Multidimensional Mesh Approaches to Calculations of Atoms and Diatomic Molecules in Strong Electric Fields

Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of atoms and molecules in strong external fields where neither the external field nor the internal interactions can be considered as a perturbation. In the framework of this method we present various approaches to calculations of quasi-steady states of these systems in strong electric fields. These approaches are aimed at obtaining precise complex wavefunctions and corresponding eigenvalues in the form E = E_0 - i\Gamma/2, where E_0 is the real part of the energy and the value \Gamma/2 determines the lifetime of the state in relation to escape of electrons from the system. The applications for single-electron systems include correct solutions of the Schroedinger equation for the H_2^+ ion (energies and decay rates) and the hydrogen atom in strong parallel electric and magnetic fields. Some results for the helium atom in strong electric fields are announced.