The quest for the value of the electron's atomic mass has been subject of continuing efforts over the last decades [1,2,3,4]. [5] and which are thus responsible for its predictive power, the electron mass me plays a prominent role, as it is responsible for the structure and properties of atoms and molecules. This manifests in the close link with other fundamental constants, such as the Rydberg constant R∞ and the fine-structure constant α [6]. However, the low mass of the electron considerably complicates its precise determination. In this work we present a substantial improvement by combining a very accurate measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state Quantum Electrodynamics. The achieved precision of the atomic mass of the electron surpasses the current CODATA [6] value by a factor of 13. Accordingly, the result presented in this letter lays the foundation for future fundamental physics experiments [7,8] and precision tests of the SM [9,10,11] Throughout the last decades, the determination of the atomic mass of the electron has been subject to several Penning-trap experiments, as continuing experimental efforts try to further explore the scope of validity of the SM and require an exceedingly precise knowledge of me. The uniform magnetic field of these traps gives the possibility to compare the cyclotron frequency of the electron with that of another ion of known atomic mass, typically carbon ions or protons. The first such direct determination dates back to 1980, when Gräff et al. made use of a Penning trap to compare the cyclotron frequencies of a cloud of electrons with that of protons, which were alternately confined in the same magnetic field, yielding a relative precision of about 0.2 ppm [2]. Since then, a number of experiments have pushed the precision by about 3 orders of magnitude [1,12,13,4]. The latest version of the CODATA compilation of fundamental constants of 2010 lists a relative uncertainty of 4•10 -10 , resulting from the weighted average of the most precise measurements (Fig. 2). Since the cyclotron frequency of the extremely light electron is subjected to troublesome relativistic mass shifts if not held at the lowest possible energy, direct ultra-high precision mass measurements are particularly delicate. To circumvent this problem, the currently most precise measurements, including this work, pursue an indirect method which allows achieving a previously unprecedented accuracy. Among the seemingly fundamental constants which parameterize the Standard Model (SM) of physicsA single electron is bound directly to the reference ion, in this case a bare carbon nucleus (Fig. 1). In this way, it becomes possible to calibrate the magnetic field B at the very place of the electron through a measurement of the cyclotron frequency

We determined the experimental value of the g factor of the electron bound in hydrogenlike ²⁸Si¹³⁺ by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)² and (Zα)⁴ and represents a stringent test of bound-state quantum electrodynamics calculations.

The determination of the electron mass from Penning-trap measurements with 12 C 5+ ions and from theoretical results for the bound-electron g factor is described in detail. Some recently calculated contributions slightly shift the extracted mass value. Prospects of a further improvement of the electron mass are discussed both from the experimental and from the theoretical point of view. Measurements with 4 He + ions will enable a consistency check of the electron mass value, and in future an improvement of the 4 He nuclear mass and a determination of the fine-structure constant.

No abstract

The nuclear shape correction to the g factor of a bound electron in 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. PACS numbers:The ever-increasing precision of measurements and theory of the g factor of a bound electron has recently delivered a new value for the electron mass [1,2], and keeps providing stringent tests for quantum electrodynamics (QED) in strong fields [1][2][3]. It also allows to access electromagnetic properties of nuclei such as charge radii, as demonstrated in a very recent proof-of-the-principle study with a Si 13+ ion [3], or, as suggested theoretically, magnetic moments [4]. Also, it is anticipated that g factor studies will yield a value for the fine-structure constant α that is more accurate than the presently established one when extending the experiments to elements with a high charge number Z [5].In a few years, measurements with the heaviest elements will be possible [6]. As higher-order nuclear and QED contributions to the theoretical value of the g factor are strongly boosted with increasing Z, at the present 10 −10 level of relative experimental accuracy [3,7] or even below, our present understanding of atomic structure will not be satisfactory. In such strong Coulomb fields, nuclear effects beyond a simple spherical model arise. Furthermore, QED and nuclear structural contributions are intertwined.In this Letter we consider the nuclear shape effect, and find that while it can be safely neglected in predictions for low-Z systems, it greatly influences the g factor value already for mid-Z elements. At high nuclear charges, its inclusion in the theoretical description is mandatory; for example, for U 91+ , its relative contribution to the total g factor reaches the 10 −6 level. We furthermore evaluate mixed nuclear-QED terms, i.e. the nuclear shape effect on the one-loop QED terms of self-energy (SE) and vacuum polarization (VP). Even these contributions will be highly relevant for the interpretation of experimental values to be obtained within a few years [6]. Furthermore, a comparison of theory and experiment may even yield more accurate values for nuclear shape parameters, relevant in explaining shape phase transitions in nuclear structure theory [8].We account for the nuclear quadrupole and hexadecapole deformation and derive a formula describing the nuclear shape correction to the g factor of a bound electron in hydrogen-like ions in the 1S-state. Then we focus on systems where the nucleus is spinless and in its ground state. Let us start with the definition of the electron g factor (we use units with c = 1, = 1, α = e 2 /(4π), and with e = − | e| unless otherwise stated)where δE stands for the energy correction due to the coupling of the...

