  The perturbation theory with respect to the potential energy of three
particles is considered. The first-order correction to the continuum wave
function of three free particles is derived. It is shown that the use of the
collective multipole expansion of the free three-body Green function over the
set of Wigner $D$-functions can reduce the dimensionality of perturbative
matrix elements from twelve to six. The explicit expressions for the
coefficients of the collective multipole expansion of the free Green function
are derived. It is found that the $S$-wave multipole coefficient depends only
upon three variables instead of six as higher multipoles do. The possible
applications of the developed theory to the three-body molecular break-up
processes are discussed.
