arXiv:physics/0011072 · Physical Review A

Ultracold collisions of metastable helium atoms

Paul J. Leo, V. Venturi, Ian B. Whittingham, J. F. Babb

Published Sep 13, 2001• 44 citations

Abstract

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.

DOI: 10.1103/physreva.64.042710

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arXiv:physics/0011072 · Physical Review A

Ultracold collisions of metastable helium atoms

Paul J. Leo, V. Venturi, Ian B. Whittingham, J. F. Babb

Published Sep 13, 2001• 44 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.64.042710

Related papers

Ultracold homonuclear and heteronuclear collisions in metastable helium

Daniel Cocks, Ian B. Whittingham, G. Peach

Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic $^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ and fermionic $^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}$ systems, and heteronuclear collisions of the mixed $^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic $^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ and fermionic $^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}$ systems, and heteronuclear collisions of the mixed $^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.

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Physical Review AMay 8, 200022 citations

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Scattering lengths for the collisions of ground and metastable state hydrogen atoms interacting via the B′1∑u +, EF 1∑g +, e3∑u + and h3∑g + molecular potentials are evaluated from published ab initio Born-Oppenheimer potentials with adiabatic corrections, matched to multipole expansions at large interatomic separations. It is demonstrated that the scattering lengths are very sensitive to the connections between the ab initio potentials and their asymptotic forms and the need is shown for accurate interatomic potential calculations at greater separations than are currently available. The density-dependent shift and broadening of the 1S–2S transition frequency in atomic hydrogen caused by two-body elastic collisions are presented.Scattering lengths for the collisions of ground and metastable state hydrogen atoms interacting via the B′1∑u +, EF 1∑g +, e3∑u + and h3∑g + molecular potentials are evaluated from published ab initio Born-Oppenheimer potentials with adiabatic corrections, matched to multipole expansions at large interatomic separations. It is demonstrated that the scattering lengths are very sensitive to the connections between the ab initio potentials and their asymptotic forms and the need is shown for accurate interatomic potential calculations at greater separations than are currently available. The density-dependent shift and broadening of the 1S–2S transition frequency in atomic hydrogen caused by two-body elastic collisions are presented.

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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

^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}

and fermionic

^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}

systems, and heteronuclear collisions of the mixed

^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}

system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.

We have observed a Bose-Einstein condensate in a dilute gas of

{}^{4}\mathrm{He}

in the

^{3}2S_{1}

metastable state. We find a critical temperature of $(4.7\ifmmode\pm\else\textpm\fi{}0.5)\ensuremath{\mu}\mathrm{K}$ and a typical number of atoms at the threshold of $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$. The maximum number of atoms in our condensate is about $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$. An approximate value for the scattering length $a\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(16\ifmmode\pm\else\textpm\fi{}8)\mathrm{nm}$ is measured. The mean elastic collision rate at threshold is then estimated to be about $2\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{s}}^{\ensuremath{-}1}$, indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is

2\mathrm{s}

, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.

Previous semiempirical determinations by Fitzsimmons et al. of the asymptotic form of the potentials

{V}_{g}

and

{V}_{u}

for the helium molecular states $^{3}\ensuremath{\Sigma}_{g,u}^{+}$ are refined to include new experimental data. The resulting potentials yield cross sections for elastic scattering, diffusion, and metastability exchange in $\mathrm{He}(2^{3}S_{1})\ensuremath{-}\mathrm{H}\mathrm{e}(1^{1}S_{0})$ collisions in agreement with various experiments from 15 to 500 \ifmmode^\circ\else\textdegree\fi{}K.

5000 {\mathrm{\AA{}}}^{2}.

Effect of shape resonances that form in the potential barriers, on the cross sections is investigated. We find that some shape resonances live for longer than 100 s. Long-range potential wells could support ``shelf'' levels. We discuss their collisional and spectroscopic properties.