The influence of radiation damping on the scattering of light and mesons by free particles. I

1941 ◽  
Vol 37 (3) ◽  
pp. 291-300 ◽  
Author(s):  
W. Heitler
Keyword(s):  
Cross Section ◽  
Free Electron ◽  
Light Wave ◽  
Equation Of Motion ◽  
Radiation Damping ◽  
Conservation Of Energy ◽  
Scattering Of Light ◽  
Relativistic Approximation ◽  
Free Particles ◽  
Image Position

1. In the classical theory there is no difficulty in treating the effect of radiation damping on the scattering of light by a free electron in so far as it is a result of the conservation of energy. In the non-relativistic approximation the equation of motion of a free electron under the influence of a light wave iswith the periodic solution The total energy radiated per second is thenand the total cross-section(1) isFormula (1) differs from the Thomson formula by the factor 1/(1 +κ2). This factor becomes appreciable for energies ħν ≥ 137mc2.

Compton Scattering of 279.1 and 661.6 keV Photons by K-shell Electrons

1981 ◽  
Vol 34 (2) ◽  
pp. 163 ◽  
Author(s):  
IB Whittingham
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Free Electron ◽  
Relativistic Effects ◽  
High Energy ◽  
Infrared Divergence ◽  
Scattered Photon ◽  
Conservation Of Energy ◽  
Energy Cutoff ◽  
Photon Spectra

The spectral distributions of 279?1 and 661? 6 keY photons incoherently scattered by the K electrons of U, Pb, Ta and Sm are calculated for a point-Coulomb potential using a theory previously developed by the author which accounts completely for electron binding and relativistic effects. WKB treatments of the regular and irregular continuum Dirac wavefunctions have been developed and used to mprove the computation of the 'absorption-first' radial matrix elements. The scattered photon spectra for the four elements and scattering angles for which the free electron Compton energy lies below the high energy cutoff due to conservation of energy have broad peaks shifted by 3 to 18 and by 30 to 50 keY, for 279?1 and 661? 6 keY photons respectively, from the free electron Compton energy towards higher scattered photon energies. An infrared divergence, whose magnitude increases strongly with atomic number, commences at ~ 56 keV and is present in those spectra where there is no peak or where the peak lies significantly above 56 keY. Differential cross sections daK' computed using a low energy cutoff, are nonzero for zero-angle scattering and are lower than the Klein-Nishina cross section daF for scattering angles ~ 50� for 661?6 keV photons and for all scattering angles for 279?1 keY photons (with the exception of 80�-130� in the case of Sm). The cross section ratio daK/daF increases with increasing scattering angle until about 100� and 80� for 279?1 and 661? 6 keY photons respectively and then subsequently decreases slowly.

The classical equations of motion of an electron

1946 ◽  
Vol 42 (3) ◽  
pp. 278-286 ◽  
Author(s):  
C. Jayaratnam Eliezer
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Cross Section ◽  
Equations Of Motion ◽  
Conservation Of Energy ◽  
Scattering Of Light ◽  
Dirac Equations ◽  
Symmetrical Form ◽  
Usual Scheme

A set of relativistic classical motions of a radiating electron in an electromagnetic field are derived from the principle of conservation of energy, momentum and angular momentum. It is shown that these equations lead to results more in harmony with the usual scheme of mechanics than do the Lorentz-Dirac equations. When applied to discuss the motion of the electron of the hydrogen atom, these equations permit the electron falling into the nucleus, whereas the Lorentz-Dirac equations do not allow this. When applied to consider the motion of an electron which is disturbed by a pulse of radiation, the solution is in a more symmetrical form. For scattering of light of frequency ν the expression for the scattering cross-section is found to be the same as the classical Thomson formula for small ν, and to vary as ν−4 for large ν.

On the classical theory of radiating electrons

1945 ◽  
Vol 41 (2) ◽  
pp. 184-186 ◽  
Author(s):  
C. Jayaratnam Eliezer ◽  
A. W. Mailvaganam
Keyword(s):  
Electromagnetic Field ◽  
Classical Theory ◽  
Proper Time ◽  
Equations Of Motion ◽  
Spherical Model ◽  
Flat Space ◽  
External Electromagnetic Field ◽  
Radiation Damping ◽  
Conservation Of Energy ◽  
Image Position

1. In Dirac's classical theory of radiating electrons, the relativistic equations of motion of a point-electron in an electromagnetic field arewhere (x0, x1, x2, x3) denote the electron's coordinates in flat space-time, dots denote differentiation with respect to the proper time , and the external electromagnetic field is described by the usual field quantities Fμν. The units are chosen so that the velocity of light is unity. These equations, which are derived from the principles of conservation of energy and of momentum, are the same as those obtained by Lorentz, when he used the spherical model of the electron and included radiation damping in an approximate way. But Dirac's method of derivation suggests that this treatment of radiation damping, and therefore the resulting scheme of equations, is exact within the limits of the classical theory.

