Eur. Phys. J. D 25, 113–121 (2003) DOI: 10.1140/epjd/e2003-00096-6 T HE EUROPEAN P HYSICAL JOURNAL D The g J -factor in the ground state of Ca + G. Tommaseo 1 , T. Pfeil 1 , G. Revalde 2 , G. Werth 1, a , P. Indelicato 3, b , and J.P. Desclaux 4 1 Johannes Gutenberg Universit¨at, Institut f¨ ur Physik, 55099 Mainz, Germany 2 Institute of Atomic Physics and Spectroscopy, University of Latvia, Raina Blvd. 19, Riga, Latvia 3 Laboratoire Kastler Brossel, ´ Ecole Normal Sup´ erieure et Universit´ e Pierre et Marie Curie, Case 74, 4 place Jussieu, 75005 Paris, France 4 15 chemin du Billery, 38360 Sassenage, France Received 9 December 2002 / Received in final form 24 February 2003 Published online 29 April 2003 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2003 Abstract. We have determined the gJ -factor of the Ca + ion in the electronic 4S 1/2 ground state on a cloud of ions confined in a Penning trap with a superimposed magnetic field of 1.43 T. We use a c.w. laser to prepare a Zeeman substate by optical pumping and induce ∆mJ = 1 transitions by a resonant microwave field at 40 GHz. Resonance is detected by a change in the fluorescence intensity originating from the ion cloud. We obtain a full width in the resonance of a few kHz and the fractional uncertainty of the line center, taking the average of several measurements, was 4 × 10 -8 . After calibrating the magnetic field by the cyclotron frequency of electrons stored in the same trap we obtain as result gJ =2.002 256 64(9). The result is supported by a relativistic Multi-Configurational Dirac-Fock calculation. PACS. 32.60.+i Zeeman and Stark effects – 32.10.Dk Electric and magnetic moments, polarizability 1 Introduction The g-factor relates the magnetic moment μ of a system to its angular momentum J by the relation μ = g e 2m J (1) where e and m are the charge and the mass of the sys- tem, respectively. Measurements of g in atomic systems have provided a means of checking theoretical predictions of relativistic quantum mechanics. The g-factor deviates for bound systems from the value of the free electron by a number of contributions. For light atoms the main con- tribution is the relativistic kinetic correction δg rel , first introduced by Breit [1]. In heavy atoms the core-valence correlation correction δg corr dominates [2]. The Breit in- teraction δg Br between the valence and core electrons also gives a significant contribution [3]. Bound-state quan- tum electrodynamic corrections are generally considered as small except for hydrogen like systems [4]. g J -factors of neutral atoms have been measured with great preci- sion particularly for the alkali atoms. Here the compari- son between theory and experiment can be made on the 10 -6 level of accuracy since the single valence electron of these systems allows to obtain accurate wavefunctions us- ing MCDF-Method (Multiconfiguration Dirac-Fock) and RMBPT (Relativistic Many Body Perturbation Theory). a e-mail: werth@mail.uni-mainz.de b e-mail: paul.indelicato@spectro.jussieu.fr Alkali like atomic ions are equally well suited to test the corresponding atomic physics calculations. Precise val- ues of g J -factors for some ions have been obtained in recent years using microwave-optical double resonance method, combined with the ion storage technique [5]. The ions are confined in Penning traps with a superimposed strong magnetic field. The storage of small ion clouds for vir- tually unlimited time under high vacuum conditions has a number of advantages: the precision of induced transi- tions between long lived ionic energy levels is not limited by the finite observation time. The small trapping volume of at most a few mm 3 makes it comparatively easy to ob- tain high spatial homogeneity of the magnetic field over the region of interest. The use of superconducting mag- nets assures at the same time high temporal stability. In case of microwave transitions, the first order Doppler ef- fect does not broaden the spectral line in spite of the fact that the average kinetic energy of trapped ions is typi- cally of the order of a few eV when no cooling methods are applied and thus much higher than in experiments on neutral atoms. The ion motion in traps leads to an unshifted and unbroadened central line and to sidebands at the ion oscillation frequencies. This is due to the fact that the amplitude of the ion oscillation in the trap is in general smaller than the wavelength of the inducing radia- tion (Dicke effect) [6]. Finally collisions with neutral back- ground atoms which may shift the resonance frequencies play a negligible role at pressures below 10 -5 mbar. The determination of ionic g J -factors in Penning traps has been restricted so far to alkali-like systems because