Does the Gogny Interaction Need a Third Gaussian?

Abstract

By considering infinite matter constraints only, we suggest in this paper that the Gogny interaction should benefit from a third Gaussian in its central part. A statistical analysis is given to select the possible ranges which are compatible with these constraints and which minimize a χ 2 function.

Mean field and beyond description of nuclear structure with the Gogny force: a review

“…Another possibility to generalize the Gogny force is to increase the number of Gaussians in the central potential part to have more flexibility to adjust nuclear matter properties. This is the path taken in [68] where the extra freedom was used to adjust the four spin-isospin channels of the nuclear matter potential energy to the results of realistic calculations. As in the other cases, no finite nuclei calculations have been carried so far and therefore the merits of the new proposal for finite nuclei remain to be demonstrated.…”

Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT

“…In a magnified scale, in Fig. D1(b) we show total energies E def (N 0 ) − E def (16) relative to that obtained for N 0 = 16. We see that at N 0 = 10 and 12, the relative energies are fairly flat; however, they also exhibit significant changes, including sudden jumps related to individual orbitals entering and leaving the space of harmonic-oscillator wave functions that are included in the basis with changing deformation.…”

“…The goal of this work is to adjust the single-reference parameters of pseudopotentials up to next-to-next-tonext-to-leading order (N 3 LO) and to compare the obtained results to experimental data on the one hand and to those obtained for the Gogny D1S EDF [15] on the other. The D1S EDF offers an excellent reference to compare to, because it contains finite-range terms of a similar nature, although its possible extensions to more than two Gaussians [16], cannot be cast in the form of an effective-theory expansion. Because EDFs adjusted in present work are intended to be used solely at the single-reference level, they include a density-dependent term.…”

Linear Response Theory with finite-range interactions

“…To improve the agreement at higher values of the density, the inclusion of a third Gaussian to the original Gogny interaction has been suggested in Ref. [127]. Up to now, no parametrization with three gaussians which takes into account finite nuclei constraints has been obtained yet: the interaction G3, based on D1S, has been adjusted only on infinite matter.…”