  The many-body-theory approach to positronium-atom interactions developed in
[Phys. Rev. Lett. \textbf{120}, 183402 (2018)] is applied to the sequence of
noble-gas atoms He-Xe. The Dyson equation is solved separately for an electron
and positron moving in the field of the atom, with the entire system enclosed
in a hard-wall spherical cavity. The two-particle Dyson equation is solved to
give the energies and wave functions of the Ps eigenstates in the cavity. From
these, we determine the scattering phase shifts and cross sections, and values
of the pickoff annihilation parameter $^1Z_\text{eff}$ including short-range
electron-positron correlations via vertex enhancement factors. Comparisons are
made with available experimental data for elastic and momentum-transfer cross
sections and $^1Z_\text{eff}$. Values of $^1Z_\text{eff}$ for He and Ne,
previously reported in [Phys. Rev. Lett. \textbf{120}, 183402 (2018)], are
found to be in near-perfect agreement with experiment, and for Ar, Kr, and Xe
within a factor of 1.2.
