Rydberg states of hydrogenlike ions in a braneworld model

Precise measurements of optical transition frequencies between Rydberg states of hydrogen-like ions could be used to obtain an improved value of the Rydberg constant, by avoiding the uncertainties about the proton radius. Motivated by this perspective, we investigate the influence of the gravitational interaction on the energy levels of Hydrogen-like ions in Rydberg states in a braneworld model. As it is known, in this scenario, the gravitational interaction is amplified in short distances. We show that, for Rydberg states, the main contribution for the gravitational potential energy does not come from the rest energy concentrated on the nucleus but from the energy of the electromagnetic field created by its electric charge. The reason is connected to the fact that, when the ion is in a Rydberg state with high angular momentum, the gravitational potential is not computable in zero-width brane approximation due to the gravitational influence of the electrovacuum in which the lepton is moving. Considering a thick brane scenario, we calculate the gravitational potential energy associated to the nucleus charge in terms of the confinement parameter of the electric field in the brane. We show that the gravitational effects on the energy levels of a Rydberg state can be amplified by hidden dimensions even when the compactification scale is shorter than the Bohr radius.     

Fundamental constants in effective theory

In the discussion between L.B. Okun, G. Veneziano, and M.J. Duff concerning the number of fundamental dimensionful constants in physics [9], they advocated, respectively, 3, 2, and 0 fundamental constants. Here, we consider this problem with an example of effective relativistic quantum field theory, which emerges in the low-energy corner of quantum liquids and which reproduces many features of our physics, including Lorentz invariance, chiral fermions, gauge fields, and dynamical gravity.     

Foil-excited Rydberg states of fast oxygen ions

The population of Rydberg states in fast oxygen ions emerging from solid targets is found to be more than ≈ 500 times as large as expected from Coulomb capture of target electrons in last-layer collisions. Furthermore, we find a population depletion for quantum states near n ≈ 10.     

QED theory of the nuclear magnetic shielding in hydrogenlike ions

The shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions.     

Graviton ionization of hydrogenlike ions

Calculations are made of the ionization process of hydrogen atom or hydrogenlike ion by gravitons in both nonrelativistic and relativistic cases. Also the process of graviton deuteron fission is examined.     

Lifetimes of Rydberg states in ions of the group II elements

Total probabilities A _nl of spontaneous radiative transitions, which determine lifetimes τ _nl = 1/A _nl of nS-, nP-, nD- and nF-states in singly charged ions of the group IIa (Be⁺, Mg⁺, Ca⁺, Sr⁺, Ba⁺) and IIb (Zn⁺, Cd⁺, Hg⁺) elements, were calculated in the single-electron Fues’ model potential (FMP) method. An asymptotic dependence is determined for highly excited states with small angular momentums and presented in the form τ _nl = τ _l ⁽⁰⁾ n ³ Q _l (1/n) and numerical values of the factors τ _l ⁽⁰⁾ and coefficients of the cubic polynomial Q _l (x) are calculated, which approximate results of numerical computations with relative error below 2% in the range of states with principal quantum numbers from n = 7 to n ≈ 2000. The comparison of the numerical results with data in literature is presented, and applicability and reliability of single-electron model calculations are discussed in detail for positive singly charged ions of the group II elements.     

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.     

Two-loop self-energy correction in high-Z hydrogenlike ions

A complete evaluation of the two-loop self-energy diagrams to all orders in Zalpha is presented for the ground state of H-like ions with Z > or =40.     

Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincaré map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map.     

Rydberg states of SiBr

New uv absorption spectra have been observed for SiBr. Five Rydberg states are identified to the states $\text{(4sσ)}{}^2\text{Σ}{}^{\mathrm{+}}$, $\text{(5sσ)}{}^2\text{Σ}{}^{\mathrm{+}}$, $\text{(4pπ)}{}^2\text{Π}$, $\text{(3dπ)}{}^2\text{Π}$, and $\text{(3dδ)}{}^2\text{Δ}$ by comparison with SiF and SiCl. The ionization potentials of SiCl and SiBr have been determined for the first time, and were 6.82 and 6.67 eV, respectively.     

Elastic and inelastic scattering of positrons from hydrogenlike ions

Summary The total elastic cross-sections of the collisions of positrons with various hydrogenlike targets (with nuclear chargeZ=1, 2, 3, 4, 5 and 11) are determined at 13 values of the incident energy lying below 6.8 e V(the positronium formation threshold of e⁺-H scattering). The inelastic scattering of positrons by the same targets is investigated for the first time at energies above the positronium formation thresholds. Both scattering processes are treated using a coupled-static formalism and an iterative Green's function partial wave expansion technique. The resulting cross-sections demonstrate the stability of this technique and emphasize the importance of exploring the aspects of positron-ion collisions more fundamentally on both theoretical and experimental levels.     

Reparameterization invariance of NRQED self-energy corrections and improved theory for excited D states in hydrogenlike systems

Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i.e., using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the virtual quanta from the nonrelativistic domain. Here, we calculate the higher-order corrections to the one-photon self-energy calculation with three different overlapping parameters (photon energy, photon mass and dimensional regularization) and demonstrate the reparameterization invariance of nonrelativistic quantum electrodynamics (NRQED) using this particular example. We also present new techniques for the calculation of the low-energy part of this correction, which lead to results for the Lamb shift of highly excited states that are important for high-precision spectroscopy.     

The anomalous magnetic moment of the electron in hydrogenlike ions

The precise determination of the anomalous magnetic moment of the electron bound in hydrogen-like ions allows for a stringent test of quantum electrodynamics (QED)in the presence of strong electric fields. g-factor measurements on the electron bound in hydrogen-like ions ¹²C⁵⁺ and ¹⁶O⁷⁺, using single ions confined in a Penning trap, have yielded values in agreement with theory on the ppb level. If the QED calculations are considered correct, the results can in turn be used for a determination of fundamental constants like the electron mass m_e, the fine structure constant α or nuclear parameters. We report about presentdevelopments towards g-factor measurements also in medium-heavy and heavy highly-charged ions.     

High-angular-momentum states in cold Rydberg gases

Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. Optical excitation on the discrete Rydberg resonances reveals long-lasting electron emission from the Rydberg gas ( >20 ms). Our observations are explained by lm-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities.