Physical Review A

Low-velocity elastic scattering of Rb-Rb

P. Westphal, S. Koch, A. Horn, J. Schmand, H. J. Andrä

Published Oct 1, 1997• 4 citations

Abstract

With reference to recent progress in preparing slow and intense Rb beams (rubidium atomic funnel and low-velocity intense source of atoms from a magneto-optical trap) we have calculated total and differential elastic scattering cross sections and scattering lengths for ground-state collisions of ${}^{85}$Rb as well as ${}^{87}$Rb. Our results are based on the state of the art ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potentials. Pronounced resonances in the total scattering cross sections occur for collision velocities below 15 m/s. We propose scattering experiments with slow Rb beams in order to check the currently known singlet and triplet potential-energy curves.

DOI: 10.1103/physreva.56.2784

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Physical Review A

Low-velocity elastic scattering of Rb-Rb

P. Westphal, S. Koch, A. Horn, J. Schmand, H. J. Andrä

Published Oct 1, 1997• 4 citations

Publisher

Abstract

{}^{85}

Rb as well as

{}^{87}

Rb. Our results are based on the state of the art

{X}^{1}{\ensuremath{\Sigma}}_{g}^{+}

and

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

potentials. Pronounced resonances in the total scattering cross sections occur for collision velocities below 15 m/s. We propose scattering experiments with slow Rb beams in order to check the currently known singlet and triplet potential-energy curves.

DOI: 10.1103/physreva.56.2784

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Elastic scattering of hydrogen atoms at low temperatures

Michael J. Jamieson, A. Dalgarno, John N. Yukich

The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of ${\mathrm{H}}_{2}$ . The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41 ${\mathit{a}}_{0}$ for the singlet case and 1.91 ${\mathit{a}}_{0}$ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ , with a different fit to the triplet potential between 12 ${\mathit{a}}_{0}$ and 15 ${\mathit{a}}_{0}$ . A more accurate triplet-state potential is needed at these separations.The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of ${\mathrm{H}}_{2}$. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41${\mathit{a}}_{0}$ for the singlet case and 1.91${\mathit{a}}_{0}$ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$, with a different fit to the triplet potential between 12${\mathit{a}}_{0}$ and 15${\mathit{a}}_{0}$. A more accurate triplet-state potential is needed at these separations.

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Michael D. Higgins, K. M. Daily, Chris H. Greene

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Information on the Σ+1 and Σ+3 Potentials of NaCs from Total Scattering Cross-Section Measurements

W. Neumann, H. Pauly

Physical Review LettersFeb 19, 196816 citations

{}^{85}

Rb as well as

{}^{87}

Rb. Our results are based on the state of the art

{X}^{1}{\ensuremath{\Sigma}}_{g}^{+}

and

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

{\mathrm{H}}_{2}

. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41

{\mathit{a}}_{0}

for the singlet case and 1.91

{\mathit{a}}_{0}

for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$

{\mathrm{cm}}^{2}

but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$

{\mathrm{cm}}^{2}

, with a different fit to the triplet potential between 12

{\mathit{a}}_{0}

and 15

{\mathit{a}}_{0}

. A more accurate triplet-state potential is needed at these separations.

R

-matrix method [Thumm and Norcross, Phys. Rev. A 45, 6349 (1992)]. For incident electrons of up to 2.8 eV kinetic energy, we compare a

{}^{3}{P}^{o}

shape resonance and

{}^{3}{P}^{e},

{}^{1}{P}_{1}^{o},

and

{}^{1}{D}_{2}^{o}

Feshbach resonances, located below the first excitation threshold of the atomic target in the low-lying spectra of the ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ negative ions, with available experimental data and other calculations. We provide the resonance parameters, partial and converged total elastic and inelastic scattering cross sections, and discuss the relative importance of relativistic effects for the three heavy-alkali-metal targets.

Low-energy elastic and inelastic scattering in the Ps(

1s

)-Ps(

2s

) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum

L=0

and parity equal to

+1

. The

s

-wave scattering lengths for the asymptotic Ps(

1s

)-Ps(

2s

) channel are calculated for each spin configuration. Results obtained for the

s

-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and

{a}_{\mathrm{ST}}=9.7(2){a}_{0}

for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.