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

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Based on a chiral approach to nuclear matter, we calculate the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter. 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 non-analytical term δ⁴ |δ| in the expansion of the energy per particle of isospin-asymmetric nuclear matter is demonstrated by evaluating a s-wave contact interaction at second order.