Expansion of the equation of state of neutron-rich nuclear matter from χEFT beyond quadratic order

Based on chiral effective field theory, the equation of state of neutron-rich nuclear matter is investigated systematically. The contributing diagrams up to three-loop order include one- and two-pion exchange together with three-body terms arising from virtual Δ(1232)-isobar excitations. The expansion of the energy per particle in the proton fraction δ for the nuclear many-body system with neutron density ρ_n = k_f³(1-δ)/3π² and proton density ρ_p = k_f³δ/3π² is performed analytically up to quadratic order: anti E(k_f, δ) = anti E_n(k_f)+δB₁(k_f)+δ^5/3B_5/3(k_f)+δ²B₂(k_f)+.. Yet higher orders in the δ-expansion are necessary for a reasonable description of the equation of state for proton fractions above 20%. The evaluation of a S-wave contact interaction to second order establishes a non-analytical δ^7/3 ln δ-term. The higher order coefficients of the expansion are determined by a least-squares fit. With terms up to order δ^8/3 a good description is obtained from pure neutron matter (δ = 0) up to symmetric nuclear matter (δ = 0.5).