Density-functional theory for resonantly interacting fermions with effective range and neutron matter

A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter xi(0) and a parameter eta(e) related to the possible influence of the effective range re at infinite scattering length a. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of (akF)(-1) values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of r(e). Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.