For N charged particles of equal masses moving in the field of a heavy residual charge, an approximate analytical solution of the many-body time-independent Schröautdinger equation is derived at a total energy above the complete fragmentation threshold. All continuum particles are treated on equal footing. The proposed correlated wave function represents, to leading order, an exact solution of the many-body Schröautdinger equation in the asymptotic region defined by large interparticle separations. Thus, in this asymptotic region the N-body Coulomb modifications to the plane-wave motion of free particles are rigorously estimated. It is shown that the Kato cusp conditions are satisfied by the derived wave function at all two-body coalescence points. An expression of the normalization of this wave function is also given. To render possible the calculations of scattering amplitudes for transitions leading to a four-body scattering state, an effective-charge method is suggested in which the correlations between the continuum particles are completely subsumed into effective interactions with the residual charge. Analytical expressions for these effective interactions are derived and discussed for physical situations.