High-precision mass measurements of hydrogen-like <Superscript>24</Superscript>Mg<Superscript>11+</Superscript> and <Superscript>26</Superscript>Mg<Superscript>11+</Superscript> ions in a Penning trap

For the determination of the bound-electron g factor in hydrogen-like heavy ions the mass of the ion is needed at a relative uncertainty of at least 1 ppb. With the SMILETRAP Penning trap mass spectrometer at the Manne Siegbahn Laboratory in Stockholm several mass measurements of ions with even-even nuclei at this level of precision have been performed so far, exploiting the fact that the mass precision increases linearly with the ion charge. Measurements of masses of the hydrogen-like ions of the two Mg-isotopes ²⁴Mg and ²⁶Mg are reported. The masses of the hydrogen-like ions are 23.979011054(14) u and 25.976562354(34) u, corresponding to the atomic masses 23.985041690(14) u and 25.982592986(34) u, respectively. The possibility to use these two isotopes for the first observation of an isotope effect in the bound-electron g factor in hydrogen-like heavy ions is discussed.     

Electron self-energy in the presence of a magnetic field: hyperfine splitting and g factor

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known Zalpha-expansion coefficients is determined. For the 3He+ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.     

A theoretical survey of QED tests in highly charged ions

Recent progress in precision tests of QED in strong nuclear fields is presented and discussed. The discussion is focused on theoretical comparisons with experiment on the 1s Lamb-shift in H-like uranium, the two-electron Lamb-shift in He-like ions, the hyperfine structure of H-like bismuth and the bound-electron g-factor in H-like ions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Recoil correction to the bound-electron g factor in H-like atoms to all orders in alphaZ

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 alphaZ. The calculation is performed in the range Z = 1--100. A large contribution of terms of order (alphaZ)(5) and higher is found. Even for hydrogen, the higher-order correction exceeds the (alphaZ)(4) term, while for uranium it is above the leading (alphaZ)(2) correction. As a result, one of the main sources of the theoretical uncertainty for the bound-electron g factor is eliminated.     

Nonrelativistic QED approach to the bound-electron g factor

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order alpha(Z alpha)(4) to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha(2)(Z alpha)(4)ln([(Z alpha)(-2)] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.     

A Penning trap for g-factor measurements in highly charged ions by laser-microwave double-resonance spectroscopy

Precise determination of bound-electron g-factors in heavy highly-charged ions (e.g. Bi^82?+?, U^91?+?) provides a stringent test of bound-state QED in extreme fields. With a laser-microwave double-resonance technique we will probe the microwave transitions between the Zeeman sub-levels of the hyperfine structure in highly charged ions. From this the bound electron g-factor g_J can be determined. We present the experimental progress of this novel method to measure the g-factor of the bound electron in highly charged ions.     

Self-energy correction to the bound-electron g factor in H-like ions

The one-loop self-energy correction to the 1s-electron g factor is evaluated to all orders in Zalpha with an accuracy essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [T. Beier, Phys. Rev. Lett. 88, 011603 (2002)]]. The new value of the electron mass is found to be m(e)=0.000 548 579 909 3 (3) u.     

Extreme-field physics in Penning traps

We present two Penning trap experiments concerned with different aspects of the physics of extreme electromagnetic fields, the ARTEMIS experiment designed for bound-electron magnetic moment measurements in the presence of the extremely strong fields close to the nucleus of highly charged ions, and the HILITE experiment, in which well-defined ion targets are to be subjected to high-intensity laser fields.     

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

The two-time Green's 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.     

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.     

g-Factor of heavy ions: a new access to the fine structure constant

A possibility for a determination of the fine structure constant in experiments on the bound-electron g-factor is examined. It is found that studying a specific difference of the g-factors of B- and H-like ions of the same spinless isotope in the Pb region to the currently accessible experimental accuracy of 7 x 10(-10) would lead to a determination of the fine structure constant to an accuracy which is better than that of the currently accepted value. Further improvements of the experimental and theoretical accuracy could provide a value of the fine structure constant which is several times more precise than the currently accepted one.     

Nuclear Recoil Effect on the g Factor of Middle-Z Boronlike Ions

The nuclear recoil correction to the g factor of boronlike ions is evaluated within the lowest-order relativistic (Breit) approximation. The interelectronic-interaction effects are taken into account to the first order of the perturbation theory in 1/Z. Higher orders in 1/Z are partly accounted for by means of the effective screening potential. The most accurate up-to-date values of this contribution are presented for the ions in the range Z = 10–20.     

Nuclear shape effect on the g factor of hydrogenlike ions

The nuclear shape correction to the g factor of a bound electron in the 1S state is calculated for a number of nuclei in the range of charge numbers from Z=6 up to Z=92. The leading relativistic deformation correction has been derived analytically, and also its influence on one-loop quantum electrodynamic terms has been evaluated. We show the leading corrections to become significant for mid-Z ions and for very heavy elements to even reach the 10(-6) level.     

