The classical limit of the quantum mechnical expressions for the kinetic theory cross sections

1981 ◽  
Vol 74 (12) ◽  
pp. 6718-6724 ◽  
Author(s):  
C. F. Curtiss
Keyword(s):  
Kinetic Theory ◽  
Cross Sections ◽  
Classical Limit

scholarly journals Semi-classical bounds on scattering cross sections in two dimensional magnetic fields

1997 ◽  
Vol 147 ◽  
pp. 25-61
Author(s):  
Hideo Tamura
Keyword(s):  
Magnetic Fields ◽  
Energy Range ◽  
Cross Sections ◽  
Classical Limit ◽  
Uniform Boundedness ◽  
Classical Dynamics ◽  
Two Dimensional ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Scattering Cross Sections

AbstractWe prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.

HIGH FREQUENCY GAS DISCHARGE BREAKDOWN IN NEON

1952 ◽  
Vol 30 (5) ◽  
pp. 565-576 ◽  
Author(s):  
A. D. MacDonald ◽  
D. D. Betts
Keyword(s):  
Kinetic Theory ◽  
Electric Fields ◽  
Cross Sections ◽  
Electrical Breakdown ◽  
Ionization Rate ◽  
Gas Discharge ◽  
Distribution Functions ◽  
Boltzmann Transport ◽  
Discharge Data ◽  
Confluent Hypergeometric Functions

Electrical breakdown of neon at high frequencies has been treated theoretically on the basis of the Boltzmann transport equation. Exciting and ionizing collisions are accounted for as energy loss terms in the Boltzmann equation and measured values of the ionization efficiency are used in the integral determining the ionization rate. Electrons are lost to the discharge by diffusion. The equations are treated separately for the cases in which the collision frequency is much less than or much greater than the radian frequency of the applied field. The electron energy distribution functions are expressed in terms of Bessel functions, confluent hypergeometric functions, and simple exponentials. The ionization rate and the diffusion coefficient are calculated using these distribution functions in kinetic theory formulas, and combined with the diffusion equation to predict breakdown fields. The theoretically predicted fields are compared with experiment at 3000 Mc. per sec. The breakdown equations, calculated from kinetic theory and using no gas discharge data other than collision cross sections, predict breakdown electric fields within the limits of accuracy determined by these cross sections over a large range of experimental variables.

Atom–diatomic molecule kinetic theory cross sections

1985 ◽  
Vol 82 (8) ◽  
pp. 3795-3801 ◽  
Author(s):  
C. F. Curtiss ◽  
M. W. Tonsager
Keyword(s):  
Kinetic Theory ◽  
Diatomic Molecule ◽  
Cross Sections

SEMI-CLASSICAL ANALYSIS FOR TOTAL CROSS-SECTIONS OF MAGNETIC SCHRÖDINGER OPERATORS IN TWO DIMENSIONS

1995 ◽  
Vol 07 (03) ◽  
pp. 443-480 ◽  
Author(s):  
HIDEO TAMURA
Keyword(s):  
Cross Sections ◽  
Classical Limit ◽  
Schrödinger Operators ◽  
Two Dimensions ◽  
Schrodinger Operators ◽  
Classical Analysis ◽  
Total Cross Sections ◽  
Total Scattering ◽  
Scattering Cross ◽  
Scattering Cross Sections

We define total scattering cross-sections for magnetic Schrödinger operators in two dimensions and prove the shadow scattering (the quantum total cross-sections double the classical ones in the semi-classical limit) under some assumptions.

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