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
23S 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 investigate the relation between the thermalization cross section ${⟨\ensuremath{\sigma}⟩}_{T}$ and the scattering length
a of spin-polarized metastable neon
(Ne∗) in the Doppler-limited temperature regime. We show that a temperature-dependent, quantum-mechanical, five-channel calculation allows one to obtain
a consistent with the mass scaling rule between
20Ne∗ and
22Ne∗ from recent data of ${⟨\ensuremath{\sigma}⟩}_{T}$ by Spoden et al. [Phys. Rev. Lett. 94, 223201 (2005)]. We find $a=+{24}_{\ensuremath{-}5}^{+5}{a}_{0}$ or $a=\ensuremath{-}{128}_{\ensuremath{-}22}^{+16}{a}_{0}$ for
20Ne∗ and $+115\ensuremath{\lesssim}a\ensuremath{\lesssim}+160{a}_{0}$ for
22Ne∗, respectively. According to numerical simulations of the evaporative cooling process, these values of
a are not large enough to make Bose-Einstein condensation of
Ne∗ feasible for realistic experimental conditions, given the measured ionization rate constants.
Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the ``slow'' evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.
We discuss the kinetic theory for evaporative cooling of a dilute collisional gas in a trap. The analysis in O. J. Luiten et al., Phys. Rev. A 53, 381 (1996) is extended to incorporate a time-dependent trap strength and truncation energy. We employ the equations obtained to predict the efficiency of evaporative cooling of sodium atoms in a Ioffe trap and realize that a time-dependent trap strength can be crucial for the cooling. The calculations are classical in the sense that no effects of quantum statistics are taken into account: nevertheless the results of the calculations are useful in order to reveal experimental routes towards a Bose-Einstein condensate of sodium atoms.
We report an experiment measuring simultaneously the temperature and the flux of ions produced by a cloud of triplet metastable helium atoms at the Bose-Einstein critical temperature. The onset of condensation is revealed by a sharp increase of the ion flux during evaporative cooling. Combining our measurements with previous measurements of ionization in a pure Bose-Einstein condensate, we extract an improved value of the scattering length a=11.3(+2.5)(-1.0) nm. The analysis includes corrections that take into account the effect of atomic interactions on the critical temperature, and thus an independent measurement of the scattering length would allow a new test of these calculations.