Acta Physica Polonica A

The Ramsauer-Townsend Effect in the Presence of the Minimal Length and Maximal Momentum

Javad Vahedi, Kourosh Nozari

Published Jul 1, 2012• 9 citations

Abstract

The scattering cross-section of electrons in noble gas atoms exhibits the minimum value at electron energies of approximately 1 eV.This is the RamsauerTownsend eect.In this letter, we study the RamsauerTownsend eect in the presence of both the minimal observable length and the maximal momentum (originating from doubly special theories) through the generalized uncertainty principle.

DOI: 10.12693/aphyspola.122.38

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Generalized uncertainty principle and the Ramsauer-Townsend effect

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In this work we study the Ramsauer-Townsend effect.First, we use the Quantum Mechanical Formalism of Schrodinger. After, it is calculated with the Quantum Mechanical Formalism of de Broglie-Bohm. In this case, we use the Kostin equation, taking into account the energy dissipation of the electrons scattered by sharp edged potential wells.

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Acta Physica Polonica A

The Ramsauer-Townsend Effect in the Presence of the Minimal Length and Maximal Momentum

Javad Vahedi, Kourosh Nozari

Published Jul 1, 2012• 9 citations

Publisher

Abstract

DOI: 10.12693/aphyspola.122.38

Related papers

Generalized uncertainty principle and the Ramsauer-Townsend effect

Javad Vahedi, Kourosh Nozari, Pouria Pedram

arXiv:1208.1660Gravitation and CosmologyJul 1, 201237 citations

Scattering of low-energy electrons and positrons by atomic beryllium: Ramsauer–Townsend effect

David D. Reid, J. M. Wadehra

Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer–Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a 0 2 at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of −0.61 a 0 for electron and a 0 for positron scattering.Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer–Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a 0 2 at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of −0.61 a 0 for electron and a 0 for positron scattering.

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The Ramsauer effect does not correspond to the decrease in optical scattering by a particle when the wave-length of the light is increased. For one may compute the cross-section for elastic collision of an electron with an atom, without making the approximations used by Born. If one does this, and neglects the resonance of the colliding electron with the atomic electrons one finds that, for atoms with no dipole moment in the normal state, the cross-section approaches a finite limit when the electronic velocity is decreased. The only general result of this calculation is that the distribution of scattered electrons tends, in this limit, to become uniform over all angles.The Ramsauer effect does not correspond to the decrease in optical scattering by a particle when the wave-length of the light is increased. For one may compute the cross-section for elastic collision of an electron with an atom, without making the approximations used by Born. If one does this, and neglects the resonance of the colliding electron with the atomic electrons one finds that, for atoms with no dipole moment in the normal state, the cross-section approaches a finite limit when the electronic velocity is decreased. The only general result of this calculation is that the distribution of scattered electrons tends, in this limit, to become uniform over all angles.

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Low-energy properties of spin-polarized electron-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ and spin-polarized positronium-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that $\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the $S$ -wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.Low-energy properties of spin-polarized electron-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ and spin-polarized positronium-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that $\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the $S$-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium$(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.

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Ramsauer-Townsend effect for electron scattering from gaseous CF4 molecules

Franco Antonio Gianturco, K. Willner

Quantum scattering calculations are carried out down to very low energy for collisions of electrons with ${\mathrm{CF}}_{4}$ molecules in the gas phase. The interaction forces are obtained from ab initio data for the static interaction and through model potentials for the exchange and correlation-polarization effects. A numerical analysis is performed to evaluate the partial wave convergence behavior over the whole energy range, to assess the reliability of modified effective range theory close to zero energy, and to extract the value and the sign of the scattering length. A comparison with experiments and earlier calculations in the low-energy domain is also presented.Quantum scattering calculations are carried out down to very low energy for collisions of electrons with ${\mathrm{CF}}_{4}$ molecules in the gas phase. The interaction forces are obtained from ab initio data for the static interaction and through model potentials for the exchange and correlation-polarization effects. A numerical analysis is performed to evaluate the partial wave convergence behavior over the whole energy range, to assess the reliability of modified effective range theory close to zero energy, and to extract the value and the sign of the scattering length. A comparison with experiments and earlier calculations in the low-energy domain is also presented.

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arXiv:0904.1216Apr 7, 20090 citations

Low-energy properties of spin-polarized electron-helium

(2\phantom{\rule{0.16em}{0ex}}^{3}S)

and spin-polarized positronium-helium

(2\phantom{\rule{0.16em}{0ex}}^{3}S)

scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium

(2\phantom{\rule{0.16em}{0ex}}^{3}S)

is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that

\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)

may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the

S

-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium

(2\phantom{\rule{0.16em}{0ex}}^{3}S)

scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.

Quantum scattering calculations are carried out down to very low energy for collisions of electrons with

{\mathrm{CF}}_{4}

molecules in the gas phase. The interaction forces are obtained from ab initio data for the static interaction and through model potentials for the exchange and correlation-polarization effects. A numerical analysis is performed to evaluate the partial wave convergence behavior over the whole energy range, to assess the reliability of modified effective range theory close to zero energy, and to extract the value and the sign of the scattering length. A comparison with experiments and earlier calculations in the low-energy domain is also presented.