Separable expansion of thetmatrix with analytic form factors

Abstract

A recently proposed separable expansion of the $t$ matrix (assuming the potential to be given) is rederived from the Schwinger variational principle. Also, analytic expressions are given for the integrals in the separable expansion if the potential is a superposition of Yukawa potentials, and for suitable choices of the expansion functions. Calculations with two commonly used $S$-wave nucleon-nucleon potentials show that the expansion can converge significantly faster than the unitary pole expansion if the freedom in the choice of the expansion functions is exploited.