Surface symmetry energy of nuclear energy density functionals

Abstract

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutronrich matter and description of fission rates for r-process nucleosynthesis.

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“…Note that besides the conventional volume asymmetry term, a surface asymmetry term has also been included [3]. The handful of empirical coefficients are determined through a least-squares fit to the thousands of nuclei whose masses have been determined accurately [4].…”

Occupation-number-based energy functional for nuclear masses

“…The last term of Eq. (14) provides both a volume-and surface-symmetry correction [40,41]. We now discuss the individual terms of the functional (13).…”

“…We now discuss the individual terms of the functional (13). The functional is developed in a leptodermous expansion [41][42][43], providing physical meaning through the separation of energy by powers of A into volume and surface contributions. We begin with the volume terms that scale as A.…”