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Previously, we proposed an empirical equation describing the relationship between the gravitational force and the temperature of the cosmic microwave background (CMB). After evaluating our equation, we discovered many empirical equations describing the electromagnetic force in terms of the CMB, including equations for the Rydberg constant, the Bohr radius, the Compton wavelength, the classical electron radius, the Hartree energy, the Coulomb’s law with distance, and the ratio between the gravitational force and electric force. The background theory is not yet complete. However, we can justify why the discovered empirical equations should not be coincidence.

From the viewpoint of general relativity theory (GRT), the obstacles are discussed that do not allow gravitational and electromagnetic fields to be used to create a model of elementary particles and atomic nuclei, including vanishingly small gravitational interaction in comparison with electromagnetic one on microcosm scales, incomplete geometrizability of the electromagnetic field itself, its long-range action in comparison with short-range action of nuclear forces, and the Coulomb repulsion of likely charged protons in a nucleus (it seems so natural that it cannot provide focusing of nucleons and holding nuclei in a compact state) – all these phenomena are differently interpreted in GRT primarily due to universality of gravitational interaction that plays the dominant role at any micro- and macrocosm scales. Based on exact solution of the Einstein–Maxwell equations for a centrally symmetric free electromagnetic field and a dust-like substance, gravitational models of a proton, an electron, and a neutron are suggested in the form of pulsing unclosed wormholes with two static necks – electric charges of opposite signs – emerging into two parallel asymptotically flat vacuum spaces. The neutron is represented in the form of a double wormhole. The calculated radii are 0.8412 fm for the proton, 386.17 fm for the electron, and 1.0049 fm for the neutron. The proton radius coincides within 4% with its experimental value equal to 0.8409 fm measured from the Lamb shift of muon-hydrogen. The electron radius is 459 times greater than the proton radius. However, when the proton is scattered on the electron, its wormhole penetrates into the center of the electron wormhole, the curvature radius of its neck decreases down to the above-indicated neutron radius at the expense of a portion of the relativistic rotational proton energy and the energy of the curved space, that is, the energy of the gravitational field transferred to the electron.

Scanning transmission electron microscopy (STEM) at low primary electron energies has received increasing attention in recent years because knock-on damage can be avoided and high contrast for weakly scattering materials is obtained. However, the broadening of the electron beam in the sample is pronounced at low electron energies, which degrades resolution and limits the maximum specimen thickness. In this work, we have studied electron beam broadening in materials with atomic numbers Z between 10 and 32 (MgO, Si, SrTiO3 , Ge) and thicknesses up to 900 nm. Beam broadening is directly measured using a multisegmented STEM detector installed in a scanning electron microscope at electron energies between 15 and 30 keV. For experimental reasons, the electron beam diameter is defined to contain only 68% of the total intensity instead of the commonly used 90% of the total beam intensity. The measured beam diameters can be well described with calculated ones based on a recently published model by Gauvin and Rudinsky. Using the concept of anomalous diffusion the Hurst exponent H is introduced that varies between 0.5 and 1 for different scattering regimes depending on t/Λel with the specimen thickness t and the elastic mean free path length Λel . The calculations also depend on the fraction of the beam intensity that defines the electron beam diameter. A Hurst exponent H of 1 is characteristic for the ballistic scattering regime with t/Λel → 0 and can be excluded for the experimental conditions of our study with 6 ≦ t/Λel ≦ 30. We deduced H = 0.75 from measured beam diameters which is larger than H = 0.5 that is expected under diffusion conditions. The deviation towards larger H values can be rationalised by our definition of electron diameter that contains only 68% of the total beam intensity and requires therefore larger sample thicknesses before the diffusion regime is reached. Our results clearly deviate from previous analytical approaches to describe beam broadening (Goldstein et al., Reed, Williams et al., Kohl and Reimer). Measured beam diameters are compared with simulated ones, which are obtained by solving the electron transport equation. This approach is advantageous compared to the commonly used Monte Carlo simulations because it is an exact solution of the electron transport equation and requires less computer time. Simulated beam diameter agree well with the experimental data and yield H = 0.80. LAY DESCRIPTION: In scanning transmission electron microscopy (STEM), a focused electron beam is scanned over an electron-transparent sample and an image is formed by detecting the intensity of the transmitted electrons by a STEM detector. STEM resolution is ultimately limited by the electron beam diameter and can be better than 0.1 nm for the best microscopes. However, the electron-beam diameter increases with increasing specimen thickness because electrons are scattered by the interaction of the specimen material and electrons. Electron scattering leads to a change of the electron propagation direction and reduces focusing of the electron beam. The associated electron-beam broadening degrades the lateral resolution of STEM and generally limits the maximum specimen thickness that can be imaged with good resolution. STEM is up to now mainly performed at high electron energies of 80 keV and above. Lower electron energies are beneficial for the study of weakly scattering and radiation-sensitive materials but electron beam broadening becomes more pronounced with decreasing electron energies. Knowledge of beam broadening is therefore particularly important for the interpretation of STEM images that are taken with low-energy electrons. In this work we have studied electron-beam broadening in different materials with thicknesses up to 900 nm at low electron energies between 15 and 30 keV. Beam broadening is directly measured with a newly developed technique. We compare measured beam diameters with different models on beam broadening from literature and find that only a recently published model is well suited to describe the experimental results under our experimental conditions. In addition, beam broadening is simulated by modelling electron propagation in the specimen. The simulation results agree well with the measured beam diameters.