We construct the most general Hamiltonian for the electromagnetic interaction of the finite-size particle-like nucleus with arbitrary spin, magnetic dipole, and electric quadrupole moments. It includes all the terms, which are important for obtaining atomic energy levels up to the order α 6 . The result is verified against spin s = 0, 1/2, and 1 cases, where the Foldy-Wouthuysen transformation is performed of the corresponding relativistic equation.

The theory of the g factor of an electron bound to a deformed nucleus is considered nonperturbatively and results are presented for a wide range of nuclei with charge numbers from Z=16 up to Z=98. We calculate the nuclear deformation correction to the bound electron g factor within a numerical approach and reveal a sizable difference compared to previous state-of-the-art analytical calculations. We also note particularly low values in the region of filled proton or neutron shells, and thus a reflection of the nuclear shell structure both in the charge and neutron number. PACS numbers: 31.30.js, 21.10.FtThe electron's g factor characterizes its magnetic moment in terms of its angular momentum. For an electron bound to an atomic nucleus, the g factor can be predicted in the framework of bound state quantum electrodynamics (QED) as well as measured in Penning traps, both with a very high degree of accuracy. This enables extraction of information on fundamental interactions, constants and nuclear structure. For example, the combination of theory and precise measurements of the bound electron g factor has recently provided an enhanced value for the electron mass [1], and bound state QED in strong fields was tested with unprecedented precision [2][3][4][5]. It also enables measurement on characteristics of nuclei such as electric charge radii, as shown for Si 13+ ion [6], or the isotopic mass difference as demonstrated for 48 Ca and 40 Ca in [7], or, as proposed theoretically, magnetic moments [8]. Also, it was argued that g-factor experiments with heavy ions could result in a value for the fine-structure constant which is more accurate than the presently established one [9]. With planned experiments involving high Z nuclei [10,11] and current experimental accuracies on the 10 −10 level for low Z, it is important to keep track also of higher order effects. In this context, the influence of nuclear size and deformation is critical. In [12], the nuclear shape correction to the bound electron g factor was introduced and calculated for spinless nuclei using the perturbative effective radius method [13,14]. This effect takes the influence of a deformed nuclear charge distribution into account, and changes the g factor on a 10 −6 level for heavy nuclei, thus being potentially visible in future experiments. Therefore, a comparison of experiment and theory for heavy nuclei demands a critical scrutiny of the validity of the previously used perturbative methods, as pointed out in [15].In this paper, we present non-perturbative calculations of the nuclear deformation correction to the bound electron g factor and show the corresponding values for nuclei across the entire nuclear chart, quantifying the nonperturbative corrections and especially observing the appearance of nuclear shell closure effects in the values of the bound electron g factor.Relativistic units with =c=1 are used throughout this work, as well as the Heavyside unit of charge with α=e 2 /4π, where α is the fine structure constant and the elementary charge e is neg...

No abstract