Comment on "Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation"

TL;DR

This paper critiques a previous study on light scattering by a parity-time-symmetric dipole, identifying a fundamental error and providing an exact scattering amplitude expression for the potential.

Contribution

It corrects a basic error in prior work and derives an exact closed-form scattering amplitude for the PT-symmetric double-delta potential.

Findings

Previous analysis was flawed due to a basic error.

Provides an exact closed-form expression for the scattering amplitude.

Clarifies the scattering behavior of the PT-symmetric dipole.

Abstract

In [J. A. Rebou\c{c}as and P. A. Brand\~{a}o, Phys. Rev. A 104, 063514 (2021)] the authors compute the scattering amplitude for a $\mathcal{P}\mathcal{T}$-symmetric double-delta-function potential in three dimensions by invoking the far-zone approximation and summing the resulting Born series. We show that the analysis of this paper suffers from a basic error. Therefore its results are inconclusive. We give an exact closed-form expression for the scattering amplitude of this potential.