SUMMARY AND OUTLOOK

The description of weakly bound complex nuclei is a demanding task as it requires the understanding and control of three crucial aspects of the nuclear many-body problem: interaction, correlations, and coupling to the low-lying particle continuum. Here, the theoretical tool of choice is nuclear density functional theory based on the self-consistent EDF approach. The quest for a truly universal nuclear EDF is one of the main themes of theoretical nuclear structure research today.

The isospin channel of the nuclear EDF still remains largely unexplored. In the existing functionals, only isoscalar and $t_z$ components of the isovector densities are used as building blocks. In a completely isospin-invariant formalism, all three isovector density components should be considered: those correspond to p-n mixed densities. For heavy nuclei, possessing significant neutron excess, the omission of p-n mixed densities can be justified as neutron and protons occupy different shells. However, for lighter systems, neutrons and protons usually occupy the same shell-model orbits and p-n mixed densities are likely to appear. Some limited experimental evidence suggests that the p-n fields play a role near the $N = Z$ line.

In the present work, we have developed a new Skyrme-EDF approach with the inclusion of p-n mixed densities [17]. The expressions for the densities and HF fields have been worked out in the axial limit. The present 2D HFBTHO implementation that includes mixed p-n densities and fields is fairly fast, and this allows for systematic large-scale surveys. The new framework has been tested in the HF limit and it was benchmarked with 3D HFODD spherical and deformed calculations [27]. The basic features of the p-n mixed HF formalism have been investigated by studying the $A=78, T\approx 11$ IAS chain. In particular, we investigated the isospin breaking effects and stability of solutions obtained for the proton-unbound systems.

The present work has been primarily devoted to the detailed test of the newly developed isospin-invariant density functional formalism. In the near future, we intend to perform realistic HFB calculations by including the generalized pairing interaction in both isoscalar and isovector channels in order to study the importance of the $T=0$ pairing densities and fields on the structure of nuclei close to the $N = Z$ line and the impact of p-n mixing on $\beta$ decays.

We would like to express our deep gratitude to our friend and colleague, Mario Stoitsov, for his contributions in the initial stages of this work. JAS would like to acknowledge I. Maqbool and P.A. Ganai for discussions. This work was supported by the U.S. Department of Energy under Contracts No. DE-FG02-96ER40963 (University of Tennessee), No. DE-SC0008499 (NUCLEI SciDAC Collaboration), and No. DE-FG02-06ER41407 (JUSTIPEN, Japan-U.S. Theory Institute for Physics with Exotic Nuclei); by the Academy of Finland and University of Jyväskylä within the FIDIPRO programme; by the Polish National Science Center under Contract No. 2012/07/B/ST2/03907; and by JSPS KAKENHI (Grants No. 20105003, No. 24105006, No. 25287065, and No. 25287066). Computational resources were provided through an INCITE award ``Computational Nuclear Structure" by the National Center for Computational Sciences (NCCS) and the National Institute for Computational Sciences (NICS) at Oak Ridge National Laboratory. A part of the numerical calculations were also carried out on SR16000 at the Yukawa Institute for Theoretical Physics in Kyoto University and on the RIKEN Integrated Cluster of Clusters (RICC) facility.