We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening key estimates in the analysis, which are much simpler than those in the previous works. Our methods give an appropriate class of short-range potentials which can be determined uniquely by scattering operators, that seems natural in terms of direct scattering problems.