Abstract
The main goal of the present work is a unitary approach of the physical origin of the corrections to the magnetic moment of free and bound electron. Based on this approach, estimations of lowest order corrections were easily obtained. In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of the order of Compton wavelength, which generates its magnetic moment. The e.m. mass (self-energy) of electron outside this region does not participate to this internal dynamics, and consequently does not contribute to the mass term in the formula of the magnetic moment. This is the physical origin of the small increase of the magnetic moment of free electron compared to the value given by Dirac equation. We give arguments that this physical interpretation is self-consistent with the QED approach. The bound electron being localized, it has kinetic energy which means a mass increase from a relativistic point of view, which determines a magnetic moment decrease (relativistic Breit correction). On the other hand, the e.m. mass of electron decreases at the formation of the bound state due to coulomb interaction with the nucleus. We estimated this e.m. mass decrease of bound electron only in its internal dynamics region, and from it the corresponding increase of the magnetic moment (QED correction). The corrections to the mass value are at the origin of the lowest order corrections to the magnetic moment of free and bound electron.
Highlights
In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of the order of Compton wavelength, which generates its magnetic moment
In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of about reduced Compton wavelength ( e ), a subject largely treated in the literature [1]-[7]
The main goal of the present work was a unitary approach of the physical origin of these corrections
Summary
In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of about reduced Compton wavelength ( e ), a subject largely treated in the literature [1]-[7]. E=2 8π e2 8πr 4 is the e.m. energy density in the electric field generated by electron This means that the electron mass (self-energy) outside the sphere of diameter λe , which does not participate to the “internal” dynamics, is:. It results a straightforward calculus of the anomalous magnetic moment of the electron [10] [11]:. The transformation of the Hamiltonian is based on the assumption of a weak interaction between matter and radiation, which means that the e.m. mass must be a small correction α m0 to the mechanical mass m0 ” This weak interaction supports the idea that the e.m. mass outside the region of diameter ≈ λe does not contribute to the “internal” dynamics, which generates the magnetic moment. Estimations of the lowest order corrections to the magnetic moment (gyromagnetic factor) of bound electron in H-like ions are presented
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