Neutron matter at finite temperature

The nuclear equation of state plays a central role in the physics of neutron stars and core-collapse supernovae. Renormalization group methods coupled with effective field theory offer a systematic approach to nuclear matter: For low-momentum interactions Vlow k with cutoffs around 2 fm−1, the strong short-range repulsion in conventional nucleon-nucleon (NN) interactions and the tensor force are tamed [1]. At sufficient density, Pauli blocking eliminates the shallow bound states, and thus the particleparticle channel becomes perturbative in nuclear matter [1]. In addition, the corresponding leading-order chiral threenucleon (3N) interaction becomes perturbative in light nuclei for Λ 2 fm−1 [2]. Consequently, the Hartree-Fock (HF) approximation is a good starting point, and perturbation theory (in the sense of a loop expansion) around the HF energy becomes tractable [1]. At finite temperature, the loop expansion around the HF free energy can be realized by the perturbative expansion of the free energy [3], where we treat the momentum dependence of the self-energy perturbatively. The free energy F (N) up to second order (for details see [4]) is given by