Abstract
The energy spectrum and angular distribution of electronsscattered by an ion in a strong laser field are investigated as a function of the incident electron velocity for small impact parameters. The energy distribution has been calculated quantummechanically by a method of wavepacket scattering from a threedimensional hydrogenlike Coulomb potential. It is compared with the energy distribution from the classical instantaneous collision model, and the quantum limitations are evaluated. The backscattered particles can have enhanced scattering rates and a very large energy gain due to the effect of correlated collisions. Their spectrum displays a ring structure similar to the rescattering plateau in the abovethreshold ionization of neutral atoms. The effect of these largeangle scatteringeffects on the electron acceleration and heating is also discussed.
Allocation of CPU time and assistance with the computer facilities from the “Centre Informatique National de l’Enseignement Supérieur” (CINES, Montpellier, France) are acknowledged.
I. INTRODUCTION
II. PRESENTATION OF THE MODELS
A. Timedependent Schrödinger equation: The spectral method
B. Timedependent Schrödinger equation: The grid method
C. Model of classical collisions
III. ELECTRON ENERGY SPECTRUM
A. Effect of initial parameters
IV. ANGULAR DISTRIBUTION OF SCATTERED ELECTRONS
V. AVERAGE CHARACTERISTICS OF THE ACCELERATED ELECTRONS
VI. DISCUSSION AND CONCLUSIONS
Key Topics
 Electron scattering
 58.0
 Collision theories
 18.0
 Electric fields
 16.0
 Electrons
 10.0
 Wave functions
 10.0
Figures
Electron energy spectra obtained from the quantum and classical models for the following set of parameters: , , , . (a) Spectrum obtained with the ADI method for (solid line) and (dotted line); (b) the same spectrum obtained with the spectral method for (solid line) and (dotted line). The thick dashed (thin dashdotted) line in panel (b) shows the result of the classical dynamical model for . The dashed line in panel (a) shows the result of the classical model of instantaneous collisions. Also shown for comparison is the energy spectrum of the electron in the ground state of hydrogen (dotteddashed line).
Electron energy spectra obtained from the quantum and classical models for the following set of parameters: , , , . (a) Spectrum obtained with the ADI method for (solid line) and (dotted line); (b) the same spectrum obtained with the spectral method for (solid line) and (dotted line). The thick dashed (thin dashdotted) line in panel (b) shows the result of the classical dynamical model for . The dashed line in panel (a) shows the result of the classical model of instantaneous collisions. Also shown for comparison is the energy spectrum of the electron in the ground state of hydrogen (dotteddashed line).
Influence of the parameter (thick dashdotted line), (thick dashed line), and (thin dotted line) on the cutoff energy in classical model simulations. The solid curve presents the distribution obtained from the quantum calculation. The parameters are the same as in Fig. 1.
Influence of the parameter (thick dashdotted line), (thick dashed line), and (thin dotted line) on the cutoff energy in classical model simulations. The solid curve presents the distribution obtained from the quantum calculation. The parameters are the same as in Fig. 1.
Energy spectrum (11) (a) and momentum spectrum (b) of scattered electrons for the incident velocity , for (solid line) and (dashed line). Other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
Energy spectrum (11) (a) and momentum spectrum (b) of scattered electrons for the incident velocity , for (solid line) and (dashed line). Other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
(Color) Position of particles at the end of classical calculations sent within the certain range of impact parameters: red, ; yellow, ; green, ; blue, . The parameters are the same as in Fig. 1.
(Color) Position of particles at the end of classical calculations sent within the certain range of impact parameters: red, ; yellow, ; green, ; blue, . The parameters are the same as in Fig. 1.
Momentum distribution of scattered particles in the propagation direction for the quantum calculations for (solid line) and (dashed line). The parameters are the same as in Fig. 1. The TDSE is solved with the spectral method.
Momentum distribution of scattered particles in the propagation direction for the quantum calculations for (solid line) and (dashed line). The parameters are the same as in Fig. 1. The TDSE is solved with the spectral method.
(Color) Probability density distributions of (a) momentum and (b) position of the scattered particle for the incident velocity . Probability decreases on a logarithmic scale from red to blue. The potential is repulsive and other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
(Color) Probability density distributions of (a) momentum and (b) position of the scattered particle for the incident velocity . Probability decreases on a logarithmic scale from red to blue. The potential is repulsive and other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
Tables
Characteristic parameters of the calculations and the accelerated electrons for the electron scattering on the attractive and repulsive charge; a comparison between the quantummechanical (qm) and classical (cl) calculations and the theoretical (th) formula (15).
Characteristic parameters of the calculations and the accelerated electrons for the electron scattering on the attractive and repulsive charge; a comparison between the quantummechanical (qm) and classical (cl) calculations and the theoretical (th) formula (15).
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