Finite nuclear size correction to the bound-electron g factor in a hydrogenlike atom

The finite nuclear size correction to the bound-electron g factor in hydrogenlike atoms is investigated in the range Z=1-20. An analytical formula for this correction which includes the non-relativistic and dominant relativistic contributions is derived. In the case of the 1s state, the results obtained by this formula are compared with previous non-relativistic analytical and relativistic numerical calculations.Comment: 5 page

Magnetic moment of the two-particle bound state in quantum electrodynamics

We have formulated the quasipotential method for the calculation of the relativistic and radiative corrections to the magnetic moment of the two-particle bound state in the case of particles with arbitrary spin. It is shown that the g-factors of bound particles contain $O(\alpha^2)$ terms depending on the particle spin. Numerical values for the g-factors of the electron in the hydrogen atom and deuterium are obtained.Comment: Talk presented at Nuclear Physics Department Conference "Physics of Fundamental Interactions" Russian Academy of Sciences, ITEP, Moscow, 27 November-1 December 2000. 11 pages, 1 figure uses linedraw.st

QED theory of the nuclear recoil effect on the atomic g factor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in \alpha Z and to first order in m/M is formulated. The complete \alpha Z-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (\alpha Z)^2 m/M for an arbitrary state of a hydrogenlike atom.Comment: 17 page

g factor of Li-like ions with nonzero nuclear spin

The fully relativistic theory of the g factor of Li-like ions with nonzero nuclear spin is considered for the (1s)^2 2s state. The magnetic-dipole hyperfine-interaction correction to the atomic g factor is calculated including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. This correction is combined with the interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtain high-precision theoretical values for the g factor of Li-like ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from g factor experiments.Comment: 20 pages, 5 figure

QED Effects in Heavy Few-Electron Ions

Accurate calculations of the binding energies, the hyperfine splitting, the bound-electron g-factor, and the parity nonconservation effects in heavy few-electron ions are considered. The calculations include the relativistic, quantum electrodynamic (QED), electron-correlation, and nuclear effects. The theoretical results are compared with available experimental data. A special attention is focused on tests of QED in a strong Coulomb field.Comment: 28 pages, 6 tables, 5 figure

Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ\alpha Z

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $\alpha Z$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(\alpha Z)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(\alpha Z)^4$ term, while for uranium it is above the leading $(\alpha Z)^2$ correction.Comment: 6 pages, 3 tables, 1 figur

Trapped electron coupled to superconducting devices

We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the Tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantum interferometers (SQUIDs) to the electron. The electron may also be coupled to a vortex which is situated in a double well potential, realized by nearby pinning centers in the superconductor, acting as a quantum mechanical two level system that can be controlled by a transport current tilting the double well potential. When the vortex is trapped in the interferometer arms of a SQUID, this would allow its detection both by the SQUID and by the electron.Comment: 13 pages, 5 figure

Nanofriction in Cold Ion Traps

Sliding friction between crystal lattices and the physics of cold ion traps are so far non-overlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices, or clusters, depending on trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, via e.g. an electric field, the trapped ion chains over a periodic corrugated potential. Unlike infinite chains where, according to theory, the classic Aubry transition to free sliding may take place, trapped chains are always pinned. Nonetheless we find that a properly defined static friction still vanishes Aubry-like at a symmetric-asymmetric structural transition, ubiquitous for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction can also be addressed by ringdown oscillations of the ion trap. Long theorized static and dynamic one dimensional friction phenomena could thus become exquisitely accessible in future cold ion tribology

Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.Comment: 92 pages, 39 figures, 7 table

Synthesis of functionalised supramolecular assemblies.

This thesis features supramolecular assemblies that have functional groups incorporated into them, with the intention of introducing the properties of these functional moieties into the supramolecular structure. The functionalities investigated included squaramide, pyrene and tribenzylamine moieties each possessing unique properties discussed further below. The ligands synthesised in this thesis were designed to produce discrete supramolecular architectures through the inclusion of converging metal binding sites. The formation of the resulting supramolecular assemblies was investigated through both solid and solution state analyses. In chapter 2, the incorporation of squaramide moieties into discrete supramolecular assemblies, through the design of flexible and rigid squaramide-based ligands, is presented. The flexible squaramide ligands created metallo-supramolecular triple-stranded helicates through various sub-component self-assembly of pro-ligands, metal ions and aldehyde ‘head groups’, which were characterised through ESI-MS. The rigid squaramide ligands formed tetrahedral [M₄L₆]⁸⁺ cages, as observed through X-ray crystallography and, upon modification of the ligand to improve solubility, complexometric UV-Vis and ¹H-NMR experiments were conducted. The host-guest capability of these discrete structures was investigated through NMR experiments, however, no signal associated with guest encapsulation was observed due to either guest exchange occurring faster than the NMR timescale or the large aperture size of the cages failing to capture the guest. The inherent guest binding properties of the squaramide nitro precursors against a series of anions were independently investigated through guest binding studies which followed trends reported in the literature. Chapter 3 investigated the pyrene moiety embedded within supramolecular assemblies, with metal ions of different geometries resulting in either cubic [M₈L₆]¹⁶⁺ cages or dimeric [M₄L₂]⁸⁺ stacks. Solution state UV-Vis complexometric titrations confirmed the formation of both species in the solution. The emission properties of both species were investigated at the beginning and end of the complexometric titrations to observe whether the luminescent properties of pyrene were translated into the supramolecular structures. For the cubic cages, no emission was observed after the formation of the cage, however, the dimeric stack retained the luminescent properties of the ligand after complexation. Chapter 4 discusses the supramolecular assemblies formed with the tribenzylamine precursor featuring salicylimine or 2-pyrrolyimine ‘head groups’ and subsequent investigations through UV-Vis complexometric titration studies. These ‘head groups’ require deprotonation before complexation which was achieved through either utilisation of basic acetate metal salts or the addition of triethylamine to the titration. The salicylimine ‘head group’ resulted in the formation of [M₃L₂] neutral complexes, with the zinc complex exhibiting luminescence. The pyrrolimine ‘head group’ led to the formation of a 1:1 ratio product forming which could be either a double-stranded helicate, molecular triangle or molecular square. Chapter 5 concludes the thesis and presents some future work and Chapter 6 details the experimental procedures