  Predicted twenty years ago, positron binding to neutral atoms has not yet
been observed experimentally. A new scheme is proposed to detect positron-atom
bound states by colliding Rydberg positronium (Ps) with neutral atoms.
Estimates of the charge-transfer reaction cross section are obtained using the
first Born approximation for a selection of neutral atom targets and a wide
range of incident Ps energies and principal quantum numbers. We also estimate
the corresponding Ps ionization cross section. The accuracy of the calculations
is tested by comparison with earlier predictions for Ps charge transfer in
collisions with hydrogen and antihydrogen. We describe an existing Rydberg Ps
beam suitable for producing positron-atom bound states and estimate signal
rates based on the calculated cross sections and realistic experimental
parameters. We conclude that the proposed methodology is capable of producing
such states and of testing theoretical predictions of their binding energies.
