From bare interactions, low-energy constants, and unitary gas to nuclear density functionals without free parameters: Application to neutron matter

We further progress along the line of Ref. [D. Lacroix, Phys. Rev. A 94, 043614 (2016)] where a functional for Fermi systems with anomalously large s-wave scattering length as was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s-andp-wave channels at low density. The functional is shown to be predictive up to densities similar to 0.01 fm(-3) that is much higher densities compared to the Lee-Yang functional, valid for. < 10(-6) fm(-3). The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in (a(s)k(F)) and (r(e)k(F)) to all orders, where r(e) is the effective range and k(F) is the Fermi momentum. One conclusion from the present work is that, except in the extremely low-density regime, nuclear systems can be treated perturbatively in -(a(s)k(F))(-1) with respect to the unitary limit. Starting from the functional, we introduce density-dependent scales and show that scales associated with the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly by low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter xi(0) and becomes independent of as. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density. similar to 0.16 fm(-3).