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Lithium ion - Helium Experiment

   The transport properties of Li ions in helium have received much interest owing to the relative simplicity of this particular ion-atom system, which has allowed the calculation of highly accurate ab initio interaction potentials. These can be used in conjunction with transport theory to give ``ab initio'' transport coefficients, which can be compared directly with experiment.

However the results from experiment were confusing. Skullerud et al.[1986] measured the ratio of of transverse diffusion to mobility,    and found that their data is in significant disagreement with values of calculated from the potential of Viehland [1983], which was based on the data of Gatland et al.[1977]. Furthermore, a highly accurate ab initio potential calculation by Senff and Burton [1986] yielded values that agrees with the measured values within the stated uncertainty of 2%.

Furthermore, there was considerable discrepancy amongst the mobility values of Takata [1975], Gatland et al. [1977] and Cassidy and Elford [1985], even allowing for the slightly different experimental conditions under which the experiments were performed. The differing data were finally reconciled by explicitly recognizing the possibility that the experiments were no longer described by a second order diffusion equation of the form (gif). Two different ad hoc methods of eliminating the effects due to the breakdown of this description were applied by England and Elford [1987] and Løvaas et al. [1988], and yielded transport data in agreement with the ab initio calculations. These effects are known as end-effects, because    the diffusion equation is expected to hold in the bulk of a homogeneous neutral gas, with a uniform field, and any departures from this state occur at the ends of the apparatus.

England and Elford [1987] assume that the end effects in time of flight mobility measurements take the form of a power series in the inverse of the drift length. By fitting this power series to their mobility measurements at different drift distances, they eliminated the end effects by extrapolating to infinite drift distance.

Løvaas et al. [1988] assume that the end effects induce a distortion to the basic gaussian solution (gif) that can be written as a series in Hermite polynomials, similar to the solution of the transport equation    (gif) given by Skullerud [1974]. By truncating the series at third order, they obtain expressions for the mean and variance of the drift time. By comparing these values at different drift distances, they can obtain values for the transport coefficients. 

In the case of lithium ions in helium, the transport properties are now considered to be well understood. However, it has highlighted a deficiency in the conventional transport theory based on the diffusion equation (gif), which needs to be overcome if the correction methods employed are to be understood. In this chapter, I develop a non-hydrodynamic theory of time-of-flight experiments which provides theoretical underpinning to the methods of England and Elford, and to those of Løvaas et al.. These results have been reported in Standish [1987] However, I have not treated the effects due to the distortion of the field near the shutter, nor the effects of absorption onto the apparatus, which are considered to be a significant contribution to the total end-effect. Much work remains to be done in this area before there is full understanding of end-effects.



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Russell Standish
Thu May 18 11:43:52 EST 1995