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The isospin-asymmetry dependence of the nuclear matter equation of stateobtained from microscopic chiral two- and three-body interactions insecond-order many-body perturbation theory is examined in detail. Thequadratic, quartic and sextic coefficients in the Maclaurin expansion of thefree energy per particle of infinite homogeneous nuclear matter with respect tothe isospin asymmetry are extracted numerically using finite differences, andthe resulting polynomial isospin-asymmetry parametrizations are compared to thefull isospin-asymmetry dependence of the free energy. It is found that in thelow-temperature and high-density regime where the radius of convergence of theexpansion is generically zero, the inclusion of higher-order terms beyond theleading quadratic approximation leads overall to a significantly poorerdescription of the isospin-asymmetry dependence. In contrast, at hightemperatures and densities well below nuclear saturation density, theinteraction contributions to the higher-order coefficients are negligible andthe deviations from the quadratic approximation are predominantly from thenoninteracting term in the many-body perturbation series. Furthermore, weextract the leading logarithmic term in the isospin-asymmetry expansion of theequation of state at zero temperature from the analysis of linear combinationsof finite differences. It is shown that the logarithmic term leads to aconsiderably improved description of the isospin-asymmetry dependence at zerotemperature.

Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory