Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

Abstract

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zerorange limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.

Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry

“…The spin-orbit term V LS N1LO is not affected by the inclusion of higher order gradient terms: in Ref. [25], we have shown that other possible spin-orbit terms are suppressed once the local gauge invariance [3,33] is imposed. In Ref.…”

Does the Gogny Interaction Need a Third Gaussian?

“…Such a result does not change if we re-fit the parameters of the interaction by taking into account only SNM properties (see Ref. [10]) for details. The additional density dependent term of D1P and D1-AS is not of much help since it explicitly enters only in the (S=1,T=0) and (S=0,T=1) channel.…”

“…The explicit expressions for Gogny interaction have been already given in Ref. [10] (for the interactions D1P and D1-AS, which have a slightly different density dependence, the results have been straigthforwardly generalised). The results are presented in Fig.2.…”

“…In a recent article [10], we have shown that the zero-range Skyrme interaction can be considered as a low-momentum expansion of the finite range one. By considering the partial-wave expansion method [11,12], we have shown that while formally a finite-range interaction gets contributions from all partial waves, in reality by restricting to S, P, D and ultimately F partial waves, we can obtain an excellent description of some basic infinite matter properties (INM) as the equation of state (EoS).…”

“…[10] that it is very difficult to get a satisfactory reproduction of these channels by using a standard Gogny interaction [7]: even a re-fit of the parameters that doesn't take into account finite nuclei constraints doesn't improve significantly the symmetric nuclear matter (SNM) properties. In the present article, we therefore discuss the possibility of modifying the Gogny interaction by adding a third range.…”