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 A4(kf) arising from 1π exchange and chiral 2π exchange in nuclear matter are calculated analytically together with three-body terms involving virtual Δ(1232) isobars. From these interaction terms one obtains at saturation density ρ0=0.16fm-3 the value A4(kf0)=1.5MeV, more than three times as large as the kinetic energy part. Moreover, iterated 1π exchange exhibits components for which the fourth derivative with the respect to the isospin asymmetry parameter δ becomes singular at δ=0. The genuine presence of a nonanalytical term δ4ln|δ| 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.