Symmetry and surface symmetry energies in finite nuclei

Abstract

A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of β stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.

Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

“…Another way is to use the TF approximation adopted in Ref. [4], or an extension of the TF expression up to T 2 terms [22]:…”

“…By using the approximate expression (9) for the kinetic energy density, Lee and Mekjian performed calculations of the volume and surface symmetry energy coefficients for finite nuclei in Ref. [22], showing that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. In the present work we calculate the kinetic energy density using the self-consistent Skyrme-HFB method and the HFBTHO code.…”

“…The temperature-dependent densities of these nuclei are calculated within a self-consistent Skyrme-HFB method using the cylindrical transformed deformed harmonic-oscillator basis (HFBTHO densities) [71,72]. The kinetic energy density is calculated either by the HFBTHO code or by the TF expression up to T 2 term [22]. We have used two parametrizations of the Skyrme force, namely, SLy4 and SkM*, which were able to give an appropriate description of bulk properties of spherical and deformed nuclei in the past.…”

“…In recent years, the temperature dependence of single-particle properties in nuclear and neutron matter was also broadly investigated, including studies in finite systems, as well (e.g., Refs. [4,[18][19][20][21][22][23][24][25]). …”

What is the Valence of Mn inGa1−xMnxN?

“…These N-t 2g are the ones being integrated out to derive the effective d 4 picture. Note that this change of perspective is the same as that employed in the construction of the well-known Zhang-Rice singlet in the cuprate high-temperature superconductors [59,60], and the same concept has been applied to the study of local excitations in correlated NiO [58,61] and LiF [62,63]. The above effective d 4 picture, while ideal to study the Jahn-Teller instability and other local properties like the local magnetic moment and local excitations, is not suitable for studying long-range properties.…”