This article has a few goals. First, a new highly accurate and anomaly free time-independent approach to reactive scattering is presented, based on the use of very-short-range imaginary potentials. The range of the imaginary potentials is extremely short - in successful one-dimensional simulations they cover only two grid points. The savings are incurred by limiting the role of the imaginary potentials to shifting the eigenvalues of the Hamiltonian away from the real axis, thereby avoiding anomalies; the imaginary potentials are not required to impose outgoing boundary conditions. Another goal is a rigorous derivation of a flux-amplitude (FA) expression, whereby (far any scattering approach, whether using negative imaginary potentials or not) reactive S-matrix amplitudes are extracted from the wavefunction at a single surface of any desired "internal" coordinate system - there is no need to project the wave function to the asymptotic products coordinates before determining its flux. With the FA expression, expensive volume integrals in state-to-state scattering are reduced to simple surface integrals. The FA expression also leads to a rigorous derivation of various alternate expressions for the scattering matrix which are useful whenever negative imaginary potentials are utilized. Finally, a new expression is presented for estimating the errors in absorbing potentials single-column calculations due to imperfections in the absorbing potentials.