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

arXiv:2602.04553v2 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations, yet their application to nuclear scattering 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 reaction 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_{ext{lab}}=20MeV) with 21 partial waves, achieving phase shift accuracy of Deltaelta lesssim 0.1^irc for the strongly absorbed channels (ell leq 4) and Deltaelta leq 0.60^irc for all channels up to ell = 10, when compared to conventional solvers. I further demonstrate the approach on heavy-ion scattering (^6Li+^{208}Pb at 40MeV) with 41 partial waves and strong Coulomb effects, where an auto-adaptive anchor warm-down for weak-source channels yields a mean S-matrix accuracy of |Delta|S_ell|| approx 3 imes 10^{-3} across the full angular momentum range, including the absorption-to-transparency transition region. 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.

Source: arXiv cs.LG | 2026-09-29