Scattering With Euclidean Green's Functions

We show that it is possible to compute differential cross sections using matrix elements of polynomials in e$^{-\beta*H}$ in normalizable states. These matrix elements can be calculated by quadrature using reflection-positive Euclidean Green functions. The the proposed method is based on an explicit ``time- dependent'' computation of the Moeller wave operators using the Kato-Birman invariance principle to replace the Hamiltonian H by e$^{-\beta*H}$ in the expression for the wave operators. The compact spectrum of e$^{-\beta*H}$ allows uniform polynomial approximations of continuous functions of e$^{-\beta*H}$. We tested the method using a solvable model with the range and strength of a typical nucleon-nucleon interaction and found convergence to the transition matrix elements for energies up to 1.5 GeV(and possibly higher).