  A many-body-theory approach has been developed to study positronium-atom
interactions. As first applications, we calculate the elastic scattering and
momentum-transfer cross sections and the pickoff annihilation rate
$^1Z_\text{eff}$ for Ps collisions with He and Ne. The cross section for He is
in agreement with previous coupled-state calculations, and the
momentum-transfer cross section for Ne agrees with available experimental data.
$^1Z_\text{eff}$ is found to be 0.13 and 0.26 for He and Ne, respectively, in
excellent agreement with the measured values.
