We use a ${\mathcal{L}}^2$-discretization technique for solving the time-dependent Schrödinger equation for H${}_2^{+}$ interacting with a short vuv laser pulse, in the Born-Oppenheimer approximation. The calculations include the electronic three-dimensional and vibrational one-dimensional motions. In this approach, we use the prolate spheroidal coordinate system to describe the electronic functions and a basis of Laguerre and Legendre functions [Phys. Rev. A 71, 053407 (2005)]. The vibrational motion is treated by using a basis of Sturmian functions. We consider the problem of two-photon dissociation of H${}_2^{+}$ with photons ranging from 0.32 to 0.4 a.u corresponding to wavelengths from 143 to 114 nm. The initial vibrational wave packet results from a vertical (Franck-Condon) transition from the H${}_2$ ground state towards a superposition of vibrational states in the $1s{\sigma }_g$ electronic state of H${}_2^{+}$. The effects of various types of nuclear interference on the population of the dissociative channels $2s{\sigma }_g$ and $3d{\sigma }_g$ are discussed in detail. In addition, we show that for 0.32-a.u. photon energy, the interference effects in the $3d{\sigma }_g$ channel whose existence has been demonstrated previously [Phys. Rev. Lett. 102, 123001 (2009)] can be observed in the total kinetic energy release spectrum.

• Received 30 January 2012

DOI:https://doi.org/10.1103/PhysRevA.86.013416