Numerical solution of time-dependent three-particle Faddeev equations: calculation of rearrangement S matrices

The time-dependent Faddeev equations (TDFEs) are employed for the first time as a computational tool for three-particle scattering problems. Rearrangement transition amplitudes over a wide range of collision energies are extracted from a single numerical wave-packet solution of the TDFE. To numerically solve the TDFE in momentum space for a given initial wave packet, finite-element-type discretizations of Jacobi momenta in terms of local basis functions is employed to convert the TDFE into a set of first-order differential equations in time. Central difference formula for the time derivative is used for the time propagation step. Two forms of TDFE are considered and incorporation of permutational symmetry for three identical particles into these equations is carried out. The proposed method is tested on a three-body model that is often used as a benchmark to compare different computational approaches to three-particle problem. Rearrangement S-matrix elements obtained from the analysis of the wave-packet solution of TDFE at asymptotic times are compared with the results of well-established time-independent methods. These results establish that the TDFE approach is a viable and competitive addition to the existing arsenal of computational methods for the three-body scattering problem.