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.     

g factor of the [(1s)2(2s)22p]2P3/2 state of middle-Z boronlike ions

Theoretical g-factor calculations for the first excited ²P_3/2 state of boronlike ions in the range Z=10–20 are presented and compared with the previously published values. The first-order interelectronic-interaction contribution is evaluated within the rigorous quantum electrodynamics (QED) approach in the effective screening potential. The second-order contribution is considered within the Breit approximation. The QED and nuclear recoil corrections are also taken into account.     

The anomalous magnetic moment of the electron

The value of the electron's magnetic moment is a fundamental quantity in physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to quantum electrodynamics (QED) as the relativistic quantum field theory of electrodynamics. In fact, the measured values both for free and for bound electrons are explained by corresponding QED calculations on the part per trillion and part per billion level of accuracy, respectively. This agreement is amongst the best known in physics today. In turn, it allows highly precise determinations of related fundamental constants like the fine structure constant α or the electron mass. The present article discusses the application of the continuous Stern–Gerlach effect to the precise measurement of magnetic moments, especially of the electron bound in highly charged ions and possible tests of calculations in the framework of QED of bound states. Also, a test of QED in a more general approach by the comparison of values for the fine structure constant derived from different measurements, will be discussed.     

Nuclear Recoil Effect on the <Emphasis Type="Italic">g</Emphasis>-Factor of Heavy Ions: Prospects for Tests of Quantum Electrodynamics in a New Region

The nuclear recoil effect on the g-factor of H- and Li-like heavy ions is evaluated to all orders in αZ. The calculations include an approximate treatment of the nuclear size and the electron–electron interaction corrections to the recoil effect. As the result, the second largest contribution to the theoretical uncertainty of the g-factor values of ²⁰⁸Pb⁷⁹⁺ and ²³⁸U⁸⁹⁺ is strongly reduced. Special attention is paid to tests of the QED recoil effect on the g-factor in experiments with heavy ions. It is found that, while the QED recoil effect on the gfactor value is masked by the uncertainties of the nuclear size and nuclear polarization contributions, it can be probed on a few-percent level in the specific difference of the g-factors of H- and Li-like heavy ions. This provides a unique opportunity to test QED in a new region of the strong-coupling regime beyond the Furry picture.     

The generalized Bethe logarithm for tightly bound electrons

We derive a closed relativistic expression that makes it possible to calculate the self-energy of multiply charged ions in an external Coulomb field without resorting to a series expansion in powers of αZ. The expression contains the generalized Bethe logarithm for tightly bound electrons. We do numerical calculations of the self-energy for the 1s _1/2-electrons of multiply charged hydrogenlike ions. The proposed method allows for self-energy calculations for any values of the nuclear charge Z. Zh. éksp. Teor. Fiz. 112, 1197–1208 (October 1997)     

K-shell ionization of atoms and ions by relativistic projectiles

We evaluate the total cross section for the single K-shell ionization of atoms and ions by the impact of relativistic electrons. The study is performed to leading orders of the QED perturbation theory with respect to the parameters αZ and 1/Z. The results obtained are in good agreement with experimental data for different atomic targets. In the case of moderate values of the nuclear charge Z, the total cross section is described by a simple analytic formula. The K-shell ionization by relativistic heavy particles is also considered.     

News from the ESR storage ring

The ESR storage ring offers unique conditions for precision investigations in the realm of nuclear and atomic research. Very recently, several technical improvements took place at the ESR which were exploited in a first series of experiments. In this report, an overview of the most recent experiments will be given. These experiments focused predominately on the study of QED effects in high- ^Z one- and few-electron ions and on the dynamics in relativistic ion–atom collisions involving high- ^Z projectiles. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two photon QED corrections in helium like highly charged ions

An overview of calculations and measurements of the energy levels of helium-like ions is presented. We focus on the two-photon QED effects, and conclude that measurements of the excited states of large Z helium-like ions are desired. This revised version was published online in August 2006 with corrections to the Cover Date.     

类钾离子4s 2S1/2─3d 2D3/2电四极矩E2光谱跃迁的理论研究

采用全相对论量子力学GRASP²程序,广义平均能级EAL模型,在核的有限体积效应,Breit和QED效应的高阶扰动基础上,考虑到原子实的极化,系统地计算了高剥离类钾离子4s ²S_1/2─3d ²D_3/2电四极矩E2光谱跃迁的能级间隔,跃迁概率和振子强度,结果表明：考虑原子实极化效应后,计算的精细能级结构间隔与实验数据之间的系统误差基本消除,其跃迁概率和振子强度属首次报道. 关键词： 高剥离态 能级间隔 振子强度     

Measurement of the gj factor of hydrogenic ions: a sensitive test of bound state QED

Theg _j factor measurement of hydrogenic ions in the 1s ground state is with an expected accuracy of 10^–7 a sensitive test of bound state QED. We expect to determine the deviations from the free electron value, caused by relativistic and radiative corrections, up to the order/4(Z) ² with an accuracy of 1%. As a first step, light ions like C⁵⁺ will be investigated. Later on, heavier hydrogenic ions up to U⁹¹⁺ will be examined using the accelerator facilities at GSI in Darmstadt.     

