Chiral Dynamics and Nuclear Matter

Abstract

We calculate the equation of state of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The contributions to the energy per particle $\bar E(k_f)$ from one- and two-pion exchange diagrams are ordered in powers of the Fermi momentum $k_f$ (modulo functions of $k_f /m_\pi$). It is demonstrated that, already at order ${\cal O}(k_f^4)$, two-pion exchange produces realistic nuclear binding. The underlying saturation mechanism is surprisingly simple (in the chiral limit), namely the combination of an attractive $k_f^3$-term and a repulsive $k_f^4$-term. The empirical saturation point and the nuclear compressibility $K\simeq 250 $MeV are well reproduced at order ${\cal O}(k_f^5)$ with a momentum cut-off of $\Lambda \simeq 0.65$ GeV which parametrizes short-range dynamics. No further short-distance terms are required in our calculation of nuclear matter. In the same framework we calculate the density-dependent asymmetry energy and find $A_0\simeq 34 $MeV at the saturation point, in good agreement with the empirical value. The pure neutron matter equation of state is also in fair qualitative agreement with sophisticated many-body calculations and a resummation result of effective field theory, but only for low neutron densities $\rho_n <0.25 $fm$^{-3}$.