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount $m_e/(\pi r_c)$, with $m_e$ the bare electron mass and $r_c=e^2/m_e c^2$ the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia $m_e (2\lambda_L)^2$, with $\lambda_L$ the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting., Comment: An error in Fig. 2 was corrected

In the equation of the crystal-field theory $$\Delta = \frac{{Q \cdot \langle r^{4} \rangle }}{{\overline{R}{^5} }}$$ , where Δ is the crystal-field splitting, $$\overline{R}$$ is the mean metal–ligand distance in the 3dN-ion-centered coordination polyhedron and Q is constant, $$\langle r^{4} \rangle$$ , the mean value of the fourth power of the 3d-electron radius, is assumed to be also constant (Burns 1993). Here, this assumption is proved by means of high-pressure optical absorption spectroscopy on octahedral Fe2+ in siderite FeCO3 in combination with the data of X-ray diffraction structural refinement by Lavina et al. (2010). It is shown that in the pressure range 1·10–4 to 44.5 GPa or $$\overline{R}$$ ranging from 2.15 to 1.97 A, the value of Q $$\cdot \langle r^{4} \rangle$$ does not deviate more than ~ 4% from its average value.

Dark Energy, a form of repulsive gravity, is causing an accelerated expansion of the Universe. Recent astrophysical measurements have confirmed this accelerated expansion where the ΛCDM model provides a quantitative description of this expansion rate. As is well known there are a number of free parameters of unknown origin in the ΛCDM model. In particular, the cosmological constant Λ (or Dark Energy (DE)) forms one of these free parameters. In this contribution we describe a recent model that attributes DE to the Born self-energy contained within the electric field which surrounds a finite-sized electron within the WHIM (Warm-Hot Intergalactic Medium). Upon using readily available literature values for the intergalactic (IG) baryon density, IG hydrogen ionization fraction, the best estimate for the electron radius, as well as, Hubble parameter data many properties associated with DE can be quantitatively explained. In particular, our model provides an explanation for (i) the magnitude of DE today, (ii) the DE to ordinary matter mass ratio today, (iii) has an equation of state of w = −1, as expected for DE, and (iv) exhibits a deceleration-acceleration transition at a redshift of z~0.8 in agreement with Hubble parameter observations. (v) Finally, the model provides a viable candidate for Dark Matter; the CDM in the ΛCDM model.Further details regarding this DE model can be found in Astrophys. Space Sci 2020, 365, 64.

For a finite-sized classical electron, energy conservation requires that the Born self-energy $U_{e}^{\mathit{Born}}$, due to the electric field which surrounds the electron, be added to the electron’s rest mass energy $m_{e}c^{2}$. $U_{e}^{\mathit{Born}}$, which scales inversely with the electron radius $R_{e}$, is very large and, in fact, would dominate all other energy contributions within the intergalactic medium (IGM). By taking into account the ionization fraction $\nu _{e}$ of atomic hydrogen in the IGM Dark Energy can be quantitatively explained using $U_{e}^{\mathit{Born}}$ without the necessity of a cosmological constant $\varLambda $.

In this paper the quantum state energies of an electron confined in a GaAs/GaxAl1−xAs core shell quantum dot were calculated using W.K.B approximation method, in the frame work of the effective mass approximation under external electric field. The study reveals that the electron energies of 1s and 2p states decreases with increase in applied external electric field at a given dot radius. Furthermore the electron energies of the states are found to decrease with increase in dot radius and become appreciably small 30 e V with electric field of strength 5 K V / c m . In addition our results show the effect of shell radius on the electronic structure. For a shell radius R 1 > 5 n m , the ground and first excited state electron energies are negligibly small and approaches to a constant value. We also display the effect of A l concentration on the electron energy levels. The electron energy increases and shows non linear dependence with the increase in A l concentration. The observed results are in agreement with the theoretical results reported in the previous literature.

