This paper demonstrates that the transport coefficients of 4 He + in 4 He can be calculated over wide ranges of , the ratio of the electrostatic field strength to the gas number density, with the same level of precision as can be obtained experimentally if sufficiently accurate potential energy curves are available for the X 2  u + and A 2  g + states and one takes into account resonant charge transfer. We start by computing new potential energy curves for these states and testing their

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... cy by calculating spectroscopic values for the separate states. It is established that the potentials obtained by extrapolation of results from d-aug-cc-pVXZ (X=6,7) basis sets using the CASSCF+MRCISD approach are each in exceptionally close agreement with the best potentials available and with experiment. The potentials are then used in a new computer program to determine the semi-classical phase shifts and the transport cross sections, and from these the gaseous ion transport coefficients are determined. In addition, new experimental values are reported for the mobilities of 4 He + in 4 He at 298.7 K, as a function of , where careful consideration is given to minimizing various sources of uncertainty. Comparison with previously measured values establishes that only one set of previous data is reliable. Finally, the experimental and theoretical ion transport coefficients are shown to be in very good to excellent agreement, once corrections are applied to account for quantum-mechanical effects.