The exact treatment of the Coulomb interaction in the presence of the strong interaction between a charged projectile and a nucleus is proposed, on the basis of the technique for many-potential problems. Also an expression for off-shell Coulomb scattering matrix element is given. § l. Introduction In the microscopic approachn to projectile-nucleus scattering problems, a mo mentum space calculation of cross sections has a good advantage over a coordinate space treatment, since the two-body scattering matrix is usually defined in momen tum space to begin with and therefore in order to obtain a coordinate space poten tial, certain approximations have, of necessity, to be introduced. In low energy scattering problems, the effect of these approximations may not be so important. However, in intermediate through high energy scattering processes it has come to be knovvn that these approximations produce sizable ambiguities. 2J By working entirely in momentum space, therefore, we can avoid unnecessary uncertainties. However, momentum space approach to scattering problems has its own dis advantages which have hitherto prevented its full fledged application from being a more accurate and desirable tool to explore nuclear properties. One of them has been the difficulty to incorporate the effect due to the Coulomb interaction between a charged projectile and a nucleus \vith a formalism which was generated to deal with the strong interaction. The exact formalism to include the Coulomb interaction has been given by Goldberger and vVatson 11 and also by Newton,'> but the expression given by them is incomplete and cannot be evaluated in any reliable way as we shall see later. Because of these situations there have been numerous approximate methods; one method is to simply assume additivity of the Coulomb and nuclear phase shifts!> Another method is to approximate the Cou lomb interfered nuclear phase shifts by the pure nuclear phase shifts. 5) The third method is to approximate the phase difference between the Coulomb and strong scattering amplitudes by using the small scattering angle and weak Coulomb field approximations_ . 6> Yet another way is to redefine an optical potential as to be