Hot electron in a polar crystal. I. The eikonal approximation

1976 ◽  
Vol 54 (20) ◽  
pp. 2093-2100
Author(s):  
B. Hede ◽  
T. McMullen
Keyword(s):  
Energy Loss ◽  
Fast Electron ◽  
Quantum Interference ◽  
Eikonal Approximation ◽  
High Energy ◽  
Function Technique ◽  
Hot Electron ◽  
Polar Crystal ◽  
The Individual ◽  
High Energy Scattering

A quantum theory of the rates of momentum and energy loss by a fast electron to the optic modes of a polar crystal as a function of time elapsed since injection of the fast electron is developed. A nonequilibrium Green function technique is used to formulate the problem, and permits inclusion of quantum interference between the individual phonon processes. An approximation, which has been called the eikonal approximation in high energy scattering and is valid when the fractional electron energy loss in a single phonon collision is small, enables us to sum the resulting diagrams. The relationship of this method to a Boltzmann equation approach is discussed.

Hot electron in a polar crystal. II. Loss to single phonon modes

1976 ◽  
Vol 54 (20) ◽  
pp. 2101-2109
Author(s):  
B. Hede ◽  
T. McMullen
Keyword(s):  
Quantum Interference ◽  
Golden Rule ◽  
Eikonal Approximation ◽  
Injection Velocity ◽  
Hot Electron ◽  
Phonon Modes ◽  
Polar Crystal ◽  
Initial Injection ◽  
Important Interaction ◽  
Average Loss

A quantum theory of momentum and energy loss of a fast electron based on the eikonal approximation but including quantum interference effects is applied to a hot electron in a polar crystal. The important interaction is assumed to be the electron–polar LO phonon coupling, and this is represented by the Fröhlich polaron model. Numerical results are presented for loss, as a function of time since injection of the hot electron, to phonon modes with wave vectors parallel to the initial injection velocity. A smaller average loss rate than predicted by the golden rule is found, and quantum oscillations are seen in the time dependence of the rate.

scholarly journals SELECTED TOPICS IN HIGH ENERGY SEMI-EXCLUSIVE ELECTRO-NUCLEAR REACTIONS

2001 ◽  
Vol 10 (06) ◽  
pp. 405-457 ◽  
Author(s):  
MISAK M. SARGSIAN
Keyword(s):  
Present Status ◽  
Short Range ◽  
Nuclear Reactions ◽  
Eikonal Approximation ◽  
High Energy ◽  
Glauber Theory ◽  
Nucleon Recoil ◽  
High Energy Scattering ◽  
Nuclear Targets ◽  
Short Range Correlations

We review the present status of the theory of high energy reactions with semi-exclusive nucleon electro-production from nuclear targets. We demonstrate how the increase of transferred energies in these reactions opens a completely new window for study of the microscopic nuclear structure at small distances. The simplifications in theoretical descriptions associated with the increase in the energies are discussed. The theoretical framework for calculation of high energy nuclear reactions based on the effective Feynman diagram rules is described in detail. The result of this approach is the generalized eikonal approximation (GEA), which is reduced to the Glauber approximation when nucleon recoil is neglected. The method of GEA is demonstrated in the calculation of high energy electro-disintegration of the deuteron and A=3 targets. Subsequently, we generalize the obtained formulae for A>3 nuclei. The relation of GEA to the Glauber theory is analyzed. Then, based on the GEA framework we discuss some of the phenomena which can be studied in exclusive reactions: nuclear transparency and short-range correlations in nuclei. We illustrate how light-cone dynamics of high-energy scattering emerge naturally in high energy electro-nuclear reactions.

