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

Departamento de Física, Universidade Federal do Ceará - Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

^(a) michael@fisica.ufc.br (corresponding author)
^(b) soares@fisica.ufc.br
^(c) auto@fisica.ufc.br

Received: 15 February 2022
Accepted: 13 May 2022

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.