Comment on the paper Eur. Phys. J. A (2019) 55:150

TL;DR

This paper revisits the stability issues of the Gogny D1M* interaction in finite-nuclei calculations, confirming some previous findings and clarifying the conditions under which instabilities occur using coordinate-space and harmonic oscillator basis methods.

Contribution

It provides an independent verification of the D1M* interaction's instabilities and clarifies their dependence on calculation methods and nuclear properties.

Findings

Instabilities confirmed with coordinate-space methods.

Certain nuclei are stable without Coulomb force.

Instabilities linked to s-orbital occupancy near the Fermi level.

Abstract

The conclusions of the study published as Eur. Phys. J. A (2019) 55:150 questioning the adequacy of the recently proposed Gogny D1M* interaction for finite-nuclei calculations using harmonic oscillator (HO) basis are revised. The existence of an instability in finite nuclei for D1M* when coordinate-space methods are used to solve the HF equations (as shown in Eur. Phys. J. A(2019) 55:150) is independently confirmed using a computer code based on a quasi-local approximation (QLA) to the HF energy density with finite-range forces. We confirm that the most affected quantity in the coordinate-space calculation is the spatial density at the origin. Our study reveals that some findings concerning these instabilities are not easy to reconcile with the arguments used in Eur. Phys. J. A (2019) 55:150. For instance, some nuclei such as $^4$He and $^{40}$Ca, which diverge in HF mesh-point calculations performed with D1M*, become perfectly stable when Coulomb force is switched off. We have also found instabilities in some nuclei when the D1M interaction is used. Finally, a connection between the occupancy of $s$-orbitals near the Fermi level and the appearance of instabilities is observed. Several convergence and stability studies are performed with HO basis of different sizes and oscillator parameters to demonstrate the robustness of the D1M* results for finite nuclei when the HO basis is used.