Wave-packet continuum discretization method for solving the three-body scattering problem

We generalize the wave-packet continuum discretization method previously developed for the scattering problem to the three-body system. For each asymptotic channel, we construct a basis of three-body wave packets given by square-integrable functions. We show that the projections of the channel resolvents on the subspace of three-body wave packets are determined by diagonal matrices, whose eigenvalues we find explicitly. We express the amplitudes of $2\to 2$ processes explicitly in terms of "wave-packet" finite-dimensional projections of the full resolvent. To illustrate our formalism, we calculate the differential cross section of elastic deuteron scattering on a heavy nucleus above the three-body breakup threshold and the $s$-wave quartet $(n-d)$-scattering amplitude. The results of the calculations agree well with the results obtained by other methods. In terms of complexity, the proposed scheme for solving the three-body scattering problem is comparable to solving a similar problem for bound states.