A Poor Man’s Approach to Semi-Quantitative Analysis with Electron Energy Loss Spectroscopy

1980 ◽  
Vol 38 ◽  
pp. 110-111
Author(s):  
M. Isaacson
Keyword(s):  
Quantitative Analysis ◽  
Energy Loss ◽  
Electron Energy ◽  
Cross Section ◽  
Electron Energy Loss Spectroscopy ◽  
Excitation Cross Section ◽  
Incident Electron ◽  
Integral Cross Section ◽  
Image Position ◽  
Electron Energy Loss

In an earlier paper1 it was found that to a good approximation, the efficiency of collection of electrons that had lost energy due to an inner shell excitation could be written as where σE was the total excitation cross-section and σE(θ, Δ) was the integral cross-section for scattering within an angle θ and with an energy loss up to an energy Δ from the excitation edge, EE. We then obtained: where , with P being the momentum of the incident electron of velocity v. The parameter r was due to the assumption that d2σ/dEdΩ∞E−r for energy loss E. In reference 1 it was assumed that r was a constant.

scholarly journals Publisher Correction: Resonant phase-matching between a light wave and a free-electron wavefunction

2021 ◽  
Author(s):  
Raphael Dahan ◽  
Saar Nehemia ◽  
Michael Shentcis ◽  
Ori Reinhardt ◽  
Yuval Adiv ◽  
...  
Keyword(s):  
Free Electron ◽  
Light Wave ◽  
Phase Matching ◽  
Electron Wavefunction

Photoproduction of Gravitational Radiation in Static Electromagnetic Fields. Radiative Corrections

1975 ◽  
Vol 53 (20) ◽  
pp. 2315-2320 ◽  
Author(s):  
G. Papini ◽  
S. -R. Valluri
Keyword(s):  
Cross Section ◽  
Gravitational Radiation ◽  
Low Energy ◽  
Radiative Corrections ◽  
Third Order ◽  
The Third ◽  
Relativistic Approximation ◽  
Effective Lagrangian ◽  
Charge Renormalization ◽  
Made In

The radiative corrections of second and third order for the process of photoproduction of gravitons in Coulomb and magnetic dipole fields have been calculated.All divergences have been removed either by charge renormalization or regularization. No approximations have been made in the calculation of the second order cross section. In the third order calculation only the extreme relativistic approximation is given. The forms of the effective Lagrangian, corresponding to the low energy approximations have been determined.

scholarly journals Resonant phase-matching between a light wave and a free-electron wavefunction

2020 ◽  
Vol 16 (11) ◽  
pp. 1123-1131 ◽  
Author(s):  
Raphael Dahan ◽  
Saar Nehemia ◽  
Michael Shentcis ◽  
Ori Reinhardt ◽  
Yuval Adiv ◽  
...  
Keyword(s):  
Free Electron ◽  
Light Wave ◽  
Phase Matching ◽  
Electron Wavefunction

THE PERIDYNAMIC EQUATION AND ITS SPATIAL DISCRETISATION

2007 ◽  
Vol 12 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Etienne Emmrich ◽  
Olaf Weckner
Keyword(s):  
Spatial Dimension ◽  
Equation Of Motion ◽  
Infinite Length ◽  
Conservation Of Energy ◽  
Spatial Discretisation

Different spatial discretisation methods for solving the peridynamic equation of motion are suggested. The methods proposed are tested for a linear microelastic material of infinite length in one spatial dimension. Moreover, the conservation of energy is studied for the continuous as well as discretised problem.

Spin-Polarized Current in the Magnetic Nano Wire

2012 ◽  
Vol 190 ◽  
pp. 101-104
Author(s):  
L. Babazadeh Habashi ◽  
F. Kanjouri ◽  
A.H. Esmailian
Keyword(s):  
Effective Mass ◽  
Cross Section ◽  
Cross Sections ◽  
Applied Voltage ◽  
Free Electron ◽  
Electron Effective Mass ◽  
Ferromagnetic Electrodes ◽  
Spin Polarized

We calculate the TMR of a quantum nanowire with circle cross section consisting of two ferromagnetic electrodes separated by an insulator based on the nearly-free-electron approximation. The dependence of TMR to applied voltage by different cross-sections of nanowire and different electron effective mass of nanowire are studied theoretically.

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