Self-energy correction to the hyperfine splitting of the 1 s and 2 s states in hydrogenlike ions

The one-loop self-energy correction to the hyperfine splitting of the 1 s and 2 s states of hydrogenlike ions is calculated for both point and finite nuclei. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike ²⁰⁹Bi⁸⁰⁺ and ¹⁶⁵Ho⁶⁴⁺. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 19–22 (10 July 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

High precision wavelength measurements of QED-sensitive forbidden transitions in highly charged argon ions

We present the results of an experimental study of magnetic dipole (M1) transitions in highly charged argon ions (Ar X, Ar XI, Ar XIV, Ar XV) in the visible spectral range using an electron beam ion trap. Their wavelengths were determined with, for highly charged ions, unprecedented accuracy up to the sub-ppm level and compared with theoretical calculations. The QED contributions, calculated in this Letter, are found to be 4 orders of magnitude larger than the experimental error and are absolutely indispensable to bring theory and experiment to a good agreement. This method shows great potential for the study of QED effects in relativistic few-electron systems.     

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Calculation of the hyperfine structure of heavy H and Li like ions

The present status of calculations of the hyperfine splitting and the transition probability between the hyperfine splitting components in hydrogen and lithium like ions is discussed. The results of the calculations are compared with recent experimental data. A special attention is focused on the hyperfine splitting in hydrogen like lead and lithium like bismuth. It is shown that the theoretical prediction for the ground state hyperfine splitting in lead based on the single particle nuclear model for the Bohr-Weisskopf effect is in fair agreement with experiment. The theoretical prediction for the ground state hyperfine splitting in lithium like bismuth is improved due to more accurate calculations of the interelectronic interaction, QED, and nuclear corrections. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quantum electrodynamic theory of multiply charged ions

A Rayleigh-Schrödinger perturbation theory is constructed within quantum electrodynamics so as to calculate energy levels nad transition probabilities in multiply charged ions. The basic features of the suggested model are renormalization and its relative simplicity. Renormalization is guaranteed by the fact that all interesting quantities (energy levels, transition probabilities, and cross sections of various processes) are expressed in terms of many-electron Green's functions, whose renormalization is achieved by standard methods. To demonstrate the simplicity of the suggested method, expressions are obtained for corrections to the ground state energy of a two-electron multiply charged ion due to two-photon exchange diagrams, whose derivation by other methods is, in our opinion, quite more complicated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 43–54, August, 1990.     

Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions

A rigorous evaluation of the two-photon exchange corrections to the hyperfine structure in lithiumlike heavy ions is presented. As a result, the theoretical accuracy of the specific difference between the hyperfine splitting values of H- and Li-like Bi ions is significantly improved. This opens a possibility for the stringent test of the many-electron QED effects on a few percent level in the strongest electromagnetic field presently available in experiments.     

The coulomb glory effect in collisions of antiprotons with heavy ions

The Coulomb glory effect in the back scattering of antiprotons with energies of from 100 eV to 3 keV from a bare nucleus of uranium and from uranium ions with closed shells is considered in terms of nonrelativistic and relativistic quantum theory. The appearance of Coulomb glory in collisions with multiply charged ions is caused by nucleus charge screening by filled electron shells. In scattering from a bare nucleus, the effect appears because of the screening properties of the vacuum polarization potential.     

Relativistic calculations of electronic excitation probabilities in U<Superscript>92+</Superscript>-U<Superscript>91+</Superscript>(1<Emphasis Type="Italic">s</Emphasis>) collisions in the monopole approximation

Heavy ion collisions U⁹²⁺-U⁹¹⁺(1s) at a 6 MeV incident particle energy per nucleon are considered. The wave function of the electron was determined by solving the Dirac time-dependent equation in a central field, which is the sum of the potential of the target nucleus and the potential of the incident nucleus taken in the monopole approximation. The Dirac equation was solved using the basis set of Hermitian B-splines. The probabilities of remaining in the 1s target state were calculated as functions of the impact parameter.     

Vacuum-Polarization Screening Corrections to the Low-Lying Energy Levels of Heliumlike Ions

We present results for the two-photon vacuum-polarization screening correction in He-like heavy ions in the range Z=20–100. Values for the ground state as well as for low-lying excited states are given. This revised version was published online in July 2006 with corrections to the Cover Date.