Analytical and numerical assessment of the accuracy of the approximated nuclear symmetry energy in the Hartree–Fock theory

• Published in: Progress of theoretical and experimental physics Vol. 2017; no. 7
• Main Authors: Tsukioka, Y., Nakada, H.
• Format: Journal Article
• Language: English
• Published: Oxford University Press 01.07.2017
• Subjects: D41; D10
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptx090

Abstract The nuclear symmetry energy is defined by the second derivative of the energy per nucleon with respect to the proton–neutron asymmetry, and is sometimes approximated by the energy difference between the neutron matter and the symmetric matter. The accuracy of this approximation is assessed analytically and numerically within the Hartree–Fock theory using effective interactions. By decomposing the nuclear-matter energy, the relative error of each term is expressed analytically; it is constant or is a single-variable function determined by the function type. The full errors are evaluated for several effective interactions, by inserting values for the parameters. Although the errors stay within 10 % up to twice the normal density irrespective of the interactions, at higher densities the accuracy of the approximation significantly depends on the interactions.