Estimating scattering potentials in inverse problems with Volterra series and neural networks

Abstract

AbstractInverse problems often occur in nuclear physics, when an unknown potential has to be determined from the measured cross sections, phase shifts or other observables. In this paper, a data-driven numerical method is proposed to estimate the scattering potentials, using data, that can be measured in scattering experiments. The inversion method is based on the Volterra series representation, and is extended by a neural network structure to describe problems, which require a more robust estimation. The Volterra series method is first used to describe the one-dimensional scattering problem, where the transmission coefficients, and the phase shifts are used as inputs to determine the unknown potentials in the Fourier domain. In the second example the scattering process described by the radial Schrödinger equation is used to estimate the scattering potentials from the energy dependence of the phase shifts, where neural networks are used to describe the scattering problem. At the end, to show the capabilities of the proposed models, real-life data is used to estimate the $${}_{}^3 S_1$$ 3 S 1 NN potential with the neural network approach from measured phase shifts, where a few percent relative match is obtained between the measured values and the model calculations.