On the Convergence of Born Expansions

Abstract

A study is made of the convergence of the Born expansions in collision problems involving a static central potential. The scattering of each partial wave, characterized by the phase shift ${\eta }_l$, is treated separately. Estimates of the radii of convergence of $tan{\eta }_l$ and of $S_l\equiv e^{2i{\eta }_l}$ (as well as of the corresponding wave functions) are established, and the truncation errors due to breaking off the Born expansions are investigated. An appendix deals with the expansion of ${\eta }_l$ itself.