Physics-Guided Neural Networks for Constructing Nucleon-Nucleon Inverse Potentials (2509.01539v1)

Abstract: We propose a physics-guided neural network (PGNN) framework for constructing nucleon-nucleon inverse potentials based on inverse scattering theory. The framework integrates the Phase Function Method (PFM) with a two-stage supervised multi-layer perceptron (MLP) model to extract the optimal parameters of the Malfliet-Tjon (MT) potential from sparse phase-shift data. A synthetic dataset of phase shifts is generated by solving the phase equation for angular momentum $\ell$ = 0, using the fifth-order Runge-Kutta method, ensuring physically consistent training data. The first neural network predicts the attractive potential strength, $\tilde{V}_A$, while the second estimates the repulsive strength, $\tilde{V}_R$. The optimal range parameter, $\mu$, is obtained through error minimization between predicted and expected phase shifts, thereby enhancing both stability and accuracy compared to conventional inversion techniques. The PGNN framework is validated for the $^1S_0$ state of neutron-proton (n-p), proton-proton (p-p), and neutron-neutron (n-n) scattering at low energies. The constructed inverse potentials accurately reproduce the phase shifts reported in the literature and exhibit the expected features of nucleon-nucleon interactions, including a short-range repulsive core and an intermediate-range attractive well, with the n-p system showing the deepest potential minimum due to stronger binding. These results demonstrate that the proposed PGNN framework provides an efficient and accurate approach for constructing nuclear potentials, effectively bridging machine learning techniques with quantum scattering theory.