The principle of the equivalence of gravitational and inertial mass is one of the cornerstones of general relativity. Considerable efforts have been made and are still being made to verify its validity. A quantum-mechanical formulation of gravity allows for non-Newtonian contributions to the force which might lead to a difference in the gravitational force on matter and antimatter. While it is widely expected that the gravitational interaction of matter and of antimatter should be identical, this assertion has never been tested experimentally. With the production of large amounts of cold antihydrogen at the CERN Antiproton Decelerator, such a test with neutral antimatter atoms has now become feasible. For this purpose, we have proposed to set up the AEGIS experiment at 0168-583X/$ -see front matter Ó 2007 Published by Elsevier B.V.

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Cross sections for positron scattering by atomic hydrogen are calculated in the energy range 0 - 110 eV using a 33-state approximation which employs the 1s, 2s and 2p eigenstates of both positronium and hydrogen together with 27 hydrogen pseudostates. Cross sections are given for elastic scattering, H(2s) and H(2p) excitation, Ps(1s), Ps(2s), Ps(2p) and total positronium formation, ionization, and total scattering. The degree of agreement with an earlier 18-state calculation of Kernoghan et al, with sophisticated single-centre approximations, and with the available experimental data, strongly suggests that the main cross sections for positron scattering off ground-state atomic hydrogen are now known to quite a high degree of accuracy. Problems with the total cross section highlighted by Kernoghan et al are now resolved by new experimental data of Stein et al which give excellent agreement with theory for both positron and electron scattering. Suggestions are made for further experimental investigations.