Isospin-invariant Skyrme energy-density-functional approach with axial symmetry
J.A. Sheikh, N. Hinohara, J. Dobaczewski, T. Nakatsukasa, W. Nazarewicz, K. Sato
Date: December 7, 2014
- Density functional theory (DFT) is the
microscopic tool of choice to describe properties of nuclei over the entire
nuclear landscape, with a focus on medium-mass and heavy complex systems.
Modern energy density functionals (EDFs) often offer a level of accuracy
typical of phenomenological approaches based on parameters locally
fitted to the data. It is clear, however, that in order to achieve high quality
of predictions to guide spectroscopic studies, current functionals must be improved, especially in the isospin channel. In this respect, experimental studies of short-lived nuclei far from
stability offer a unique test of isospin aspects of the many-body theory.
- We develop the
isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed
has the most general form that
depends quadratically on the isoscalar
and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space.
- We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant
EDF approach with all possible p-n mixing terms.
have been derived for all the densities and potentials that appear in the
isospin representation. In practical tests, we consider the Skyrme EDF SkM and, as a first
concentrate on Hartree-Fock aspects of the problem, i.e., pairing has been disregarded.
- Calculations have been performed for the (
), and (
) isobaric analog chains. Isospin structure of self-consistent p-n mixed solutions
has been investigated with and without the Coulomb
interaction, which is the sole source of isospin symmetry breaking in our approach. The extended axial HFBTHO solver has been benchmarked against the symmetry-unrestricted HFODD code for deformed and spherical states.
- We developed and tested a general isospin-invariant Skyrme-EDF framework. The new approach permits spin-isospin densities that may give rise to, hitherto, unexplored modes in the excitation spectrum. The new formalism has been tested in the Hartree-Fock limit.
A systematic comparison between HFODD and HFBTHO results show a maximum deviation of about
10keV on the total binding energy for deformed nuclei when the Coulomb term is included. Without this term, the results of both solvers agree down to a 10eV level.