Machine learning S-wave scattering phase shifts bypassing the radial Schrödinger equation

Abstract

We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schr\"{o}dinger equation. In out work, we discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor. The good performance, even in presence of bound states in the data sets, exhibited by our model that accordingly is trained on the Hamiltonian through each scattering potential, demonstrates the feasibility of this proof of principle.