Molecular Siegert states in an electric field

Abstract

The Siegert states of atoms and molecules in a static electric field are the solutions of the stationary Schr\"odinger equation satisfying the regularity and outgoing-wave boundary conditions. Recently, an efficient method for calculating Siegert states in the single-active-electron approximation based on the adiabatic expansion in parabolic coordinates was proposed [P. A Batishchev et al., Phys. Rev. A 82, 023416 (2010); O. I. Tolstikhin et al., Phys. Rev. A 84, 053423 (2011)]. So far, this method has been implemented only for axially symmetric potentials, which corresponds to atoms and linear molecules aligned along the field. In the present work, we extend its implementation to a general class of soft-core molecular potentials. This makes it possible to calculate the Siegert eigenvalue $E=\mathcal{E}\ensuremath{-}i\ensuremath{\Gamma}/2$ defining the energy $\mathcal{E}$ and ionization rate $\ensuremath{\Gamma}$ of the corresponding state as functions of the electric field for arbitrarily oriented polyatomic molecules. The method is illustrated by calculations for the $1s\ensuremath{\sigma}$ and $2p\ensuremath{\pi}$ states of H${}_{2}^{+}$. Comparison of the results with the predictions of perturbation theory for $\mathcal{E}$ and weak-field asymptotic theory for $\ensuremath{\Gamma}$ is discussed.