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.