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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2602.04553 |
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| _version_ | 1866917247830720512 |
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| author | Lei, Jin |
| author_facet | Lei, Jin |
| contents | 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 $Δδ< 0.1^\circ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exterior complex scaling enables physics-informed neural networks for quantum scattering Lei, Jin Nuclear Theory Computational Physics 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 $Δδ< 0.1^\circ$ 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. |
| title | Exterior complex scaling enables physics-informed neural networks for quantum scattering |
| topic | Nuclear Theory Computational Physics |
| url | https://arxiv.org/abs/2602.04553 |