Calculation of the scattering length in atomic collisions using the semiclassical approximation

Journal Article · Thu Jul 01 00:00:00 EDT 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.48.546· OSTI ID:6429850

Gribakin, G F; Flambaum, V V ^[1]

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1. School of Physics, University of New South Wales, Kensington, New South Wales 2033 (Australia)

A simple analytical formula, [ital a]=[ital [bar a]][1[minus]tan([pi]/[ital n][minus]2)]tan[l brace][Phi][minus][[pi]/2([ital n][minus]2)][r brace], is obtained for the scattering length in atomic collisions. Here [ital [bar a]]=cos[[pi]/([ital n][minus]2)][l brace] [radical]2[ital M][alpha] /[[h bar]([ital n][minus]2)][r brace][sup 2]/([ital n][minus]2)[[Gamma]([ital n][minus]3)/([ital n][minus]2)]/[[ital T]([ital n][minus]1)/([ital n][minus]2)] is the mean scattering length determined by the asymptotic behavior of the potential [ital U]([ital r])[similar to][minus][alpha]/[ital R][sup [ital n]], ([ital n]=6 for atom-atom scattering or [ital n]=4 for ion-atom scattering), [ital M] is the reduced mass of the atoms, and [Phi] is the semiclassical phase calculated at zero energy from the classical turning point to infinity. The value of [ital [bar a]], the average scattering length, also determines the slope of the [ital s]-wave phase shifts beyond the near-threshold region. The formula is applicable to the collisions of atoms cooled down in traps, where the scattering length determines the character of the atom-atom interaction. Our calculation shows that repulsion between atoms ([ital a][gt]0) is more likely than attraction with a probability'' of 75%. For the Cs-Cs scattering in the [sup 3][Sigma][sub [ital u]] state, [ital [bar a]]=95.5[ital a][sub [ital B]] has been obtained, where [ital a][sub [ital B]] is the Bohr radius. The comparison of the calculated cross-section energy dependence with the experimental data gives evidence for a positive value for the Cs-Cs scattering length, which makes cesium Bose gas stable.

• OSTI ID: 6429850
• Journal Information: Physical Review A; (United States), Vol. 48:1; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOM-ATOM COLLISIONS
SCATTERING LENGTHS
ION-ATOM COLLISIONS
CESIUM
COOLING
ELASTIC SCATTERING
PHASE SHIFT
S WAVES
SEMICLASSICAL APPROXIMATION
TRAPPING
ALKALI METALS
ATOM COLLISIONS
COLLISIONS
DIMENSIONS
ELEMENTS
ION COLLISIONS
LENGTH
METALS
PARTIAL WAVES
SCATTERING
664300* - Atomic & Molecular Physics- Collision Phenomena- (1992-)