Quartic isospin asymmetry energy of nuclear matter from chiral pion-nucleon dynamics

Based on a chiral approach to nuclear matter, the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter is calculated. The contributions to the quartic isospin asymmetry energy A(4)(k(f)) arising from 1 pi exchange and chiral 2 pi exchange in nuclear matter are calculated analytically together with three-body terms involving virtual Delta(1232) isobars. From these interaction terms one obtains at saturation density rho(0) = 0.16 fm(-3) the value A(4)(k(f0)) = 1.5 MeV, more than three times as large as the kinetic energy part. Moreover, iterated 1 pi exchange exhibits components for which the fourth derivative with the respect to the isospin asymmetry parameter delta becomes singular at delta = 0. The genuine presence of a nonanalytical term delta(4) ln \delta\ in the expansion of the energy per particle of isospin-asymmetric nuclear matter is demonstrated by evaluating an s-wave contact interaction at second order.