Validity of Born Approximation for Nuclear Scattering in Path Integral Representation

TL;DR

This paper investigates the validity of the Born approximation in nuclear scattering using path integral methods, demonstrating convergence at high energies and justifying neglecting higher-order terms.

Contribution

It provides an analytical study of the Born series convergence in nuclear scattering with a Woods-Saxon potential using path integral representation.

Findings

Born series converges at high energies

Higher-order Born approximations can be neglected

Analytical approach with approximate Woods-Saxon potential

Abstract

The first and second Born approximation are studied with the path integral representation for $ {\cal T} $ matrix. The $ {\cal T}$ matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it shown that the Born series is converge at high energies and orders higher than two in Born approximation series can be neglected.