The application of variational methods to atomic scattering problems III. The elastic scattering of electrons by helium atoms

1953 ◽  
Vol 219 (1136) ◽  
pp. 102-109 ◽  
Keyword(s):  
Differential Equation ◽  
Wave Function ◽  
Elastic Scattering ◽  
Phase Shift ◽  
Variational Method ◽  
Zero Order ◽  
Scattering Problems ◽  
Helium Atoms ◽  
Atomic Scattering ◽  
Slow Electrons

The variational method of Hulthèn has been applied to the elastic scattering of slow electrons by helium atoms, the effect of exchange being taken into account in calculating the zero-order phase shift. Satisfactory agreement has been obtained with the results given by numerical integration of the integro-differential equation determining the scattering when the total wave function is taken to be completely antisymmetric. Even at very low electron energies (0·04 eV) the agreement with experiment is good.

The application of variational methods to atomic scattering problems - I. The elastic scattering of electrons by hydrogen atoms

1951 ◽  
Vol 205 (1083) ◽  
pp. 483-496 ◽  
Keyword(s):  
Wave Function ◽  
Elastic Scattering ◽  
Variational Methods ◽  
Zero Order ◽  
Hydrogen Atoms ◽  
Scattering Problems ◽  
Polarization Effects ◽  
Numerical Integrations ◽  
Atomic Scattering ◽  
Slow Electrons

The variational methods proposed 'by Hulthèn and by Kohn have been applied to the investigations of the elastic scattering of slow electrons by hydrogen atoms. Allowance has been made for both exchange and polarization effects in determining the zero-order phase shift. By comparison with results obtained by direct numerical integrations of the differential equations determining the scattering when the total wave function is assumed to have a separable form, it seems likely that both variational methods, which yield very nearly the same results, give satisfactory results except in certain sensitive cases, even when simple trial functions are employed. It is found that the inclusion of polarization (in the form of a nonseparable wave function) is less important when exchange is included than when it is not. Reasons why this would be expected are given. Detailed results are obtained for electrons with energies up to 50 eV.

The application of variational methods to atomic scattering problems V. The zero energy limit of the cross-section for elastic scattering of electrons by hydrogen atoms

1957 ◽  
Vol 241 (1227) ◽  
pp. 522-530 ◽  
Keyword(s):  
Elastic Scattering ◽  
Variational Methods ◽  
Cross Section ◽  
Trial Function ◽  
Central Field ◽  
Zero Energy ◽  
Hydrogen Atoms ◽  
Scattering Problems ◽  
Atomic Scattering ◽  
Exchange Polarization

Calculations have been made using the central-field, exchange and exchange-polarization approximations. In agreement with previous work it is found that the wave functions are profoundly modified by inclusion of exchange. The exchange radial equations are solved by numerical integration and by variational methods; consideration of the form of the equations for moderately large radial distances suggests an improved two-parameter trial function which is found to give satisfactory results. Polarization, i. e. the inclusion of the interelectronic distance r 12 in the trial function, is much more important for the symmetric than for the anti-symmetric case. A symmetric exchange-polarization trial function is obtained which appears more satisfactory than those previously employed. It may be hoped that the final result for the zero-energy elastic scattering cross-section, Q (0) = 5·76 x 10 -15 cm 2 , is correct to within about 15%.

scholarly journals Resonance in the Elastic Scattering with Exchange of Slow Electrons by Helium Atoms

1970 ◽  
Vol 43 (6) ◽  
pp. 1624a-1624a
Author(s):  
Yukikazu Itikawa ◽  
Takashi Ohmura ◽  
Kazuo Takayanagi
Keyword(s):  
Elastic Scattering ◽  
Helium Atoms ◽  
Slow Electrons

Calculation of Zeff for low-energy positron scattering by the hydrogen molecular ion

1996 ◽  
Vol 74 (7-8) ◽  
pp. 501-504 ◽  
Author(s):  
E. A. G. Armour ◽  
J. M. Carr
Keyword(s):  
Wave Function ◽  
Phase Shift ◽  
Variational Method ◽  
Partial Wave ◽  
Born Approximation ◽  
Low Energy ◽  
Positron Scattering ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Coulomb Phase

The Kohn variational method has recently been applied to the calculation of the addition to the Coulomb phase shift, in positron scattering, by the hydrogen molecular ion below the positronium-formation threshold at 9.45 eV. In this paper the wave function obtained for the lowest spheroidal partial wave of [Formula: see text] symmetry is used to calculate the contribution to Zeff from this symmetry. The results are significantly larger than those obtained using the Coulomb–Born approximation.

Singular-value decomposition method in atomic scattering

2003 ◽  
Vol 81 (10) ◽  
pp. 1215-1221 ◽  
Author(s):  
E Zerrad ◽  
A -S Khan ◽  
K Zerrad ◽  
G Rawitscher
Keyword(s):  
Wave Function ◽  
Phase Shift ◽  
Singular Value Decomposition ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Kernel ◽  
Singular Value ◽  
Singular Value Decomposition Method ◽  
Atomic Scattering ◽  
Value Decomposition

A new numerical method for solving the integro-differential equations that appear in the theory of atomic scattering is devised. It consists of decomposing the kernel into separable terms via the method of singular-value decomposition. A set of integro-differential equations involving the residual integral kernel are then solved to obtain the wave function and from this the phase shift is evaluated. PACS Nos.: 23.23.+x, 56.65.DY

scholarly journals On the Elastic Scattering of Slow Electrons by Helium Atoms

1963 ◽  
Vol 30 (6) ◽  
pp. 918-919 ◽  
Author(s):  
Tasuke Hashino ◽  
Hidehiko Matsuda
Keyword(s):  
Elastic Scattering ◽  
Helium Atoms ◽  
Slow Electrons

scholarly journals Resonance in the Elastic Scattering with Exchange of Slow Electrons by Helium Atoms

1969 ◽  
Vol 42 (5) ◽  
pp. 993-1002 ◽  
Author(s):  
Yukikazu Itikawa ◽  
Takashi Ohmura ◽  
Kazuo Takayanagi
Keyword(s):  
Elastic Scattering ◽  
Helium Atoms ◽  
Slow Electrons

Deep Impurities with Collision Delay

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Kinetic Equation ◽  
Elastic Scattering ◽  
Response Function ◽  
Plasma Oscillation ◽  
Impurity Scattering ◽  
Fermi Momentum ◽  
Screening Length ◽  
Plasma Mode ◽  
Dissipative Mechanism

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.

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