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Screening of a Positron in An Inhomogeneous Electron Gas

100%
Stachowiak H.
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vol. 95
|
issue 4
663-670
EN
Calculations of the local annihilation rate of positrons in inhomogeneous media have been recently performed. However, the problem was solved only for the positron at the center of the inhomogeneity. This allowed to benefit of the spherical symmetry of the problem. Since the positron is usually an itinerant particle, it is necessary in practical applications to perform computations for every possible coordinates of this particle. In the present work local annihilation rates were obtained for noncentral coordinates of the positron.
2
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Electron-Positron Interaction in Jellium: Modification of the Perturbed Hypernetted-Chain Approach

63%
Stachowiak H., Boroński E.
Acta Physica Polonica A
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2008
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vol. 113
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issue 5
1523-1532
EN
The approach of Kahana to the electron-positron interaction in an electron gas contains the superfluous assumption that electron scattering on the positron can occur only to momentum states lying outside the Fermi sphere. The perturbed hypernetted-chain approach avoids that assumption, but self-consistency was achieved only in the Born approximation. In the present work a modification of perturbed hypernetted-chain approach allowed to reach self-consistency also at the Kohn-Sham level, at least for 1 ≤ r_s ≤ 3.5. The electron-positron correlation functions obtained in this way are compared to figures resulting from other approaches.
3
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Electron-Positron Interaction in Jellium: Optimization of the Perturbed Hypernetted-Chain Approach

63%
Stachowiak H., Boroński E.
Acta Physica Polonica A
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2006
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vol. 110
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issue 5
709-720
EN
The perturbed hypernetted-chain approach to electron-positron interaction in jellium consists in assuming the wave function of the system in the form of a Slater determinant built of single-electron functions presented asψi k(s)=w(s)φ_i k(s). s is the distance between the electron and the positron. The function w(s) is obtained by solving the equation of Gondzik and Stachowiak. The functionφ_{i k}(s) is computed by applying a self-consistent Born approximation. The idea of the paper is to modify the function w(s) in such a way as to obtain from the Born approximation as precise results as possible. It is shown that the influence of such modifications on physical predictions is small. This shows how good is the perturbed hypernetted-chain approach. The annihilation rates obtained in such a way decrease somewhat, becoming closer to experimental expectations.
4
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Electron-Positron Interaction in Metals. Theory and Experiment

63%
Stachowiak H., Boroński E.
|
EN
The electron-positron interaction greatly complicates the interpretation of positron annihilation data. The two-detector Doppler measurements of Mijnarends et al. as well as our theoretical calculations point at the conclusion that the local density approximation to e^+-e^- interaction is a good way of treating this problem in real metals, at least the simplest ones. This shows that e^+-e^- interaction in an electron gas is the key to understanding this phenomenon also in inhomogeneous systems. On the basis of dozens of experiments one comes to the conclusion that the well known formula of Boroński and Nieminen for the electron accumulation on the positron in jellium describes the best the positron lifetimes in metals. However, it is based on the calculations of Lantto which start from a physically oversimplified trial function. The results of Arponen and Pajanne, of Rubaszek and Stachowiak, and of Stachowiak and Lach lead to too short positron lifetimes in spite of using less controversial assumptions. The discrepancy is of the order of 8 to 15% for r_s=2. This shows that we still do not fully understand e^+-e^- interaction even in an electron gas.
5
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Enhancement Factors for Electrons in Solids for Some Simple Cases

51%
Stachowiak H., Boroński E., Banach G.
Acta Physica Polonica A
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2001
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vol. 99
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issue 3-4
503-513
EN
The approach to e^+-e^- interaction in jellium proposed by Gondzik and Stachowiak proved to be simple numerically and leading to reasonable results. This is why it seemed to be particularly suited for generalizations to real solids, a problem that in spite of more than thirty years of research in this direction did not get yet a satisfactory solution. An obstacle up to now was the necessity to solve integro-differential equations in two dimensions. After overcoming this difficulty we were able to compute e^+-e^- enhancement for core and valence electrons in lithium and for core electrons in other two-electron core elements. Properties of the electronic cloud screening the positron are investigated for different coordinates of this particle. The results are compared to such simplifying guesses concerning this problem as the local density, the generalized gradient and the weighted density approximations.
6
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Electroni-Positron Scattering in Real Metals

51%
Boroński E., Daniuk S., Stachowiak H.
Acta Physica Polonica A
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1993
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vol. 83
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issue 3
255-260
EN
The purpose of the paper is to point at the importance of some detailed studies of electron-positron scattering in real metals using wave functions obtained from band structure calculations. In this work some preliminary investigations of the matrix elements of electron-positron scattering, e.g. the transitions from occupied to non-occupied states close to the Fermi surface are presented. One can observe that for s → s transitions of the positron (s, p are orbital quantum numbers) electrons do not change their orbital quantum numbers but for s → p transitions of the positron, electron quantum numbers change by unity.
7
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The Effective Electron-Positron Potential in Jellium

51%
Stachowiak H., Boroński E., Lach J.
Acta Physica Polonica A
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1993
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vol. 83
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issue 3
391-394
EN
One of the methods of determining theoretical annihilation characteristics in real metals is the approximation called Bloch modified ladder approach. In this approach a Bethe-Goldstone type equation is solved with an effective electron-positron potential obtained previously for jellium of the corresponding electron density. If one wishes to include the dependence on the local electron density of the e^{+}-e^{-} effective potential in this formalism, it is necessary to know this potential for jellium, for metallic and above metallic densities. A review of different proposed e^{+}-e^{-} potentials is presented and their correctness is evaluated from the point of view of their application in a Bethe-Goldstone type formalism which is the jellium analogue of Bloch modified ladder approach.
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