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.

The comparison of different models (the Ore, spur and blob models) of positronium (Ps) formation is presented. Because in molecular media Ps is formed in the terminal positron blob and not in an ordinary spur, the application of the blob model seems to be the most adequate. We extend this model for consideration of the Ps formation in the presence of external electric field ($<100$ kV/cm). In the simplified limiting case, this approach provides a formula similar to the Onsager one for the geminate recombination probability. The influence of ion-electron recombination and other intrablob processes on Ps formation is taken into account. The role of quasifree positronium in Ps formation process is discussed

The interaction of positronium with molecular oxygen dissolved in liquids is experimentally investigated. A computer software has been developed for fitting the positron annihilation lifetime spectra using parameters with clear physical meaning.

This chapter reviews the following items: 1. Energy deposition and track structure of fast positrons: ionization slowing down, number of ion-electron pairs, typical sizes, thermalization, electrostatic interaction between e + and its blob, effect of local heating;2. Positronium formation in condensed media: the Ore model, quasifree Ps state, intratrack mechanism of Ps formation;3. Fast intratrack diffusion-controlled reactions: Ps oxidation and ortho-para conversion by radiolytic products, reaction rate constants, interpretation of the PAL spectra in water at different temperatures; 4. Ps bubble models. "Non-point" positronium: wave function, energy contributions, relationship between the pick-off annihilation rate and the bubble radius.

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Abstract. In application to positron annihilation spectroscopy, Ps atom is considered not as a point particle, but as a finite size e + e − pair localized in a bubble-state in a medium. Variation of the internal Coulombic e + -e − attraction vs. the bubble radius is estimated.Introduction Typical lifetimes (up to annihilation) of a para-positronium atom(p-Ps; spin = 0) 1 in condensed medium are about 130-180 ps. They are close to the p-Ps lifetime in vacuum (125 ps). The ortho-positronium lifetime in a medium is considerably shorter (about 100 times; some ns) in comparison with that in vacuum. This is due to the so-called pick-off processprompt 2γ-annihilation of the e + , composing Ps atom, with one of the nearest e − of surrounding molecules, whose spin is antiparallel to the e + spin. Just this property turns Ps into a nanoscale structural probe of matter. The theoretical task consists in calculating the pick-off annihilation rate λ po , i.e. in relating λ po with such properties of the medium like surface tension, viscosity, external pressure and size of the Ps trap.Originally, to explain the unexpectedly long lifetime of the ortho-Ps atom in liquid helium R.Ferrel [1] suggested that the Ps atom forms a nanobubble around itself. This is caused by a strong exchange repulsion between the o-Ps electron and electrons of the surrounding He atoms. Ferrel approximated this repulsion by a spherically symmetric potential barrier of radius R ∞ . To estimate the equilibrium radius of the Ps bubble he minimized the sum of the Ps energy in a spherically symmetric potential well, i.e. π 2 2 /4mR

A model is described for positronium ͑Ps͒ formation in molecular liquids and polymers. The developed model explicitly takes into account the electrostatic attraction between a deenergized positron and the terminal positron blob. This interaction is caused by the Debye screening of e + by intrablob electrons. The positron distribution function is divided into two parts, one describing the positrons e in + residing within the blob and the other describing the positrons e out + originally thermalized outside the blob. Because of the energy preference for e + to reside within the blob, diffusing e out + is partially converted to e in + . An external electric field shifts the e out + distribution aside from the center of the blob, reduces its diffusion flux into the blob and decreases the Ps yield. The model is compared with experimental data of the electric field effect on Ps formation in neat liquids, amorphous SiO 2 , and polymers.