A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

Fedus, Kamil

doi:10.1140/epjd/e2016-70452-6

Cited by 8 publications

(8 citation statements)

References 79 publications

(197 reference statements)

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“…above few eV) would correspond to geometrical dimensions of molecules. This concept was further exploited by Franz, Fedus and Karwasz [29]; then Fedus [30] and independently, Franz [31] showed that flat TCS is caused by trapping positrons in some effective positron-molecule interaction potential, with a quantum well at about the "geometrical dimensions" distance. Zammit et al [32] and Gribakin [33] in ab initio calculations for molecular hydrogen and noble gases, respectively, reproduced such flat parts of TCS by introducing inelastic channels, including formation of virtual positronium.…”

Section: Resultsmentioning

confidence: 99%

Positronium Formation in Molecular Gases --- from Experiment to Modeling

Karbowski¹,

Fedus²,

Karwasz³

2017

Acta Phys. Pol. B

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Results of positron annihilation lifetime measurements of three organic liquids: benzene (C 6 H 6), cyclohexane (C 6 H 12) and methanol (CH 3 OH) are reported. The lifetime spectra are acquired at several temperatures for non-degassed, degassed and oxygen-saturated samples. The influence of oxygen on each lifetime and intensity component is discussed. Comparison of lifetime components with experiments in gas phase is done.

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Section: Resultsmentioning

confidence: 99%

Positronium Formation in Molecular Gases --- from Experiment to Modeling

Karbowski¹,

Fedus²,

Karwasz³

2017

Acta Phys. Pol. B

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“…where r 0 is the radius of rigid sphere. Since the radial Schrödinger equation for the potential V(r) can be solved exactly using Mathieu functions, we showed in reference [27] that the expression for the scattering phase-shift of l th partial wave takes a following form:…”

Section: Rigid Sphere Approachmentioning

confidence: 99%

“…where m l , ν l and δ l are the same parameters as in Equation ( 4). Energy-dependent parameter C l (k) can be determined from the continuity conditions imposed on the Mathieu functions at r = r 0 (see [27] for more details). The only adjustable parameter is r 0 , the radius of the rigid sphere.…”

Section: Rigid Sphere Approachmentioning

confidence: 99%

“…In [27], we showed that an even simpler semi-empirical model than MERT could describe very low-energy positron (antielectron) interaction with noble gases, namely the rigid sphere approach. In this model, the interaction is described as a combination of an infinitive wall (hard-sphere) and the long-range polarization potential (∼r −4 ).…”

Section: Introductionmentioning

confidence: 99%

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Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

Fedus

2021

Atoms

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We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.

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“…In the rigid sphere model A s = R which means that the term (1/R − 1/A s ) measures, in a given sense, how the semiempirical model used here departures from the ideal rigid sphere model. In particular, Fedus developed a simple model for positron scattering by atoms and molecules using this approach [41]. In Fig.…”

Section: Phase Shifts Polarization and The Low-energy Elastic Integmentioning

confidence: 99%

The Hidden Ramsauer-Townsend Effect in Positron Scattering by Rare Gas Atoms

et al. 2020

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The aim of this work is to present and discuss the Ramsauer-Townsend effect in the context of low-energy positron scattering by rare gas atoms. Opposed to what happens in electron-atom scattering, the competition between the static repulsive and polarization attractive potentials makes the phenomenon improbable in positron case. Nonetheless, we show using a semiempirical potential formulation that, while the effect is explicitly observed in the total cross sections for He and Ne, for the heavier noble gases it becomes "hidden" or implicit. We show that as the atomic polarizability increases, the suppression of s-wave goes to higher energies due to the variation of the scattering length with the polarizability. No specific signature for the effect is found in the shape of the differential cross sections but curiously, while the effect is implicit in the total cross section for Ar, it generates a minimum structure in the momentum transfer cross section. The theme is presented for non-specialist audience with emphasis in basic atomic and scattering theories along with practical results, the main objective being to boost the traditional discussions with a new view on the subject.

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A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

Cited by 8 publications

References 79 publications

Positronium Formation in Molecular Gases --- from Experiment to Modeling

Positronium Formation in Molecular Gases --- from Experiment to Modeling

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

The Hidden Ramsauer-Townsend Effect in Positron Scattering by Rare Gas Atoms

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