Screening potentials derived from the central force problem in a deformed space

The action of long-range potentials can be hindered by the collective effect of free charges in a medium, a process dubbed screening. This effect is usually modeled by adding an exponential crossover to a power-law potential. We show here how these exponential cutoffs can be obtained from first principles in the central force problem through the addition of a radial deformation of space, del(eta) = (1+gamma r)del(r). When considering a potential in the form V = -(K-1/r+ K-2/r(2)), we find that the radial part of the Schrodinger equation displays an effective potential that takes the form of two well-known screening potentials, namely, the Eckart and the Manning-Rosen potentials. Copyright (C) 2022 EPLA