Polarization correlations in the two--photon decay of hydrogen--like ions

Polarization properties of the photons emitted in the two-photon decay of hydrogen-like ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two-photon) coincidence measurement performed by polarization-sensitive detectors. Detailed calculations of this function are performed for the $2s_{1/2} \to 1s_{1/2}$ transition in neutral hydrogen as well as Xe$^{53+}$ and U$^{91+}$ ions. The obtained results allow us to understand the influence of relativistic and non-dipole effects on the polarization correlations in the bound-bound two-photon transitions in heavy ions

K α₁ Radiation from Heavy, Heliumlike Ions Produced in Relativistic Collisions

Bound-state transitions in few-electron, heavy ions following radiative electron capture are studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock approach. Special attention is paid to the K α1 (1 s1/2 2 p3/2 1.3PJ=1,2→1s21/2 1SJ=0) radiative decay of heliumlike uranium U90+ projectiles. This decay has recently been observed at the GSI facility in Darmstadt, giving rise to a surprisingly isotropic angular distribution, which is inconsistent with previous experiments and calculations based on a one-particle model. We show that the unexpected isotropy essentially results from the mutual cancellation of the angular distributions of the 1P1 → 1S0 electric dipole and 3P2 → 1S0 magnetic quadrupole transitions, both of which contribute to the K α1 radiation. Detailed computations on the anisotropy of the K α1 radiation have been carried out for a wide range of projectile energies and are compared to available experimental data

Angular and Polarization Analysis of X-Rays Emitted from Highly-Charged, Few-Electron Ions

The recent theoretical progress in studying the x-ray emission from highly-charged, few-electron ions is reviewed. These case studies show that relativistic, high-Z ions provide a unique tool for better understanding the interplay between the electron-photon and electron-electron interactions in strong fields. Most naturally, this interplay is probed by the radiative capture of a (quasi-) free electron into the bound states of projectile ions, and by varying the charge state and the energy of the projectiles. For the capture into initially hydrogen-and lithium-like ions, here we summarize the recent results for the angular distribution and polarization of the recombination photons as well as the subsequent Kα emission, if the electron is captured into an excited state of the ion

Effects of Configuration Interaction on the Alignment of Beryllium-Like Ions

The radiative electron capture into (initially) lithium-like ions is studied within the framework of the density matrix approach. Special attention is paid to the magnetic sublevel population of the residual ionic states which is described by a set of alignment parameters. Detailed calculations of these parameters have been performed for the capture into the 1s2 2s 3d3/2 Jf2 level of high-Z ions along the beryllium isoelectronic sequence. We devote special attention to the modifications in the many-electron case as opposed to singleelectron systems. The electron correlation leads to an enhancement of the alignment, which becomes more pronounced as the nuclear charge decreases and the electron-electron interaction gains in strength as compared to the electron-nucleus interaction

Radiative Electron Capture into High- Z Few-Electron Ions: Alignment of the Excited Ionic States

We lay out a unified formalism for the description of radiative electron capture into excited states of heavy, few-electron ions and their subsequent decay, including a full account of many-electron effects and higher-order multipoles of the radiation field. In particular, the density-matrix theory is applied to explore the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. For the electron capture into the initially hydrogenlike U91+ and lithiumlike U89+ uranium projectiles, the alignment parameters are calculated, within the multiconfiguration Dirac-Fock approach, as a function of the collision energy and for different ionic states. From these calculations, we find that the many-electron interactions may result in a small enhancement of the alignment, and that this effect becomes more pronounced for highly excited levels

Alignment of Heavy Few-Electron Ions Following Excitation by Relativistic Coulomb Collisions

The Coulomb excitation of highly charged few-electron ions in relativistic collisions with protons and low- Z atoms is studied within the framework of first-order perturbation theory and the multiconfiguration Dirac-Fock method. Apart from the computation of the total excitation cross sections, a detailed theoretical analysis has been performed for the magnetic sublevel population of the residual ions. To describe this population, general expressions are derived for the alignment parameters of the excited states of the ions, taking into account the relativistic and many-electron effects. Calculations are performed for the K→L and K→M excitation of helium- and lithiumlike uranium ions and for a wide range of projectile energies. It is shown that the alignment of heavy few-electron ions is sensitive to relativistic and magnetic-interaction effects and, hence, to the collision energies of the projectiles. The theoretical predictions are discussed in the context of recent measurements on the Coulomb excitation of heliumlike uranium U90+ ions which were recently performed at the GSI storage ring in Darmstadt

Angular distribution studies on the two-photon ionization of hydrogen-like ions: Relativistic description

The angular distribution of the emitted electrons, following the two-photon ionization of the hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium- and high-Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with the electric-dipole approximation. This includes a strong forward emission while, in dipole approxmation, the electron emission always occurs symmetric with respect to the plane which is perpendicular to the photon beam. Detailed computations for the dependence of the photoelectron angular distributions on the polarization of the incident light are carried out for the ionization of H, Xe$^{53+}$, and U$^{91+}$ (hydrogen-like) ions.Comment: 16 pages, 4 figures, published in J Phys

Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics

This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which has a particular property: the perturbation series for the ground-state energy vanishes to all orders in the coupling parameter, but the actual ground-state energy is positive and dominated by instanton configurations of the form exp(-a/g), where a is the instanton action. The instanton effects are most naturally taken into account within the modified Bohr-Sommerfeld quantization conditions whose expansion leads to the generalized perturbative expansions (so-called resurgent expansions) for the energy values of the Fokker-Planck potential. Until now, these resurgent expansions have been mainly applied for small values of coupling parameter g, while much less attention has been paid to the strong-coupling regime. In this contribution, we compare the energy values, obtained by directly resumming generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling expansion, for which we determine the first few expansion coefficients in powers of g^(-2/3). Detailed calculations are performed for a wide range of coupling parameters g and indicate a considerable overlap between the regions of validity of the weak-coupling resurgent series and of the strong-coupling expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck Hamiltonian, we also briefly discuss the computation of its eigenfunctions. These eigenfunctions may be utilized for the numerical integration of the (single-particle) time-dependent Schroedinger equation and, hence, for studying the dynamical evolution of the wavepackets in the double-well-like potentials.Comment: 13 pages; RevTe