Tests of quantum electrodynamics using ion traps

Experiments in ion traps on the g factors for the free and the bound electron in low-Z, hydrogen-like ions have provided the most accurate tests of quantum-electrodynamics calculations. Moreover they have been used to determine new and precise values for fundamental constants. Extensions to more stringent tests using ions of higher values of the nuclear charge Z are on the way. Also other QED tests such as Lamb shifts or hyperfine structures in H-like ions using traps will be feasible in the near future. The tests in bound systems, however, will be limited by nuclear structure effects which are difficult to calculate. Assuming the QED calculations as correct, the experimental results may be used to determine nuclear contributions and thus support nuclear models. Contribution presented at the TCP06, Vancouver Island, 2006.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Multiple electromagnetic excitation with relativistic heavy ions

The multiple electromagnetic excitation with fast projectiles (heavy ions) is studied theoretically in the sudden approximation. Of special interest is the excitation of rotational states coupled to giant (dipole) vibrations. Closed form expressions are obtained for the excitation of a rigid rotor. The strong pulse of high energy equivalent photons in relativistic heavy ion collisions opens up new possibilities for nuclear structure studies, not possible e.g. with electron scattering or nuclear Raman scattering. It is also pointed out that the “Brink-hypothesis” can be investigated in a new way by means of multiple electromagnetic excitation with relativistic heavy ions of low lying states coupled to the giant dipole mode.     

Hyperfine structure of highly charged 23892U ions with rotationally excited nuclei

The hyperfine structure (hfs) of electron levels of 23892U ions with the nucleus excited in the low-lying rotational 2(+) state with an energy E(2(+)) = 44.91 keV is investigated. In hydrogenlike uranium, the hfs splitting for the 1s(1/2) ground state of the electron constitutes 1.8 eV. The hyperfine-quenched (hfq) lifetime of the 1s2p 3P0 state has been calculated for heliumlike 23892U and was found to be 2 orders of magnitude smaller than for the ion with the nucleus in the ground state. The possibility of a precise determination of the nuclear g(r) factor for the rotational 2(+) state by measurements of the hfq lifetime is discussed.     

Calibration of CN and CR-39 track detectors for measurements of fast deuterons and nitrogen ions

The paper reports on the analysis of responses of CN-type films and CR39-plastic nuclear track detectors (NTDs) to fast deutrons and nitrogen ions emitted from high-current Plasma-Focus (PF) facilities, as operated at SINS and INFIP. In order to separate the deutrons and nitrogen ions of different energy, the use was made of a Thomson-type mass-spectrometer adapted to measurements within dense plasma streams. Deutron and ion parabolaen were registered the CN-80 and CN-LR115 films as well as with the CR39 plastic NTDs, which were undergone routine etching procedures. On the basisof known characteristics of the spectrometer applied energy- and mass-scales for the obtained ion paraboale were determined. Using an optical microscope, a detailed analysis of track dimensions was performed in chosen points along the registered parabolae, and the calibration diagrams (i.e. a track diameter for the chosen ion energy and different etching times) were determined. Results of the calibration procedure, after comparing with other calibration data obtained with conventional particle accelerators, may be applicable for measurements of fast deutrons (i.g., in nuclear fusion experiments) and energetic nitrogen ions (i.g., in some plasma- and ion-facilities used for technological applications).     

Ni2+—6X-络合物g因子的双自旋—轨道耦合系数模型

本文提出一个计算Ni²⁺—6X^-络合物g因子的双自旋-轨道耦合系数模型,并用以计算NaCl:Ni²⁺和NaBr:Ni²⁺的g因子。计算中采用了一种半经验方法来确定分子轨道系数。结果表明,对Br^-或I^-这类具有大的自旋-轨道耦合系数的配体离子,配体自旋-轨道耦合作用对g因子的贡献不可忽略。这表明,对某些共价晶体,g因子的计算必须用双自旋-轨道耦合系数模型的理论公式而不能用只包括 关键词：     

Energy loss of charged particles in matter

A new method of determining the differential energy loss of charged excited nuclei in matter is described. The method is based on the velocity dependence of the Doppler shift of the gamma quanta emitted by moving nuclei. No theoretical assumptions concerning the velocity dependence of atomic or nuclear collisions are necessary. The method and mathematical analysis, described in detail, are applied to the energy loss of Li ions emitting gamma quanta of 477 keV in the kinetic energy range between 100 and 800 keV. It is found that the energy loss of Li ions is linearly proportional to the velocity within 2% for several substances ofZ=1 to 74. The small limits of error, which can be obtained, allow an application of this method to questions as e.g. theZ-dependence of the stopping power on the nuclear charge of the stopping material, chemical binding effects, the time dependence of the adjustment of the equilibrium charge of the projectile after nuclear reactions, or the determination of nuclear angular correlations.