Auto-stabilized electron

We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the [Formula: see text]-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius [Formula: see text]m, where [Formula: see text] is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at [Formula: see text] GeV in terms of the Planck mass [Formula: see text]. The unified field depends on [Formula: see text] and [Formula: see text] alone, independent of [Formula: see text]; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at [Formula: see text].

The Abraham–Lorentz force and electrodynamics at the classical electron radius

The Abraham–Lorentz force is a finite remnant of the UV singular structure of the self-interaction of a point charge with its own field. The satisfactory description of such an interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However, one can construct point-splitting regulators which keep the Abraham–Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing the classical radiation reaction forces.

Pointlike Electric Charge in Gravitational Field Theory

The existence of charged elementary 'point particles' still is a basically unsolved puzzle in theoretical physics. The present work takes a fresh look at the problem by including gravity---without resorting to string theory. Using Einstein's equations for the gravitational fields in a general static isotropic metric with the full energy-momentum tensor (for the charged material mass and the electromagnetic fields) as the source term, a novel exact solution with a well-defined characteristic radius emerges where mass and charge accumulate: $r_{\rm c}{=}\sqrt{r_{\rm e}r_o/2}$---with $r_{\rm e}{=}Q^2\!/4\pi\epsilon_omc^2$ being the 'classical' radius associated with the total charge $Q$ and where $r_o{=}2mG/c^2$ is the Schwarzschild radius belonging to the observable mass $m$ (for the electron one has $r_{\rm e}{\approx}10^{-15}$m and $r_o{\approx}\,10^{-57}$m). The resulting 'Einstein-Maxwell' gravitational electron radius can also be written as $r_{\rm c}{=}\ell_{\rm P}\sqrt{\alpha_{\rm e}}$, where $\ell_{\rm P}{=}\sqrt{\hbar G/c^3}{\approx}10^{-35}$m is the fundamental Planck length and $\alpha_{\rm e}{=}e^2\!/4\pi\epsilon_o\hbar c{\approx}1/137$ the fine-structure constant, which yields $r_{\rm c}^{\rm electron}{=}1.38063{\times}10^{-36}$m.

Excitons of the Structure in Zinc-Blende InxGa1-xN and their Properties

ABSTRACTThe existence of excitons of the structure in zinc-blende InxGa1-xN is reported in this paper. The LCAO electron band structure of zinc-blende InxGa1-xN is calculated as function of both the electron wave vector and the electron radius-vector. The observed optical absorption edge in In-rich regions in InxGa1-xN is explained on the basis of this electron band structure. The excitons of the structure are found on the basis of the electron band structure of zinc-blende InxGa1-xN. The binding energy and the hydrogen like energy levels of these excitons are determined. It is found that these excitons are localized. The observed photoluminescence spectrum in In-rich regions of InxGa1-xN is explained by the excitons of the structure. It is found that destroying of these excitons occurs in their interactions with hetero-junction and that the electrons and the holes of exciton origin penetrate in the semiconductor of wider energy band gap. This phenomenon is used for explanation of the observed spectral blue shift of the electroluminescence in the quantum well structures on InxGa1-xN.

Simulation of Phosphorus Implantation into Silicon with a Single Parameter Electronic Stopping Power Model

We simulate dopant profiles for phosphorus implantation into silicon using a new model for electronic stopping power. In this model, the electronic stopping power is factorized into a globally averaged effective charge [Formula: see text], and a local charge density dependent electronic stopping power for a proton. There is only a single adjustable parameter in the model, namely the one electron radius [Formula: see text] which controls [Formula: see text]. By fine tuning this parameter, we obtain excellent agreement between simulated dopant profiles and the SIMS data over a wide range of energies for the channeling case. Our work provides a further example of implant species, in addition to boron and arsenic, to verify the validity of the electronic stopping power model and to illustrate its generality for studies of physical processes involving electronic stopping.