Exterior complex scaling enables physics-informed neural networks for quantum scattering

TL;DR

This paper introduces a novel approach combining exterior complex scaling with physics-informed neural networks to accurately solve quantum scattering problems, overcoming previous limitations related to oscillatory wave functions.

Contribution

The work demonstrates for the first time that ECS enables PINNs to handle quantum scattering, including nuclear and heavy-ion cases, with high accuracy and potential for inverse problem applications.

Findings

Achieved phase shift accuracy of <0.1° for nucleon-nucleus scattering

Successfully applied method to heavy-ion scattering with strong Coulomb effects

Established foundation for PINNs in inverse quantum scattering problems

Abstract

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations, yet their application to quantum scattering problems has been hindered by the oscillatory, non-decaying nature of scattering wave functions. In this work, I demonstrate that exterior complex scaling (ECS) transforms scattering boundary conditions into exponentially decaying waves suitable for neural network solutions, enabling PINNs to solve nuclear scattering problems for the first time. I develop a driven-equation formulation where the source term is confined to the real axis, avoiding the need to analytically continue nuclear potentials into the complex plane. The method is validated on nucleon-nucleus scattering (n+$^{40}$Ca at $E_{\text{lab}}=20$~MeV) with 21 partial waves, achieving phase shift accuracy of $\Delta\delta < 0.1^\circ$ for most channels when compared to conventional solvers. I further demonstrate the approach on heavy-ion scattering ($^6$Li+$^{208}$Pb at 40~MeV) with 41 partial waves and strong Coulomb effects. This work establishes the foundation for extending PINNs to inverse problems where end-to-end differentiability enables direct fitting of optical potential parameters, coupled-channel reactions, and few-body scattering where traditional grid methods face exponential scaling.