STUDY OF THE HIGH ORDER TERMS OF THE BORN SERIES: THE B1B-CDW APPROXIMATION FOR ELECTRON CAPTURE S. E. Corchs, O. A. Foj\'on and R.D. Rivarola Instituto de F\'{\i}sica Rosario (CONICET-UNR), Av. Pellegrini 250, 2000 - Rosario, Argentina In this work we study the contribution to the electron capture process of the higher orders of the Born series with correct boundary conditions. A new approximation is developed within the distorted wave model. Single differential and total cross sections are obtained for hydrogenic targets and heavy projectiles at high and intermediate energies.