The Thomson cross section of light scattering is calculated for a moving particle within classical electrodynamics.

Energy relaxation of single protons in an ultracold electron gas in the presence and absence of a uniform magnetic field is studied by the method of molecular dynamics. For the case with a magnetic field, the situation is considered in which the electron Larmor radius is much smaller than the classical minimal approach distance. The calculations are performed for electron densities of 108–109 cm–3, magnetic fields of В = 1–3 T, electron temperatures of 10–50 K, and proton energies of 100–300 000 K.

The processes of the nonlinear Compton and the nonlinear Thomson scattering in a field of intense plane electromagnetic wave in terms of photon yield have been considered. The quantum consideration of the Compton scattering process allows us to calculate the probability of a few successive collisions k of an electron with laser photons accompanied by the absorption of n photons (nonlinear regime) when the number of collisions and the number of absorbed photons are of random quantities. The photon spectrum of the nonlinear Thomson scattering process was obtained from the classical formula for intensity using the Planck's law. The conditions for which the difference between the classical and the quantum regimes is manifested was obtained. Such a condition is determined by a discrete quantum radiation mechanism, namely, by the mean number of photons k ¯ emitted by an electron passing through the laser pulse.

Some integral effects of electromagnetic interactions, such as the electromagnetic mass and the anomalous magnetic moment of the electron, are discussed on the basis of covariant methods of classical electrodynamics.

A model of the electron is examined, allowing us to obtain its mass, spin and magnetic moment. The electron is represented as a sphere of classical radius (protoelektron) with zero rest mass, the rotating orbit radius of which is reduced value of the Compton wavelength of the electron. The ratio of the radius of the sphere to the radius of the orbit is equal to the fine structure constant. The sphere has a single charge distributed over its surface. Due mutual repulsion of parts of charge sphere acquires a mass equal to half of the rest mass of an electron, rotating mechanical mass protoelektron on orbit provides its characteristic electron spin 1/2 and kinetic energy, which creates 1/4 of the rest mass. Rotation of charge, similar to the ring current generates a magnetic moment equal to the Bohr magneton and magnetic energy, creating 1/4 of the rest mass of an electron. The total energy of the electron is the sum of its electrostatic, magnetic and kinetic energy. Accordingly, the total mass of the electron is the sum of the masses of electrostatic, magnetic and kinetic origin. The model is applicable to the muon and tau leptons. The correct ratio between the mass, spin and magnetic moment for them observed under the condition in the ratio of the radius of the charged sphere to the radius of the orbit equal to the fine structure constant. The model allows us to understand the physical nature of a number of problems: the Heisenberg uncertainty principle, Lorentz transformations and wave properties of the electron. The cause of the orbital rotation proto-particles is a magnetic field which creates self-acting rotation proto-particles around its own axis.

We have studied self-conjugate second-order equations with spinor wavefunctions for fermions moving in an external Coulomb field. For stationary states, the equations are characterized by separated states with positive and negative energies, which render probabilistic interpretation possible. For the Coulomb field of attraction, the energy spectrum of the second-order equation coincides with the spectrum of the Dirac equation, while the probability densities of states are slightly different. For a Coulomb field of repulsion, there exists an impermeable potential barrier with radius depending on the classical electron radius and on the electron energy. The existence of the impermeable barrier does not contradict the results of experiment for determining the inner electron structure and does not affect (in the lowest order of perturbation theory) the Coulomb electron scattering cross section. The existence of the impermeable barrier can lead to positron confinement in supercritical nuclei with $Z \geq 170$ in case of realization of spontaneous emission of vacuum electron-positron pairs., 23 pages, 4 figure

The electron density dependence of the electron spin relaxation time in a system of electrons interacting with phonons through phonon-modulated spin-orbit coupling was calculated using the formula for electron spin resonance derived by the projection-reduction method. The electron spin relaxation time in GaAs increased with increasing electron density, and the electron density was found to affect the electron spin relaxation differently according to temperature. The electron spin in GaAs was relaxed mainly by optical phonon scattering at high electron densities and piezoelectric phonon scattering at relatively low electron densities.

