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arXiv:1208.1660 · Gravitation and Cosmology

Generalized uncertainty principle and the Ramsauer-Townsend effect

Javad Vahedi, Kourosh Nozari, Pouria Pedram

Published Jul 1, 2012• 37 citations
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Abstract

The scattering cross-section of electrons in noble gas atoms exhibits a minimum value at electron energies of approximately 1 eV. This is the Ramsauer-Townsend effect. In this letter, we study the Ramsauer-Townsend effect in the framework of the Generalized Uncertainty Principle.
DOI
10.1134/s0202289312030097

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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.
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.
Quantum scattering calculations are carried out down to very low energy for collisions of electrons with CF4{\mathrm{CF}}_{4}CF4​ 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.
A pseudopotential for positronium-atom interaction, based on electron-atom and positron-atom phase shifts, is constructed, and the phase shifts for Ps-Kr and Ps-Ar scattering are calculated. This approach allows us to extend the Ps-atom cross sections, obtained previously in the impulse approximation [I. I. Fabrikant and G. F. Gribakin, Phys. Rev. Lett. 112, 243201 (2014)], to energies below the Ps ionization threshold. Although experimental data are not available in this low-energy region, our results describe well the tendency of the measured cross sections to drop with decreasing velocity at v<1v<1v<1 a.u. Our results show that the effect of the Ps-atom van der Waals interaction is weak compared to the polarization interaction in electron-atom and positron-atom scattering. As a result, the Ps scattering length for both Ar and Kr is positive, and the Ramsauer-Townsend minimum is not observed for Ps scattering from these targets. This makes Ps scattering quite different from electron scattering in the low-energy region, in contrast to the intermediate energy range from the Ps ionization threshold up to $v\ensuremath{\sim}2$ a.u., where the two are similar.