Finite-size instabilities in finite-range forces

It has been recently shown that some Gogny finite-range interactions suffer from finite-size instabilities in coordinate-space calculations [Eur. Phys. J. A 55, 150 (2019)]. We confirm this finding by using the Hartree-Fock (HF) method quasilocal approximation to forces. The use of substantially simplifies as compared with those including exact exchange contribution energy and HF fields. quantity most affected is spatial density at origin wildly oscillates iterative process proceeds. In addition recent ${\mathrm{D1M}}^{*}$ parametrization force, we find D1M also shows deficiency several nuclei. harmonic-oscillator basis its ultraviolet cutoff provides converged results a wide realistic range sizes. This result serves justification numerous finite nuclei show no trace instability.