal coordinates is solved to extract the angle-differential cross section of the photo\-electron. The spatical coordinates are discretized by means of a finite-element discrete-variable representation. We discuss the confinement effect [3] in the parallel geometry, in which the emission mode of the photoelectron along the laser polarization direction is dynamically forbidden. This confinement appears periodically, with the details depending on both the momentum of the electron and the internuclear separation. On the other hand, the effect disappears in the perpendicular geometry. We compare our results to those obtained from a simple plane-wave model based on time-independent perturbation theory.\\[4pt] [1]~X.~Guan, E.~Secor, K.~Bartschat, and B.~I.~Schneider, Phys.~Rev.~A~{\bf 84} (2011) 032420.\\[0pt] [2]~I.~G.~Kaplan and A.~P.~Markin, Sov. Phys. Dokl. {\bf 14} (1969) 36.\\[0pt] [3]~J.~Fern\'andez, F.~L.~Yip, T.~N.~Rescigno, C.~W.~McCurdy, and F.~Mart\'in, Phys. Rev. A {\bf 79} (2009) 043409.