Finite-volume two-pion energies and scattering in the quenched approximation.

We investigate how L uscher's relation between the nite-volume energy of two pions at rest and pion scattering lengths has to be modiied in quenched QCD. We nd that this relation changes drastically, and in particular, that \enhanced nite-volume corrections" of order L 0 = 1 and L 2 occur at one loop (L is the linear size of the box), due to the special properties of the 0 in the quenched approximation. We deene quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various eeects in some numerical examples, and nd that they can be substantial.