An attempt to obtain a new theoretical derivation of the size of the electron microparticle has been done. To this purpose first the Maxwell equation for the electron current has been examined for the case of the one-electron current present in the Bohr model of the hydrogen atom. It has been shown that the equation is satisfied on condition that the microstructure properties of the electron particle are taken into account. In the next step, the quanta of the magnetic field characteristic for the Bohr atom and the electron time periods specific for the electron current along the orbits were substituted in place of parameters entering the classical Oersted equation. This gives an expression for the cross-section radius of the orbits not much different than results for the radius of the electron microparticle obtained in a former electron theory

With an assumption of n = 2 in the Dirac quantization condition,when the sequence comprised of the Bohr radius, reduced Compton wavelength and classical electron radius is extended and matched with its velocity sequence, these fundamental lengths are mirrored with a corresponding set of fundamental monopole lengths with the speed of light as the axis ofsymmetry. Monopole charge is g = 137 ecand mass is found to be 1 . 45 × 10- 3 eV / c2 . This result may fit with the extended relativity (tachyon) theory of Recami with a modification of the proposed charge quantization and electromagnetic coupling constant.

In this paper we purpose a fluctuation mechanism of the continuously appearing and disappearing lepton-antilepton pairs in vacuum. Within this approach, a semi-classical study on the Sauter-Schwinger effect is accomplished. We examined the suggested mechanism by comparing calculation of the Schwinger threshold our mechanism provides with the original one ( m 2 c 3 / e ℏ ). While derivation we observed that the fluctuation mechanism suggests that muons and tauons should maintain the idea of classical lepton radius just as electrons maintain the idea of classical electron radius. The mechanism provides that lepton-antilepton pairs have initial total energies proportional to their rest mass energies with common constant of proportionality equal to 1.47858037433852 .

The radiative response of the classical electron is commonly described by the Lorentz-Abraham-Dirac (LAD) equation. Dirac's derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: "We ... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms". To substantiate Dirac's approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac's approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincar\'e cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy-momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient {\theta}. The value of {\theta} depends on the composition of the adjacent potential which generates Poincar\'e forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization., Comment: More details are added in the introduction concerning similarities and differences between the original Dirac's approach and our treatment. Several typos are corrected

An approximate solution to the dispersion equation for the dynamics of an X-ray beam trapped in a plane waveguide with smooth walls is used to study the dependence of extinction depth on the optical density of wall material and X-ray energy. For angles of incidence of the X-ray beam that are no greater than the Fresnel angle, the extinction depth in nonabsorbing medium depends only on difference N e1–N e1 of electron densities in the wall material and waveguide layer as (πr 0(N e1–N e2))–1/2, where r 0 ~ 2.81794 × 10–13 cm is the classical electron radius. The results are in good agreement with the penetration depth of X-ray radiation into surface that is obtained using the Fresnel formulas in the approximation of plane waves at grazing angles that range from zero to one half of the critical angle of total external reflection.

In the present work, numerical studies on the effects of weakly relativistic ponderomotive force and space charge in the nonlinear interaction of a high-power microwave beam with a plasma are carried out. It is shown that, the profiles of the electron density and dielectric permittivity contain high peaks, and modulation of wavelength occurs in electron density distribution by increasing the microwave energy flux. In addition, it is indicated that the profiles of the electric and magnetic fields in relativistic regime are lengthened more than non-relativistic regime by increasing the initial electron density and the relativistic effects cause the increase in oscillation wavelength of electron density, dielectric permittivity and space charge field, in comparison with the non-relativistic regime. Finally, the results of the research show that the steepening in electron density distributions and their oscillation wavelength are enhanced, when the relativistic effects appear.

On the basis of the theory of bound charges the calculation of the motion of the charged particle at the Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb centres is carried out. It is shown that the proton and electron can to create a stable connection with the dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom coincide with the Born orbits.

In this paper, we review the main challenges related to laser Thomson scattering on low temperature plasmas. The main features of the triple grating spectrometer used to discriminate Thomson and Raman scattering signals from Rayleigh scattering and stray light are presented. The main parameters influencing the detection limit of Thomson scattering are reviewed. Laser stray light and plasma emission are two limiting factors, but Raman scattering from molecules inside the plasma will further decrease it. In the case of non-thermal plasmas at high pressure, Thomson scattering is the only technique which allows us to obtain the electron density without any prior knowledge of the plasma properties. Moreover, very high 3D spatial and temporal resolutions can easily be achieved. However, special care still needs to be taken to verify that Thomson scattering is non intrusive. The mechanisms that will lead to possible measurement errors are discussed. The wavelength-resolved scattering signal also allows us to get direct information about the electron energy distribution function in the case of incoherent light scattering. Finally, we discuss some recent applications of Thomson scattering on atmospheric pressure plasma jets, but also in the field of electron collision kinetics. Thomson scattering can be applied on atomic but also molecular plasmas. In the latter case, one needs to take into account the possible contribution of rotational Raman scattering.

