On the Scattering of a Particle by a Static Potential

Abstract

The behavior of the solutions of scattering integral equations is studied as a function of the potential strength $\lambda$. From an analysis of the second Born approximation for a Yukawa potential it seems indicated that the Born expansion for a nuclear potential has no useful domain of applicability. The convergence of the Born expansion is discussed. It is shown that the Fredholm theory of integral equations enables one to express the solutions as a quotient of infinite power series in $\lambda$ which still converge when the Born expansion breaks down. Only in exceptional cases can this method be used for obtaining rapid numerical estimates.