Energy loss of relativistic electrons in plasma in accordance with covariant Fokker–Planck formalism

1980 ◽  
Vol 24 (1) ◽  
pp. 75-88 ◽  
Author(s):  
P. S. Ray
Keyword(s):  
Energy Loss ◽  
Green's Function ◽  
High Energy ◽  
Stopping Power ◽  
Function Technique ◽  
Relativistic Electrons ◽  
Relativistic Generalization ◽  
Ion Scattering ◽  
High Energy Electrons ◽  
Fokker Planck

A relativistic generalization of the Fokker–Planck formalism has been constructed. This is applied to the study of energy loss of high-energy electrons in plasma. Both the electron–electron and electron–ion scattering have been considered in a relativistic way. The expression obtained for the stopping power differs from that derived with the help of thermodynamic Green's function technique.

scholarly journals More on eikonal approximation for high energy scattering

2009 ◽  
Vol 818 (3-4) ◽  
pp. 232-245 ◽  
Author(s):  
Tolga Altinoluk ◽  
Alex Kovner ◽  
Javier Peressutti
Keyword(s):  
Eikonal Approximation ◽  
High Energy ◽  
Energy Scattering ◽  
High Energy Scattering

scholarly journals LPM EFFECT AS THE ORIGIN OF JET FRAGMENTATION SCALING IN HEAVY ION COLLISIONS

2012 ◽  
Vol 21 (10) ◽  
pp. 1250088 ◽  
Author(s):  
FRASHËR LOSHAJ ◽  
DMITRI E. KHARZEEV
Keyword(s):  
Energy Loss ◽  
Free Path ◽  
Quantum Interference ◽  
Mean Free Path ◽  
Heavy Ion ◽  
High Energy ◽  
Meson Mass ◽  
Quark Charge ◽  
Jet Fragmentation ◽  
String Models

We address a recent puzzling result from the LHC: the jet fragmentation functions measured in Pb–Pb and pp collisions appear very similar in spite of a large medium-induced energy loss (we will call this jet fragmentation scaling (JFS)). To model the real-time nonperturbative effects in the propagation of a high energy jet through the strongly coupled QCD matter, we adopt an effective dimensionally reduced description in terms of the (1+1) quasi-Abelian–Schwinger theory. This theory is exactly soluble at any value of the coupling and shares with QCD the properties of dynamical generation of "mesons" with a finite mass and the screening of "quark" charge that are crucial for describing the transition of the jet into hadrons. We find that this approach describes quite well the vacuum jet fragmentation in e+e- annihilation at z≥0.2 at jet energies in the range of the LHC heavy ion measurements (z is the ratio of hadron and jet momenta). In QCD medium, we find that the JFS is reproduced if the mean free path λ of the jet is short, λ≤0.3 fm, which is in accord with the small shear viscosity inferred from the measurements of the collective flow. The JFS holds since at short mean free path the quantum interference (analogous to the Landau–Pomeranchuk–Migdal (LPM) effect in QED) causes the produced mesons to have low momenta p~m, where m≃0.6 GeV is the typical meson mass. Meanwhile the induced jet energy loss at short mean free path is much larger than naively expected in string models.

scholarly journals Optical Potentials and Eikonal Approximations

1972 ◽  
Vol 25 (6) ◽  
pp. 643 ◽  
Author(s):  
W Williamson Jr
Keyword(s):  
Optical Potential ◽  
Free Particle ◽  
Eikonal Approximation ◽  
High Energy ◽  
Target System ◽  
Scattering Approximation ◽  
Intermediate States ◽  
High Energy Scattering ◽  
Particle Propagator

An intermediate and high energy scattering approximation is developed by approximating the sum of intermediate states of the target system and expanding the free particle propagator. The resulting expression plays the role of an optical potential and reduces to the eikonal approximation if the average of the excitation energy for the intermediate states is negligible in comparison with the energy of the incident particle.

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

Study of potential curves by UHF type methods. CH4 molecule and its dissociation products

1986 ◽  
Vol 51 (4) ◽  
pp. 731-737
Author(s):  
Viliam Klimo ◽  
Jozef Tiňo
Keyword(s):  
Experimental Data ◽  
Quantum Chemistry ◽  
High Energy ◽  
Basis Set ◽  
Electronic Correlation ◽  
Exact Methods ◽  
Energy Parameters ◽  
Bond Functions ◽  
The Individual ◽  
Potential Curves

Geometry and energy parameters of the individual dissociation intermediate steps of CH4 molecule, parameters of the barrier to linearity and singlet-triplet separation of the CH2 molecule have been calculated by means of the UMP method in the minimum basis set augmented with the bond functions. The results agree well with experimental data except for the geometry of CH2(1A1) and relatively high energy values of CH(2II) and CH2(1A1) where the existence of two UHF solutions indicates a necessity of description of the electronic correlation by more exact methods of quantum chemistry.

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