Three-body breakup within the fully discretized Faddeev equations

Abstract

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three-and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process n+d → n+n+p with non-local and local N N interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.

Wave-packet continuum discretization for quantum scattering

“…First of all, instead of eq. (94), one uses the equivalent form of the Faddeev equation for the transition operator U [29,42]:…”

“…The elastic on-shell amplitude in the wave-packet representation is calculated as a diagonal (on-shell) matrix element of U-matrix [29]:…”

Fast GPU-based calculations in few-body quantum scattering

“…In this section we outline briefly the method of stationary wave packets that is necessary for understanding the subsequent material by reader. For detail we refer to our previous original papers [11,13] and the recent review [10].…”

“…A matrix element of the operator P in the lattice basis is proportional to the overlap between basis functions defined in different Jacobi sets [11]. Such a matrix element can be calculated by integration with the weight functions over the momentum lattice cells:…”

“…(i) A complete discretization of the continuous spectrum of the scattering problem, i.e. the replacement of continuous momenta and energies with their discrete counterparts, by projecting all the scattering functions and operators onto a space spanned on the basis of the stationary wave packets [10,11,12,13]. As a result, the integral equations of the scattering theory (like the Lippmann-Schwinger, Faddeev etc.…”