This article presents the formulation and numerical implementation of a time-independent wave-packet (TIWP) asymptotic projection scheme for extracting sharp-energy rearrangement and breakup $S$ matrices from wave-packet solutions of the time-dependent Faddeev equations. The TIWP scheme is based on time-to-energy transforms of the numerically propagated interacting and free wave packets and allows the extraction of scattering observables in energy space. The time-dependent Faddeev equations are solved in momentum space for a given initial wave packet using finite-element-type discretizations of the Jacobi momenta in terms of local basis functions and a central-difference scheme for time propagation. Concurrently with the step-by-step numerical time evolution of the wave packet, its time-to-energy-transform is accumulated by trapezoidal rule to be obtained at selected values of the energy. Projection of the time-to-energy transform of the post-collision wave packet on the two-particle bound and continuum states yield sharp-energy rearrangement and breakup $S$ matrices, respectively. Rearrangement and breakup amplitudes over a wide range of collision energies are obtained from a single wave-packet propagation. For benchmark three-body models, rearrangement $S$ matrices are found to be in very good quantitative agreement with reference time-independent calculations. For breakup, the TIWP scheme reproduces the main qualitative features of the breakup amplitudes, although the numerical accuracy is presently limited by discretization and asymptotic-time constraints.

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• Breakup reactions
• Few-body systems