Nenad S. Simonović

Shape transitions in excited states of two-electron quantum dots in a magnetic field

We use entanglement to study shape transitions in two-electron axially symmetric parabolic quantum dots in a perpendicular magnetic field. At a specific magnetic field value the dot attains a spherical symmetry. The transition from the axial to the spherical symmetry manifests itself as a drastic change of the entanglement of the lowest state with zero angular momentum projection. While the electrons in such a state are always localized in the plane (x − y) before the transition point, after this point they become localized in the vertical direction.

Over-the-barrier electron detachment in the hydrogen negative ion

The electron detachment from the hydrogen negative ion in strong fields is studied using the two-electron and different single-electron models within the quasistatic approximation. A special attention is payed to over-the-barrier regime where the Stark saddle is suppressed below the lowest energy level. It is demonstrated that the single-electron description of the lowest state of ion, that is a good approximation for weak fields, fails in this and partially in the tunneling regime. The exact lowest state energies and detachment rates for the ion at different strengths of the applied field are determined by solving the eigenvalue problem of the full two-electron Hamiltonian. An accurate formula for the rate, that is valid in both regimes, is determined by fitting the exact data to the expression estimated using single-electron descriptions.

The collinear helium atom: adiabatic potential curves and quasi-separable approximation in hyperspherical coordinates

The collinear models of the helium atom, where the electrons reside on the opposite sides of the nucleus (eZe configuration) and on the same side (Zee configuration), are studied using the adiabatic approach in hyperspherical coordinates. Adiabatic potential curves are evaluated for both configurations and related to hyperspherical channels. The eigenenergies are calculated by applying the quasi-separable (single-channel) approximation and found to be in good agreement with those obtained using other methods. It is demonstrated that the widths of autoionizing states can be estimated by taking into account the coupling between different channels. The adiabatic potential curves and energy levels for the collinear atom are compared to those for the full three-dimensional (3D) model. It is shown that the S states of the 3D model with minimal and maximal angular excitations, as well as the corresponding adiabatic potential curves at large values of the hyperradius, can be related to the eZe and Zee collinear configurations, respectively. It is demonstrated that a set of curves of the 3D atom converging to the same ionization threshold is then confined in the area delimited by the pair of eZe/Zee curves also converging to this threshold. A class of anticrossings of the adiabatic potential curves in the 3D model, located along the eZe adiabatic curves at small values of the hyperradius, is observed and related to the unstable character of the classical configuration corresponding to the eZe collinear model in this domain.

Semiclassical calculations of 1Se intra-shell resonant states of the hydrogen negative ion

We analyse the classical dynamics of electrons in the hydrogen negative ion within the so-called asynchronous model, previously successfully applied to the helium atom. The motion is near separable in the prolate spheroidal coordinates, which allows for an approximative torus quantization of the configuration, yielding the energies of doubly excited intra-shell resonances comparable with quantum-mechanical values.