The EOS of neutron matter and neutron stars

Recent advances in experiments of the symmetry energy of nuclear
matter and in neutron star observations yield important new insights
on the equation of state of neutron matter at nuclear densities.
In this regime the equation of state of neutron matter plays a critical role in
determining the mass-radius relationship for neutron stars. We show how
microscopic calculations of neutron matter, based on realistic two- and
three-nucleon forces that reproduce very accurately properties of light
nuclei, make clear predictions for the relation between the
isospin-asymmetry energy of nuclear matter and its density dependence,
and the mass and radius for a neutron star.

On the other side, several microscopic calculations suggested that
the inclusion of hyperons softens the equation of state such that
the corresponding maximum mass of neutron stars is much lower that
astrophysical observations. This fact is particularly evident in non-relativistic
calculations.
We show that small changes in the nucleon-nucleon-Lambda
interactions have a dramatic role to the equation of state, while
Lambda binding energies in hypernuclei are qualitatively insensitive to the
same adjustments. These results suggest that current experimental constraints are
perhaps not sufficient to find a solution to the so called 'hyperon puzzle'.