Nucleon--nucleon dynamics from variational matrix Pade approximants

The operator Pade approximant (O.P.A.) method in potential scattering is summarized and analyzed. The exact phase shifts are reproduced within 0.1% at any energy with no more than three mesh points. Rigorous results supporting this procedure are given. Next the extension of this procedure to Lagrangian field theories is discussed for strong interactions at low energy and the essentials of the techniques given. The Yukawa interaction is analyzed and then chiral effects and vector mesons are taken into account through the nonlinear sigma model and a renormalizable ω interaction. The results obtained with only one mesh point corresponding to the physical momentum are reported. Phase shifts coupling constants and scattering lengths are calculated for NN interactions. 17 references