Considerations about the measurement of the magnetic moment and electric dipole moment of the electron

Abstract

The goal of the measurement of the magnetic moment of the electron $\mu$, is to experimentaly determine the gyromagnetic ratio. The factor $g/2$ is computed by the accurate measurement of two frequencies, the spin precession frequency $\nu_s$, and the cyclotron frequency $\nu_c$, and is defined as $\nu_s/\nu_c=g/2$. These experiments are performed with a single electron confined inside a Penning trap. The existence of the electric dipole moment ${\bf d}_e$, involves the idea of an asymmetric charge distribution along the spin direction such that ${\bf d}_e=d_e{\bf S}/(\hbar/2)$. The energy shift $\Delta U=2{d}_eE_{eff}$ of the interaction of the electric dipole of electrons with a huge effective electric field ${\bf E}_{eff}$, close to the nucleus of heavy neutral atoms or molecules, is calculated by a spin precession measurement and the value $d_e$ is determined. By using a classical model of a spinning electron, which satisfies Dirac's equation when quantized, we determine classically the time average value of the electric and magnetic dipole moments of this electron model when moving in a uniform magnetic field and in a Penning trap, with the same fields as in the real experiments, and obtain an estimated value of these dipoles. We compare these results with the experimental data and make some interpretation of the measured dipoles. The conclusion is that experiments do not measure what they purport to measure.