Atomic Siegert states in an electric field: Transverse momentum distribution of the ionized electrons

The Siegert states of atoms in a static uniform electric field, defined as the solutions to the stationary Schroedinger equation satisfying the regularity and outgoing-wave boundary conditions, are discussed. An efficient method to calculate not only the complex energy eigenvalue, but also the eigenfunction for a general class of one-electron atomic potentials is introduced. An exact expression for the transverse momentum distribution of the ionized electrons in terms of the Siegert eigenfunction in the asymptotic region is derived. The method is illustrated by calculations of the energy, ionization width, and transverse momentum distribution as functions of the electric field for several lowest states of H, outer p shells of Ne, Ar, Kr, and Xe, and the active electron in H-. We also discuss the ionization of Ar by the pulse of a unidirectional time-dependent electric field, which illustrates the role of the Siegert states in the recently developed adiabatic theory of ionization of atoms by intense laser pulses [O. I. Tolstikhin et al., Phys. Rev. A 81, 033415 (2010)].