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 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 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%.

The elastic scattering of slow electrons by neon and argon

1966 ◽  
Vol 294 (1437) ◽  
pp. 160-174 ◽  
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Energy Range ◽  
Orbital Method ◽  
Polarization Effects ◽  
Polarization Contribution ◽  
Slow Electrons ◽  
Good Agreement

The theory of the scattering of electrons by neon and argon in the energy range 0 to 13.6 eV is worked out with allowance for both exchange and polarization effects. The polarized orbital method introduced by Temkin has been used to estimate the polarization contribution and good agreement is obtained with the experimental data, right down to the lowest energies. Inclusion of exchange alone is not sufficient.

The Elastic Scattering of Slow Electrons by Hydrogen Atoms

1958 ◽  
Vol 71 (6) ◽  
pp. 877-892 ◽  
Author(s):  
B H Bransden ◽  
A Dalgarno ◽  
T L John ◽  
M J Seaton
Keyword(s):  
Elastic Scattering ◽  
Hydrogen Atoms ◽  
Slow Electrons

The elastic scattering of neutrons by deuterons with allowance for polarization

1959 ◽  
Vol 252 (1269) ◽  
pp. 177-186 ◽  
Keyword(s):  
Wave Function ◽  
Elastic Scattering ◽  
Ground State ◽  
Trial Function ◽  
Ground State Wave Function ◽  
Low Energy ◽  
Radial Dependence ◽  
Exchange Force ◽  
Polarization Effects ◽  
Scattering Lengths

Previous calculations of the elastic scattering of low energy (< 10 MeV) neutrons by deuterons have shown a discrepancy between the calculated and observed doublet scattering lengths. It has been suggested that this may be partly due to the neglect of polarization of the deuterons and the present paper attempts to make an allowance for this effect. The problem is formulated in a variational manner and a trial function is adopted which includes an explicit polarization parameter. The internucleonic interaction is assumed to be central with Gauss radial dependence and the unperturbed deuteron ground state wave-function is represented by two Gauss terms. Using the Kohn method and taking an M. H. W. B. type exchange force, S phases were evaluated on DEUCE and compared with the non-polarization results of Burke & Robertson (1957). Polarization effects in this approximation are found to be negligible.

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.

Elastic scattering of slow electrons from Ar and Kr atoms

1983 ◽  
Vol 16 (10) ◽  
pp. 1819-1825 ◽  
Author(s):  
F Kemper ◽  
B Awe ◽  
F Rosicky ◽  
R Feder
Keyword(s):  
Elastic Scattering ◽  
Slow Electrons

The elastic scattering of fast electrons and positrons by hydrogen and helium atoms

1959 ◽  
Vol 250 (1262) ◽  
pp. 337-345 ◽  
Keyword(s):  
Elastic Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Born Approximation ◽  
Logarithmic Singularity ◽  
Hydrogen Atoms ◽  
Fast Electrons ◽  
Helium Atoms ◽  
Electrons And Positrons ◽  
Angle Scattering

A simplification of the second Born approximation due to Massey & Mohr is used to calculate the differential cross-sections for the elastic scattering of fast electrons and fast positrons by hydrogen atoms and helium atoms, the method of Dalitz being applied to evaluate all the relevant integrals. Although the logarithmic singularity which is found in the differential cross-section for zero-angle scattering is shown to be absent in the true second Born approximation the use of the simplification of this approximation is justified at sufficiently high impact energies provided the angle of scattering is not too small. The results of the calculations for incident electrons in helium are compared with the available experimental data.

Sign in / Sign up

Export Citation Format

Share Document