A modified Born approximation for singular potentials

1970 ◽  
Vol 48 (5) ◽  
pp. 511-512
Author(s):  
Byung Chan Eu
Keyword(s):  
Cross Sections ◽  
Born Approximation ◽  
Phase Shifts ◽  
Phase Method ◽  
Singular Potentials ◽  
Variable Phase ◽  
Scattering Cross ◽  
Lennard Jones ◽  
Variable Phase Method ◽  
Scattering Cross Sections

The variable-phase method is used to obtain nondiverging Born phase shifts for a singular (Lennard–Jones (12,6)) potential. An exemplary calculation is made for the parameters kσ = 18 and εσ2 = 125, and the agreement between the approximate and exact differential scattering cross sections is fairly good.

scholarly journals Mott-Schwinger Effect in the Elastic Scattering of Neutrons from 209Bi

1994 ◽  
Vol 47 (6) ◽  
pp. 681 ◽  
Author(s):  
N Alexander ◽  
K Amos ◽  
L Berge
Keyword(s):  
Elastic Scattering ◽  
Electric Field ◽  
Cross Sections ◽  
Magnetic Moment ◽  
Born Approximation ◽  
Exact Results ◽  
Specific Solution ◽  
Scattering Cross ◽  
The Past ◽  
Scattering Cross Sections

The Mott-Schwinger potential arising from the interaction of the magnetic moment of a neutron incident upon an electric field (of 209Bi) is found to have a profound effect upon the elastic scattering cross sections and polarisations at 0�5, 14�5 and 24 MeV. These effects are evaluated by specific solution of the relevant Schrodinger equations (for 100 partial waves) and with the Born approximation used to define the influence upon all higher ones. These 'exact' results agree with the estimations made under approximation in the past, but not Schr6dinger 100 with 'exact' results calculated by a different method.

ELECTRON – HYDROGEN ATOM SCATTERING IN BORN APPROXIMATION

1960 ◽  
Vol 38 (12) ◽  
pp. 1654-1660 ◽  
Author(s):  
Ta-You Wu
Keyword(s):  
Hydrogen Atom ◽  
Cross Sections ◽  
Born Approximation ◽  
Matrix Elements ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Atom Scattering ◽  
The Matrix ◽  
Scattering Cross Sections

The elastic (1s–1s) and the inelastic (1s–2s, 1s–2p) scattering cross sections in the Born approximation at energies of 1, 4, 9, 16 rydbergs have been calculated exactly from the closed formulas of the matrix elements for these transitions. Both the differential and the total cross sections are given here.

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