  The residual interaction for a meson-meson system is computed utilizing the
cumulant, or cluster, expansion of the momentum-space time correlation matrix.
The cumulant expansion serves to define asymptotic, or free, meson-meson
operators. The definition of an effective interaction is then based on a
comparison of the full (interacting) and the free (noninteracting) time
correlation matrices. The proposed method, which may straightforwardly be
transcribed to other hadron-hadron systems, here is applied to a simple 2+1
dimensional U(1) lattice gauge model tuned such that it is confining. Fermions
are treated in the staggered scheme. The effective interaction exhibits a
repulsive core and attraction at intermediate relative distances. These
findings are consistent with an earlier study of the same model utilizing
L\"{u}scher's method where scattering phase shifts are obtained directly.
