Accueil du site > Publications récentes > From bare interactions, low-energy constants, and unitary gas to nuclear density functionals without free parameters : Application to neutron matter
Denis Lacroix, Antoine Boulet, Marcella Grasso, and C.-J. Yang
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-
and p-wave
channels at low density. The functional is shown to be predictive
up to densities ∼0.01 fm−3
that is much higher densities compared to the Lee-Yang functional,
valid for ρ<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 (askF)
and (rekF)
to all orders, where re
is the effective range and kF
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 −(askF)−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 ξ0
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 ρ≃0.16 fm−3.
Voir en ligne : Phys. Rev. C 95, 054306 (2017)
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