标题： 非自治Volterra级数展开的可变相位近似及其在核-核反散射问题中的应用 显示英文标题

标题： Nonautonomous Volterra Series Expansion of the Variable Phase Approximation and its Application to the Nucleon-Nucleon Inverse Scattering Problem

摘要： 本文中，非线性Volterra级数展开被推广并用于描述与核物理中逆散射问题相关的某些类型的非自治微分方程。 非自治Volterra级数展开使我们能够确定可变相位近似（VPA）的动态多项式逼近，该近似用于通过一阶非线性微分方程从核势中确定相移。 通过使用一阶Volterra展开，针对弱势和/或高能情况，制定了对逆散射问题的稳健近似。 然后借助径向基函数神经网络扩展了该方法，通过对测量的相移施加非线性变换，以能够用由一阶Volterra展开给出的线性逼近来建模散射系统。 该方法被应用于描述中子-质子散射下低于200 MeV实验室动能的1S0 NN势，给出了物理上有意义的势，并且重新计算的相移与测量值之间的平均相对误差低于1%。 显示英文摘要

摘要： In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the 1S0 NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below 1% averaged relative error between the recalculated and the measured phase shifts.