Free‐Electron Energy Levels for Symmetric Three‐Dimensional Frameworks

1968 ◽  
Vol 48 (1) ◽  
pp. 273-277 ◽  
Author(s):  
George H. Duffey ◽  
Joel A. Houtman ◽  
Joseph Riashy
Keyword(s):  
Electron Energy ◽  
Free Electron ◽  
Energy Levels ◽  
Three Dimensional

scholarly journals Low-lying electron energy levels in three-particle electron-muon ions of Li, Be, and B

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
A. E. Dorokhov ◽  
V. I. Korobov ◽  
A. P. Martynenko ◽  
F. A. Martynenko
Keyword(s):  
Electron Energy ◽  
Energy Levels

scholarly journals SPECTRAL CORRELATIONS IN DISORDERED MESOSCOPIC METALS AND THEIR RELEVANCE FOR PERSISTENT CURRENTS

1996 ◽  
Vol 10 (28) ◽  
pp. 1397-1406 ◽  
Author(s):  
AXEL VÖLKER ◽  
PETER KOPIETZ
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Average Density ◽  
Electron Interaction ◽  
Energy Window ◽  
Persistent Currents ◽  
Dependent Part ◽  
The Difference ◽  
Aharonov Bohm ◽  
Grand Canonical

We use the Lanczos method to calculate the variance σ2(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ2(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.

Three-Dimensional Nonlinear Theory of the Free Electron Laser

AIAA Journal ◽  
1981 ◽  
Vol 19 (9) ◽  
pp. 1164-1168 ◽  
Author(s):  
P. Sprangle ◽  
Cha-Mei Tang
Keyword(s):  
Nonlinear Theory ◽  
Free Electron ◽  
Free Electron Laser ◽  
Three Dimensional

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

Numerical study of the second harmonic generation in FELs

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
A. M. Kalitenko
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Free Electron ◽  
Numerical Study ◽  
Second Harmonic ◽  
Three Dimensional ◽  
X Ray ◽  
Linac Coherent Light Source ◽  
The Individual ◽  
Analytical Expressions

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

scholarly journals The Uehling correction to the energy levels in a pionic atom

2006 ◽  
Vol 84 (2) ◽  
pp. 107-113 ◽  
Author(s):  
S G Karshenboim ◽  
E Yu. Korzinin ◽  
V G Ivanov
Keyword(s):  
Free Electron ◽  
Vacuum Polarization ◽  
Energy Levels ◽  
Analytic Form ◽  
Electron Mass ◽  
Mass Ratio ◽  
Pionic Atom ◽  
Closed Analytic Form

We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l = n–1). The result is obtained in a closed analytic form as a function of Zα and the pion-to-electron mass ratio. Certain asymptotics of the result are also presented.PACS Nos.: 12.20.Ds, 36.10.Gv

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