Analytical Representation of Hartree Potentials and Electron Scattering

Byatt, W.J.

doi:10.1103/physrev.104.1298

Cited by 71 publications

(13 citation statements)

References 8 publications

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“…(17), is much simpler for practical calculations than equ. (6). Table II shows that our results for ~t agree quite well with the exact McDouGALL [13] values.…”

supporting

confidence: 78%

“…The interaction potential V(r) based on the THOMAs--FERMI or HAaTREV. scheme [6] may be written Tabulated numerŸ values of the quantity Zp/Z exist for a number of atoms and ions. RVAUK [7], BYATŸ [8], ROZENTAL [9] and MOLIi~RE [10] have shown that Zp/Z can be represented analytically as follows:…”

mentioning

confidence: 99%

“…Equ. (6) in our case can be presented analytically, but the phases fulfil a transcendental equation of infinite order. Our formula, equ.…”

mentioning

confidence: 99%

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Pais approximate formula for the phase shift and electron scattering in the Thomas-Fermi theory

Tietz

1963

Acta Physica

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In this paper we calculate the phase shifts by means of a simplified PAxs method los the THOMAS-FEaMI and analytical HAaTRE~ potentials. The calculation presented in thir paper shows that our method gives more accurate results for the phase shifts than the BoRN approximation, having moreover the advantage that it is much more practical than the P~~s method. For the scattering of electrons by a central ficld, the scattering amplitude f(O), as known, is given by the following FAXE~--HOLTZMA~tK formula [1]: 1 ~ (2/ § 1) (e 2'~~-1) P~(cos ~) = f(vq)-2ik l=0 [2 / --1 ~Ÿ 6l----3--d~-+-...+i O~--k l~0 31 ~~+ )]P,(cos9)The usual first BORN approximation for the phase shift ~~1) is obtained ir 91 small; as is knowtl the formar has the forro [2] y~m ; 2 @) --~~ V(r / Jl+~ (kr) r dr ,O where Jt+ 89 (kr) denotes the Bessel function characterizing the free particle solutions. The BORN approximation for the phase shifts for small quantum number l does not give adequate numerical values. Therefore PAis [3] gave another method for the dctermination of the phase shifts al. The PAIS method consists in the following. We write the radial wave equation in the form d2w! ~_[k2__ l(l-~1)--c2

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“…(17), is much simpler for practical calculations than equ. (6). Table II shows that our results for ~t agree quite well with the exact McDouGALL [13] values.…”

supporting

confidence: 78%

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confidence: 99%

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Pais approximate formula for the phase shift and electron scattering in the Thomas-Fermi theory

Tietz

1963

Acta Physica

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“…It was calculated by the partial wave method (the necessary calculations are described e.g. by Lin [8,9]) using a screened atomic potential [10].…”

Section: A Use Of Reference Methodsmentioning

confidence: 99%

Measurement of the absolute cross section for the elementary process of atomic field bremsstrahlung

1977

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Coincidence measurements of the absolute cross section for the production of bremsstrahlung by electrons in the field of gold atoms are reported. The incident electron energy T o was 300keV. Measurements were made for four different combinations of electron scattering angle and photon emission angle over a wide range of the relative photon energy kiT o up to k/To=0.83. The measured cross sections are compared with results of Bethe-Heitler and Elwert-Haug calculations

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“…Using BYATT'S [3] fits for the HAIITREE field as well as approximations for the TnOMAS--FERMI functions and the theory of electron scattering we shall discuss the scattering of polarized electrons by atoms in a relativistic case. To discuss the polarization of electrons by double scattering we use the DIRAC theory for elastic scattering of electrons by atoms.…”

Section: Introductionmentioning

confidence: 99%

The scattering and polarization of electrons by Hartree and Thomas-Fermi atoms

Tietz

1963

Acta Physica

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Using the analytical fits for the effective nuclear charge and the theory of scattering of a beato of particles by a centre of force in the relativistic case, we discuss the asymmetry in double scattering. We have presented the theory in such a simple manner that the asymmetry in double scattering can be calculated without any difficulty in an analytical way. "Yhis paper gives a generalization of the paper of MOHR and TASSIE.

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Analytical Representation of Hartree Potentials and Electron Scattering

Cited by 71 publications

References 8 publications

Pais approximate formula for the phase shift and electron scattering in the Thomas-Fermi theory

Pais approximate formula for the phase shift and electron scattering in the Thomas-Fermi theory

Measurement of the absolute cross section for the elementary process of atomic field bremsstrahlung

The scattering and polarization of electrons by Hartree and Thomas-Fermi atoms

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