To explain superconductivities and make up for the lack of current theory, a new quantum theory of cold electron was proposed. The key point is that we accepted the concept of electron orbital rotation instead of traditional electron spin. It leads to an important conclusion that the electron at low temperature is running in a flat orbital. The physical mechanism of superconductivities is so explained preferably. Under the assumption that the electrons have their motion tracks and the tracks can be described in atoms, the situations of electron will be changed a lot. The new concept of cold electron is then established. It means that the electrons can feel temperature. The Schrodinger function is the function of ideal electron indeed. Hot electron looks like the electron of the ideal electron. As temperature goes much lower, the electron orbits will obviously departure to what Schrodinger function described, and run in a flat one. The orbital shape of paired electron depends on temperature, transitioning from three- to two-dimension. Comparing the orbital shape to that of common electron, the paired cold electron saved quite some space in atomic crystal lattice. It created the preconditions for the phase transition at low critical temperature.

Observations of radar and optical meteors at altitudes above the ablation-defined meteor zone point to a “new” sputtering source of high-altitude metals while also yielding clues to the radio science of radar meteors. That high-altitude radar meteors (HARMs) are visible at altitudes of up ∼180 km using the 50 MHz Jicamarca Radio Observatory (JRO) implies that a significant fraction of the directly-sputtered meteoroid material is ionized as the collisional mean free path (MFP) at these altitudes is many tens of meters. Also, that high-altitude klB FAI (Field-Aligned Irregularity) trail-echoes are observed in association with HARM head-echoes offers insight into the meteor-associated plasma processes as well as the radar scattering mechanism. In particular, HARMs reveal the onset, as the meteoroid enters the upper atmosphere, of radar scattering which must be from the minimum, radar detectible, electron production. The maximum Radar backscattering Cross-Section (RCS) from N electrons, σ BS = 4πν2 e N2, is the result of totally coherent scattering from N, equally illuminated and closely spaced, electrons where r e , is the classical electron radius. An estimate for N is given. Overall, this approach yields a direct, physics-based path linking the RCS of observed head- and trail-echoes to the meteoroid sputtering process and to the ion atmospheric “capture” process whereby the head-echo “plasma” is embedded into the atmosphere. In addition, recent lidar observations of atomic Fe, Na, and K at altitudes well above the traditional meteor zone violate the usual assumptions regarding thermospheric metals and form an instructive complication to the above “simple meteoroid” scenario as many meteoroids appear to be fragmenting at high altitudes. This “cold fragmentation” likely points to complex “dirty-ice” and “dust-ball” meteoroids comprised of small, dense grains weakly bound together by more volatile substances. These meteoroids may disperse into an extended “coma” that presents a more complex and larger surface area atmospheric-interaction region. We briefly discuss sputtering, the impact energies needed for onset of sputtering, sputtering yield, and the observational evidence available for interpretation of meteoroid sputtering as a source of aeronomically interesting metals above the classical meteor zone. We further suggest that a thermospheric “reservoir” of nanometer-sized dust play an important aeronomic role.

SPIE Optics + Optoelectronics, Prague, Czech Republic; Proceedings of SPIE 10239, 102360H (2017). doi:10.1117/12.2267939, In this paper, we present an extension to our code, XCASCADE [Medvedev, Appl. Phys. B 118, 417], that enables to model time evolution of electron cascades following low-intensity X-ray excitation in various materials consisting of elements with atomic numbers Z = 1 - 92. The code is based on a classical Monte-Carlo scheme and uses atomistic cross sections to describe electron impact ionization. The new extended version, XCascade-3D, also tracks the electron trajectories with 3D spatial resolution. This model takes into account anisotropic scattering of electrons on atoms. We show that the calculated electron ranges in various materials are in a good agreement with the available data, confirming the potential for high accuracy applications at FEL pulse diagnostics., Published by SPIE, Bellingham, Wash.

