Analysis of the differential cross section for ionization of a hydrogen atom by fast electrons in a uniform electric field

2000 ◽  
Vol 26 (5) ◽  
pp. 446-455
Author(s):  
V. I. Krylov ◽  
V. V. Pivkin
Keyword(s):  
Hydrogen Atom ◽  
Differential Cross Section ◽  
Electric Field ◽  
Cross Section ◽  
Differential Cross ◽  
Uniform Electric Field ◽  
Fast Electrons

The influence of screening on the creation and stopping of electrons

1934 ◽  
Vol 30 (4) ◽  
pp. 524-539 ◽  
Author(s):  
H. A. Bethe
Keyword(s):  
Differential Cross Section ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Main Part ◽  
Primary Particle ◽  
Asymptotic Value ◽  
Fast Electrons ◽  
High Energies ◽  
Γ Rays

The cross-sections for the emission of radiation by very fast electrons (energy great compared with mc2) and for the production of pairs of positive and negative electrons by very hard γ-rays is calculated, considering the screening of the atomic field in which the processes happen. The main part of the paper deals with the integration of the differential cross-section over the angles. It is found that the integral cross-section increases steadily with increasing energy of the primary particle, reaching an asymptotic value for extremely high energies.

scholarly journals Mott scattering in strong laser fields revisited

2009 ◽  
Vol 87 (4) ◽  
pp. 299-310
Author(s):  
B. Manaut ◽  
Y. Attaourti ◽  
S. Taj ◽  
S. Elhandi
Keyword(s):  
Differential Cross Section ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Cross Section ◽  
Differential Cross ◽  
Laser Field ◽  
Bessel Functions ◽  
Strong Laser ◽  
Mott Scattering

In this work, we review and correct the first Born differential cross section for the process of Mott scattering of a Dirac–Volkov electron, namely, expression (26) derived by Szymanowski et al. (Phys. Rev. A, 56, 3846 (1997)). In particular, we disagree with the expression of (dσ/dΩ) that they obtained and we give the exact coefficients multiplying the various Bessel functions appearing in the scattering differential cross section. Comparison of our numerical calculations with those of Szymanowski et al. shows qualitative and quantitative differences when the incoming total electron energy and the electric-field strength are increased particularly in the direction of the laser propagation. Such corrections are very important since the relativistic electronic dressing of any Dirac–Volkov charged particle gives rise to these coefficients that multiply the various Bessel functions, and the relativistic study of other processes (such as excitation, ionization, etc….) depends strongly upon the correctness and reliability of the calculations for this process of Mott scattering in the presence of a laser field. Our work has been accepted, Attaourti and Manaut (Phys. Rev. A, 68, 067401 (2003)) but only as a comment. In this paper, we give full details of the calculations as well as a clear explanation of the large discrepancies that their results could cause when working in the ultra relativistic regime and using a very strong laser field corresponding to an electric field strength ε = 5.89 au.

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