Speaker
Description
The $g$ factor of bound electrons in light and medium-light hydrogen-like ions (e.g. C, Si) has been measured with an accuracy of a few parts in $10^{11}$ [S. Sturm et al., Nature 506, 467 (2014)]. Experiments such as ALPHATRAP and HITRAP aim at reaching this accuracy with heavy, few-electron ions, motivating the evaluation of two-loop radiative corrections.
We calculate a specific set of two-loop corrections to the bound-electron $g$ factor in the hydrogen-like ground state. Diagrams belonging to this set include the magnetic loop as a subprocess and vanish in the free-loop approximation [V.A. Yerokhin and Z. Harman, Phys. Rev. A 88, 042502 (2013)]. At the lowest nonvanishing order, they involve the scattering of the external magnetic field in the Coulomb field of then ionic nucleus. We computed the electric-loop-magnetic-loop diagram, the magnetic-loop-after-loop diagram, and the self-energy-magnetic-loop diagrams, while also shedding light on some other diagrams, which feature a self-energy loop inside the magnetic loop. Our approach treats the binding of the electron to the nucleus nonperturbatively.
The computed corrections to the $g$ factor are of order up to $10^{−7}$ in the case of $^{82}$Pb. These corrections will be relevant to the projected determination of the fine-structure constant from g-factor measurements.
