We report scattering lengths for the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+},$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ adiabatic molecular potentials relevant to collisions of two metastable $2{}^{3}S$ helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.We report scattering lengths for the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+},$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ adiabatic molecular potentials relevant to collisions of two metastable $2{}^{3}S$ helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.

arXiv:physics/0011072Physical Review ASep 13, 200144 citations

Short-range physics of the three-body recombination for ultracold helium atoms

Binbin Wang, Yong‐Chang Han

Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length $a$ of the He-He interaction and a three-body parameter ${a}_{*}$ as input, where ${a}_{*}$ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to $1/{a}_{*}$ versus $1/a$ should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational $1/{a}_{*}$ versus $1/a$ to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum $J>0$ are also discussed.Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length $a$ of the He-He interaction and a three-body parameter ${a}_{*}$ as input, where ${a}_{*}$ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to $1/{a}_{*}$ versus $1/a$ should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational $1/{a}_{*}$ versus $1/a$ to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum $J>0$ are also discussed.

Physical Review ADec 6, 20231 citation

Collisions of ultra-cold helium* atoms

Arend Niehaus, P. van der Straten, G.R. Woestenenk

Sep 1, 19960 citations

Scattering lengths and low-energy cross sections for Na-He collisions

Chih-Yuan Lin, Phillip C. Stancil, Heinz–Peter Liebermann +2 more

Bulletin of the American Physical SocietyMay 18, 20060 citations

2{}^{3}S

helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.

a

of the He-He interaction and a three-body parameter

{a}_{*}

as input, where

{a}_{*}

is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to

1/{a}_{*}

versus

1/a

should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational

1/{a}_{*}

versus

1/a

to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum

J>0

are also discussed.