The present work deals with the single ionization of atoms by fast bare ion impact within the continuum distorted wave (CDW) [

1] and the continuum distorted wave-eikonal initial state (CDW-EIS) [

2] distorted wave theories. Originally, the three-body CDW and CDW-EIS distorted wave theories were developed to investigate ion-atom processes for monoelectronic targets. They were introduced in order to accelerate the convergence of a Born series description. Later, an extension of the CDW-EIS description for the single ionization of multielectronic targets was made by Fainstein et al. [

3]. They reduced the multielectronic case to a monoelectronic treatment within a three-body approximation, the three bodies considered being the projectile, the residual target, and the active electron (the one to be ionized as a consequence of the collision). The other electrons, the passive ones, were supposed to remain as frozen in their initial orbitals during the reaction (see [

3]). This allowed the extension of these distorted theories to complex electronic systems. Since that time, they were used in a reliable way to calculate the differential, as well as the total cross-section for a wide variety of collision systems with projectiles ranging from antiprotons to highly-charged bare ions and targets going from atoms to a large diversity of molecules [

3,

4,

5,

6,

7,

8,

9]. In the distorted wave formalism, the action of the perturbative potentials can either be applied to the initial channel distorted wave function or to the final channel distorted one, giving place to the prior and post versions of the transition matrix element, respectively [

10,

11]. To calculate them, effective Coulomb potentials were chosen to represent the interaction between the residual target and the active electron (the ionized one) in the exit channel. The use of this Coulombic potential gave place to post-prior discrepancies [

12,

13]. In a previous work [

14], we revisited the formulation of the post version of the CDW-EIS approximation, showing that the inclusion of an additional potential in the exit channel, which was neglected in the previous post version calculations, almost completely removes these discrepancies. This potential is associated with a first-order description of the dynamic screening produced by the passive electrons on the evolution of the active one. In this work, we deal with the post-prior discrepancies in the CDW theory and the inclusion of the dynamic screening in the post-CDW theory. It has been shown (see [

15]) that the prior version of the CDW theory for single ionization has an intrinsic logarithmic divergence near the binary-encounter peak, which prevents the transition amplitude from being integrated in order to obtain the differential and total cross-sections. Although there was an abstract sent by Dubé and Dewangan to the ICPEACXIX Conference [

16] stating that an integration of such divergences was feasible, to the best of our knowledge, there is no further evidence or proof of how to perform such an integration. In this paper, we study the terms containing the logarithmic divergences present in both the post and prior versions of the CDW theory, and we propose a way of including the dynamic screening in the post-CDW theory without encountering such divergences. Atomic units will be used throughout this work unless otherwise stated.