Comment on "Breakdown of the tensor component in the Skyrme energy density functional''

TL;DR

This paper critiques a recent claim that the Skyrme tensor interaction is invalid, clarifying misconceptions about Fourier transforming tensor interactions and demonstrating its straightforward derivation in momentum space.

Contribution

It refutes the misconception that Fourier transforming tensor interactions is impossible, showing a clear method to obtain the Skyrme force in momentum space from general interactions.

Findings

Fourier transform of tensor interactions is feasible and straightforward.

The Skyrme tensor interaction can be derived from general interactions with radial dependence.

The critique clarifies misconceptions in the previous claim about the Skyrme tensor force.

Abstract

In a recent paper [Phys. Rev. C 101, 014305 (2020)], Dong and Shang claim that the Skyrme original tensor interaction is invalid. Their conclusion is based on the misconception that the Fourier transform of tensor interaction is difficult or even impossible, so that the Skrme-type tensor interaction was introduced in an unreasonable way. We disagree on their claim. In this note, we show that one can easily get the Skyrme force in momentum space by Fourier transformation if one starts from a general central, spin-orbit or tensor interaction with a radial dependence.