Three-particle breakup amplitudes from wave-packet solutions of time-dependent Faddeev equations

Abstract

A time-dependent wave-packet method is devised to compute three-particle rearrangement and breakup amplitudes over a wide range of collision energies from a single wave-packet solution of the time-dependent Faddeev equations (TDFE). The TDFE is 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. Central difference formula for the time derivative is used for the time propagation step. Projection of the postcollision wave packet on the two-particle bound and continuum states yield state-to-state (sharp energy) rearrangement and breakup S matrices, respectively. 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. The wave-packet results for rearrangement are in good agreement with the reference results from a time-independent calculation. With the rather coarse discretization grid used in the present calculations, one is able to recover the general qualitative features of the breakup process, but quantitatively the state-to-state breakup results are not on par with the rearrangement results.