The g_j-factor in the ground state of Ca⁺

We have determined the g_J-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 Δm_J = 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 g_J = 2.002 256 64(9). The result is supported by a relativistic Multi-Configurational Dirac-Fock calculation.