Complex energies and the polyelectronic Stark problem: II. The Li n=4 levels for weak and strong fields

We computed nonperturbatively, via the state-specific matrix complex eigenv alue Schrodinger equation (CESE) theory, the energy shifts and widths of al l ten Li n = 4 levels which are produced by electric fields of strength, F, in the range 0.0-0.0012 au (6.17 x 10(6) V cm(-1)). By establishing the na ture of the state vector to which every physically relevant complex eigenva lue corresponds, we delineated the field strength region where it is possib le to characterize the perturbed levels in terms of small superpositions of unperturbed Li states (called here the weak field region) from the region where the mixing of the discrete and the continuous states renders such an identification impossible (the strong field region). For both regions, syst ematic and accurate CESE calculations have produced a complete adiabatic sp ectrum of perturbed energies. It turns out that the behaviour of the energi es of the m = +/-1, +/-2 and +/-3 levels is smooth. In contrast, the Stark spectrum of the m = 0 levels contains not only all the n = 4 levels but als o parts of the n = 3 and 5 manifolds, and is characterized by regions of cr ossing as well as of avoided crossing of the real part of the complex energ ies as a function of F. In the former case, the widths of the crossing (diabatic) levels differ con siderably-even by two orders of magnitude. In the latter case, there are ab rupt changes in the widths, a result of significant changes in the perturbe d wavefunctions. For weak fields, which, for example, for the in = 0, n = 4 levels correspond to values up to about 2 x 10(-4) au, the one-electron se miclassical Ammosov, Delone and Krainov (ADK) formula for the widths produc es reasonable trends. However, when the wavefunction mixing increases with field strength, it fails completely. For the four m = 0 levels, comparison is made with the results of Sahoo and Ho, obtained nonperturbatively by applying the complex absorbing potential (CAP) method. For a range of relatively weak fields, the CAP results for t he widths do not follow a physically meaningful curve and deviate from our CESE results by orders of magnitude. As regards the energy spectrum, the on e given by Sahoo and Ho for strengths up to 0.0005 au and the one given by us are substantially different, the former presenting a simple picture, wit hout any avoided crossings. Given these differences, we take the opportunit y to comment, via exemplars, on problems and solutions pertaining to the ca lculation of resonance states of polyelectronic atoms and molecules in term s of non-Hermitian approaches employing square-integrable function spaces.