Auxiliary function approach for determining symmetry energy at suprasaturation densities

Abstract

Nuclear symmetry energy E sym (ρ) at density ρ is normally expanded or simply parameterized as a function of χ = (ρ – ρ 0 )/3ρ 0 in the form of Esym(ρ) ≈ S + Lχ + 2 –1 K sym χ 2 + 6 –1 J sym χ 3 + … using its magnitude S, slope L, curvature K sym and skewness J sym at the saturation density ρ0 of nuclear matter. Much progress has been made in recent years in constraining especially the S and L parameters using various terrestrial experiments and astrophysical observations. Furthermore, such kind of expansions/parameterizations do not converge at supra-saturation densities where χ is not small enough, hindering an accurate determination of high-density E sym (ρ) even if its characteristic parameters at ρ0 are all well determined by experiments/observations. By expanding the E sym (ρ) in terms of a properly chosen auxiliary function Π sym (χ,Θ sym ) with a parameter Θsym fixed accurately by an experimental E sym (ρ r ) value at a reference density ρr, we show that the shortcomings of the χ-expansion can be completely removed or significantly reduced in determining the high-density behavior of E sym (ρ). In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher χ-order contributions and converges to the same E sym (ρ) much faster than the conventional χ-expansion at densities ≲3ρ 0 . Several quantitative demonstrations using Monte Carlo simulations are given.