A covariant relativistic formalism for the electron-photon and nuclear dynamics is summarised making more accurate predictions in agreement with experiments for Compton scattering in shells with large electron binding energy. An exact solution for the Dirac equation for an electron in the nuclear Coulomb field is obtained, in order to write the relativistic dynamics for this QED process. This is a preparation for the calculation of the relativistic cross-section for Compton scattering on bound electrons; as a precision test for QED., 10 pages , 5 figures

In the paper, nonlinear structure of electromagnetic field, electron temperature, and electron density in interaction with relativistic laser and collisional underdense rippled plasma are investigated. The results are shown that due to the combination influence of relativistic effect, ohmic heating and plasma density ripple, electromagnetic field profile presents obvious asynchronism, which the peak of electric field run ahead of the peak of magnetic field. Furthermore, the electromagnetic field profiles show obvious non-sinusoidal, and the profile of electron temperature and density become highly peaked. Especially, compared with the previous work, due to the added influence of plasma density ripple, electromagnetic field, electron temperature and electron density present obvious oscillation along plasma length rather than stabilization amplitude, and their peak are out of sync.

We derive and qualitatively analyze nonlinear and linear equations for the scattering length and effective radius. We find and investigate exact solutions of these equations in the case of a centrally symmetric rectangular potential and elucidate a relation between the effective radius and the scattering length. We are especially interested in the cases of zero and unbounded scattering lengths.

Mach's principle of immanence of the universe states that the properties of local matter depend upon the pres- ence of the remainder of the universe. The discrete solution for the intrinsic duration of any space is the product of Hub- ble's expansion parameter and the length of the space divided by �� Gc -3 . For the typical "space" occupied by protons and electrons these values are ~3 ms and ~1 ms, respectively. Recently we demonstrated that the durations of photon emis- sions from chemiluminescent reactions doubled during simultaneous local+nonlocal activations if both loci shared a spe- cific pattern of changing angular velocities of 1 ms point-duration configurations of magnetic fields within circular arrays. In the present experiments we varied the point durations in integers between 1 and 10 ms and found only the predicted 3 ms and 1 ms point durations produced this effect. On the bases of these earth-based measures Hubble's constant would be ~74.8 km·s -1 ·MParsec -1 . The results suggest an easier and more economic inference of this important cosmological pa- rameter and alternative applications to protons and electrons during chemical reactions.

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 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., final version, Int. J. Mod. Phys. 43 1950077 (2019)

A theoretical analysis is proposed to investigate the Compton scattering as well as the inverse Compton scattering. In this analysis, the incident and scattered electromagnetic (EM) waves are classically described using Maxwell's equations, while the interacting electron is represented quantum mechanically by a wavepacket with a finite spreading length. The density matrix formalism is introduced to analyze the interaction between the electron wave and the EM field in a quantum mechanical manner. The interaction mechanism is caused by the effective coupling between EM and electron waves satisfying the energy and momentum conservation rules. The effects of the electron relaxation time due to Coulomb collisions among electrons, as well as the finite spreading size of an electron, are newly considered. Expressions for the radiated power of the scattered wave are derived for Compton and inverse Compton scattering.

To study the electron transport properties in high electron mobility transistors (HEMTs), it is essential to have a correct estimation for electron density distribution. The introduction of back barriers in GaN-based HEMTs leads to a modified profile of a two-dimensional (2D) electron wave function, which can no longer be described by the standard Fang-Howard model. To address this change, a numerical model is developed for the wave function calculation based on the variational Hartree method. An electron density profile in the GaN channel with AlGaN top and back barriers has been simulated. The results are in good agreement with those obtained from self-consistent Poisson-Schrodinger simulation. The centroid of the 2D electron gas is also calculated as a function of the Al composition in the AlGaN back barrier.

The role of electron-electron interaction in the process of electron capture to a deep quantum well is investigated. Using two-level and three-level quantum wells as examples, the basic electron-capture mechanisms, i.e., the interaction with optical phonons and the Coulomb electron-electron interaction, are considered, and the corresponding capture probabilities and electron lifetimes are calculated. The effect of Auger recombination on the charge-carrier distribution in a quantum well is also taken into account. With this taken into consideration, a set of rate equations is solved for a nonsteady-state mode, and the time dependences of the electron concentration at the ground energy level in the quantum well are found. The contributions of each of the recombination processes under consideration are shown.

The concept of electromagnetic mass was developed in the last half of the nineteenth century and has been studied till date from various approaches. Here we have discussed some of those approaches and later we have focused on the mass corresponding to the charge of an electron in the framework of the spinning sphere of electrons. It is shown how the charge and the mass contribute together to the total energy of electrons. The dependence of the charge and the mass on the velocity is also discussed.