Wave-packet continuum discretisation for nucleon-nucleon scattering predictions

In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon-nucleon (NN) scattering amplitudes with the wave-packet continuum discretisation method (WPCD). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit (GPU) to explore the benefits of this inherent parallelism. From a theoretical perspective, the WPCD method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLO$_{\rm opt}$ interaction to demonstrate that WPCD enables efficient computation of NN scattering amplitudes provided one can tolerate an averaged method error of $~1-5$ mb in the total cross section at scattering energies $0-350$ MeV in the laboratory frame of reference. Considering only scattering energies $\sim40-350$ MeV, we find a smaller method error of $\lesssim 1-2$ mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the WPCD method will be offset by the increased size of the resulting discretisation mesh. In practice, a GPU-implementation is mainly advantageous for matrices that fit in the fast on-chip shared memory. We find that WPCD is a promising method for computationally efficient, statistical analyses of nuclear interactions from effective field theory, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.