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Isospin-invariant Skyrme energy-density-functional approach with axial symmetry

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. Explicit expressions 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 application, concentrate on Hartree-Fock aspects of the problem, i.e., pairing has been disregarded. Calculations have been performed for the (A=78, T~11), (A=40, T~8), and (A=48, T~4) 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 10 keV 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 ~10 eV level.