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

Abstract

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, . When considering a potential in the form , we find that the radial part of the Schrödinger equation displays an effective potential that takes the form of two well-known screening potentials, namely, the Eckart and the Manning-Rosen potentials.