H. Haeffner, N. Hermanspahn, H.-J. Kluge, G. Marx, W. Quint, S.
Stahl, T. Valenzuela, J. Verdu and G. Werth

Gesellschaft fuer Schwerionenforschung, 64291 Darmstadt, Germany
and Institut fuer Physik, Universitaet Mainz, 55099 Mainz, Germany
 
 

The experimental determination of the magnetic moment of the bound
electron in hydrogen-like ions is an important test of the theory
of Quantum Electrodynamics in strong Coulomb fields. It represents
a clean test of pure QED effects because it is not very sensitive
to nuclear structure effects.

In our experiment a single hydrogenlike carbon-ion is stored in a
Penning trap, which consists of a strong magnetic field (4 T) and
an electrostatic quadrupole potential. Due to the low background
gas pressure in the cryopumped vacuum chamber (p < 10^-16 mbar)
the storage time of the hydrogenlike carbon-ion is longer than one
year. A new measurement technique has been developed, where the
induction and detection of spin flips is spatially separated. This
leads to an improvement in the measurement accuracy by 3 orders of
magnitude. The new experimental value in the case of hydrogenlike
carbon reads:

     g = 2.001 041 596 (1)(1)(4)

The first error is the statistical uncertainty, the second error
arises from possible systematic shifts and the third one denotes
the uncertainty in the knowledge of the atomic mass of the
electron. This result has to be compared to the theoretical value
which had been improved recently to an accuracy of about 10^-9:

     g = 2.001 041 590 (1)(1)(1)

where the uncertainties are due to the numerical accuracy of the
one loop bound state QED calculations, to the nuclear recoil
contribution and an estimation of the two loop bound state QED
effects.

The knowledge of the electron mass is therefore presently the main
limitation to the interpretation of the g factor of hydrogenlike
carbon as a test of bound state QED.