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Journal of Physics B Atomic Molecular and Optical Physics

The magnetic moment anomaly of the electron bound in hydrogen-like oxygen16O7

J Verd, Thomas Beier, S Djeki, H H ffner, H-J Kluge, W. Quint, T. Valenzuela, Manuel Vogel, Günther Werth

Published Jan 24, 2003• 13 citations
Publisher

Abstract

The measurement of the g -factor of the electron bound in a hydrogen-like ion is a high-accuracy test of the theory of quantum electrodynamics (QED) in strong fields. Here we report on the measurement of the g -factor of the bound electron in hydrogen-like oxygen ( 16 O 7+ ). In our experiment a single highly charged ion is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern–Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down ) are induced by a microwave field at the spin precession frequency of the bound electron. The g -factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips. The comparison of our experimental values for the g -factor of the bound electron with the theoretical values shows excellent agreement and confirms the recent non-perturbative QED calculations.

DOI
10.1088/0953-4075/36/3/322

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The measurement of the g -factor of the electron bound in a hydrogen-like ion is a high-accuracy test of the theory of quantum electrodynamics (QED) in strong fields. Here we report on the measurement of the g -factor of the bound electron in hydrogen-like oxygen ( 16 O 7+ ). In our experiment a single highly charged ion is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern–Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down ) are induced by a microwave field at the spin precession frequency of the bound electron. The g -factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips. The comparison of our experimental values for the g -factor of the bound electron with the theoretical values shows excellent agreement and confirms the recent non-perturbative QED calculations.
We report on the measurement of the g-factor of the electron bound in an atomic ion. A single hydrogenic ion (12C5+) is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern-Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down) are induced by a microwave field at the spin precession frequency of the bound electron. The g-factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips for a fixed time interval. Applications of the continuous Stern-Gerlach effect include high-accuracy tests of bound-state quantum electrodynamics (QED), the measurement of the atomic mass of the electron, the determination of the fine structure constant α, and the measurement of nuclear g-factors.
We report on the first observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion. The measurement was performed on a single hydrogenlike ion ( 12C5+) in a Penning trap. The measured g factor of the bound electron, g = 2.001 042(2), is in excellent agreement with the theoretical value, confirming the relativistic correction at a level of 0.1%. This proves the possibility of g-factor determinations on atomic ions to high precision by using the continuous Stern-Gerlach effect. The result demonstrates the feasibility of conducting experiments on single heavy highly charged ions to test quantum electrodynamics in the strong electric field of the nucleus.
ALPHATRAP is a Penning-trap based experiment located at the Max-Planck-Institut für Kernphysik (MPIK). It is dedicated to the exploration of ground-state properties of heavy, highly charged ions (HCI). The major goal of the ALPHATRAP \nexperiment are high precision measurements of the bound-electron g-factor. The comparison of the experimental result with recent theoretical calculations will not only serve as a sensitive test of bound-state quantum electrodynamics (BS-QED) but also yields a new approach for the determination of fundamental constants such as the electron mass or the fine structure constant. The measurement of the bound-electron g-factor of a single HCI is performed in an optimized cryogenic double Penning-trap setup, utilizing the continuous Stern-Gerlach effect. For injection of externally produced HCI up to 208Pb81+ the ALPHATRAP experiment is \ncoupled to various ion sources, including the Heidelberg Electron-Beam Ion Trap. \nThis thesis describes the setup and preparation of the ALPHATRAP experiment on its way towards its first g-factor measurement. In this context a new highly sensitive detection system was implemented and successfully tested. This enabled a first commissioning of the whole apparatus with in situ generated HCI as well as HCI injected through the room temperature beamline. The first-time integration \nof an externally operable cryogenic valve allowed for excellent vacuum conditions with long ion storage times. The implementation of typical ion detection and manipulation techniques was demonstrated by characterization measurements of the detection system and the trapping fields. The commissioning culminated in the first direct observation of induced bound-electron spin transitions at the \nALPHATRAP experiment.
The conflict between Bohr's assertion that the magnetic moment of the electron cannot be measured with experiments based on the concept of classical trajectories, and the measurement of the magnetic moment of electrons in a modified Penning trap by Dehmelt et al. has led us to reevaluate other implications of Bohr's assertion. We show that, contrary to the analysis of Bohr and Pauli, the assumption of classical trajectories in a Stern-Gerlach--like device can result in a high degree of spin separation for an electron beam. This effect may persist within a fully quantum-mechanical analysis. The magnetic fields considered are such that a tabletop Stern-Gerlach electron spin filter is feasible.
Abstract We propose a phenomenological theory of spin behavior in a magnetic field, which explains from the point of view of classical physics the two-valued result of the Stern-Gerlach experiment. The behavior of the spin and intrinsic magnetic moment of an electron wave of an atom in an external magnetic field is considered. We show that in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector. Within the framework of classical electrodynamics, the calculation of the motion of an atomic beam in an inhomogeneous magnetic field is carried out, which reproduces the results of the Stern-Gerlach experiment.
In the late 1920s Niels Bohr propagated the idea that the magnetic moment of a free electron could not be observed. This derived from the idea that the spin degree of freedom characterized the electron only when it is bound in an atom. This view initiated a lively discussion, which involved many of the most prominent theoreticians of the time. The independent existence of the electron spin became an issue of principle. In particular it was deemed that quantum effects would destroy the separated classical trajectories in a Stern-- Gerlach type of experiment. We review these discussions and some later developments. Quantum effects do prove to be essential, but they do not overwhelm the magnetic effects of spin. In addition to these arguments, it has been possible experimentally to determine the electron g -factor with high accuracy in electromagnetic traps. In fact no principle seems to prevent the observation of the magnetic moment of the free electron.