Relativistic calculations of one-photon transition probabilities in hydrogen-like ions

The one-photon transition probabilities in hydrogen-like ions are calculated for nuclear charge numbers in the range 1 ≤ Z ≤ 100. The calculations are performed in the framework of the relativistic Dirac’s theory for the states with the principal quantum numbers n = 2,3, 4. The finite nuclear size effect is taken into account. The role of the quantum electrodynamics (QED) and nuclear recoil corrections is also considered.     

Relativistic configuration interaction calculations for the K α X-ray transitions of Co XV to Co XXVI ions

Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics (QED) and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wave functions on the wavelengths, electric dipole rates, oscillator strengths and line strengths of cobalt ions with a single vacancy in the K shell. The calculated values are compared with the other available data on He-like to Be-like cobalt and are found to be in very good agreement with them. This confirms the present calculations. We predict new data for several levels where no other theoretical and/or experimental results are available. These data provide reference values for level lifetimes, charge state distribution and the average charge of cobalt plasmas.     

Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

Nuclear-polarization correction to the bound-electron g factor in heavy hydrogenlike ions

The influence of nuclear polarization on the bound-electron g factor in heavy hydrogenlike ions is investigated. Numerical calculations are performed for the K- and L-shell electrons taking into account the dominant virtual nuclear excitations. This determines the ultimate limit for tests of QED utilizing measurements of the bound-electron g factor in highly charged ions.     

Asymptotics of the cross section of the electron loss by fast ions in light media

The dependence of the single electron loss cross section on the nuclear charge Z of a projectile and on the nuclear charge Zt of a target atom for fast collisions is studied theoretically using the plane-wave Born approximation and the sum rule. The results of calculations for fast singly and triply charged ions show that the single electron loss cross section increases monotonically as Z and Zt increase. This can be used to interpolate cross sections of processes if there are no experimental data. The results of calculations compare with the experimental and theoretical data of other authors.     

Systematic trends in the line strengths of E1 transitions in the oxygen isoelectronic sequence

Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ ² S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s²2s²2p^{4 1}S.     

类铍离子磁四极M2 2s2 1S0—2s2p3P2 (Z=10—103)禁戒跃迁

利用全相对论多组态Dirac-Fock方法系统地计算了高离化类铍离子的磁四极M2 2s²¹S₀—2s2p³P₂ (Z=10—103)自旋禁戒跃迁的能级间隔、跃迁概率和振子强度，计算中考虑了重要核的有限体积效应，Breit修正和QED修正，所得结果和最近的实验数据以及理论值进行了比较，结果表明：高原子序数的高电荷离子(Z≥70)磁四极M2自旋禁戒跃迁几乎可以和中性原子的光学允许跃迁相比拟，不仅在天体等离子体中，在ICF和MCF高温激光等离子体中，磁四极自旋禁戒跃迁和其他自旋禁戒跃迁（磁偶极、电四极）一样不容忽视，在双电子复合、不透明度、自由程等理论计算中应该考虑其影响. 关键词： 磁四极M2 能级间隔 跃迁概率 振子强度     

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.     

Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions

The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: ⁴⁵Sc¹⁶⁺, ⁵⁷Fe²¹⁺, ²⁰⁷Pb⁷⁷⁺, and ²⁰⁹Bi⁷⁸⁺. For lead and bismuth the experimental values of the 1s hyperfine splitting are employed to improve significantly the theoretical results by reducing the uncertainty due to the nuclear effects.     

Improving \alpha_{\rm QED} (M_Z^2) and the charm mass by analytic continuation

The standard determination of the QED coupling on the Z pole is performed using the latest available data for R. The direct application of analytic continuation techniques is found not to improve the accuracy of the value of . However they help to resolve an ambiguity in the values of R in the energy region , which, in turn, reduces the uncertainty in . Moreover, they provide a sensitive determination of the mass of the charm quark. The favoured solution, which uses the inclusive data for R for , has a pole mass and ; whereas if the sum of the exclusive channels is used to determine R in this region, we find . Received: 19 December 2000 / Published online: 6 April 2001