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arXiv:physics/0209052

Dipolar relaxation of cold sodium atoms in a magnetic field

Bernard Zygelman

Published Sep 12, 2002• 0 citations
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Abstract

A quantum mechanical close coupling theory of spin relaxation in the stretched hyperfine level of sodium is presented. We calculate the dipolar relaxation rate of magnetically trapped cold sodium atoms in the magnetic field. The influence of shape resonances and the anisotropy of the dipolar interaction on the collision dynamics are explored. We examine the sensitivity of the calculated cross sections on the choice of asymptotic atomic state basis.

DOI
10.48550/arxiv.physics/0209052

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We perform rigorous quantum mechanical calculations for collisions between magnetically trapped Eu atoms to elucidate the results of recent experimental studies. We show that the relaxation from the maximally stretched ms=7/2{m}_{s}=7/2ms​=7/2 level is entirely determined by the magnetic dipole-dipole interaction and analyze the role of the electronic spin-exchange interaction in transitions from the lower-energy Zeeman levels. The relaxation of the ms=5/2{m}_{s}=5/2ms​=5/2 state is shown to be very sensitive to the spin-exchange parameter that determines the splitting between the lowest electronic states of the Eu dimer. We suggest that cold collision experiments with trapped atoms can be used as a tool for obtaining accurate information on the electronic spin anisotropy in complex molecules such as Eu2{}_{2}2​.
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The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
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We study hyperfine transitions in collisions between cold ground-state 23Na^{23}\mathrm{Na}23Na atoms, which are of crucial importance for the decay of the atomic density in magnetic traps. For comparable densities we find the initial decay by exchange collisions to be roughly a factor of 10 more rapid than that in atomic hydrogen. The doubly polarized atomic gas that thus forms spontaneously in this initial process subsequently decays by dipolar relaxation with a rate that is about a factor of 5 larger than that in atomic hydrogen. The sensitivity of the calculated rate constants associated with uncertainties in the singlet and triplet potentials is discussed.