Physical Review A

Ramsauer-Townsend effect for electron scattering from gaseous CF4 molecules

Franco Antonio Gianturco, K. Willner

Published Jun 27, 2007• 10 citations

Abstract

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.

DOI: 10.1103/physreva.75.062714

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Physical Review A

Ramsauer-Townsend effect for electron scattering from gaseous CF4 molecules

Franco Antonio Gianturco, K. Willner

Published Jun 27, 2007• 10 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.75.062714

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Yi Zhang, M.-S. Wu, Ying Qian +2 more

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

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Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.

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Positronium-atom scattering at low energies

I. I. Fabrikant, G. F. Gribakin

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 $v<1$ 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.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 $v<1$ 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.

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

{\mathrm{CF}}_{4}

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.

The numerical approach to calculating the

S

-matrix poles associated with virtual states in electron-molecule collisions is proposed within the modified effective-range theory frame. The

S

-matrix continuation into the complex momentum plane is possible thanks to the analytical properties of modified Mathieu functions, that is, the exact solutions of the Schr\"odinger equation with the long-range polarization potential ($\ensuremath{\sim}{r}^{\ensuremath{-}4}$). The short-range electron-molecule interaction is included in the introduced numerical approach by model comparison with experimental integral, differential, and momentum-transfer elastic cross sections. The influence of the polarization potential on the virtual-state pole positions is analyzed for nonpolar targets such as

{\mathrm{N}}_{2}, {\mathrm{CH}}_{4}, {\mathrm{CO}}_{2}

, and

{\mathrm{SF}}_{6}

. The relation between the

S

-matrix pole position and the

s

-wave scattering length is discussed.

v<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.