Theory of the nuclear proton-neutron pairing
Many nuclear observables can be explained in terms of the presence of a condensate of like-nucleon Cooper pairs in nuclei. However, nucleons form two types of condensate: made of the standard isovector (T=1) pairs and much less known isoscalar (T=0) pn pairs. The T=1 condensate manifests itself in nuclei with a variety of phenomena, but what about the T=0 one? The overarching question of the proton-neutron (pn) theme is thus: is it possible to observe experimentally and describe theoretically the T=0 condensate? If yes, in which region of the nuclear chart would its signature be best visible?
A major scientific investigation is in progress in N~Z nuclei in the mass 90 region following publication of a Nature paper  that suggested that spin-aligned (T=0) pn pairs in the g9/2 shell formed significant components of the wave functions of low-lying states. To validate the hypothesis of a T=0 condensate, experimentalists are looking for observables that would decisively show the existence of such a condensate. Attempts to study the impact of spin-aligned T=0 pairs on experimental features, such as B(E2) transition rates and nucleon knockout cross-sections in neutron-deficient Pd, Ag, and Cd nuclei, are being led by York (submitted or planned proposals to the next RIKEN PAC and an accepted proposal at JYFL), which together with Stockholm have the world lead here experimentally.
At present, the Nuclear Energy Density functional (NEDF) theory is probably the most promising technique to back up this experimental effort with new theoretical input. This theory requires advanced theoretical technology, which is currently available only at York. Within the framework of the PhD thesis of A. Márquez Romero, we have focused on developing novel NEDF methods to study the T=0 pairing in detail. Very recently, within a solvable SO(8) model Hamiltonian, we were able to implement the NEDF techniques with full spin and isospin symmetry-restoration. We showed  that the obtained ground-state energies and deuteron-transfer matrix elements are almost identical to the exact ones given by this model.
This methodology, which is unparalleled worldwide, has to be now ported to a realistic setting of the full NEDF approach. To this end, we will put to STFC a request to extend Antonio’s PhD studentship by 6 months, till March 2020. However, we cannot expect that such an extension could cover the exploitation phase of the project. The latter requires a new PhD student, who should start in September 2019, so that the two have sufficient overlap to ensure a smooth continuation of the projected research. The potential success of the future knockout proposal in the Pd/Cd nuclei may crucially depend on having credible NEDF calculations for cross-sections. Strong interest in proton-neutron pairing at York, both among experimentalists and theorists, together with their outstanding expertise in this area, makes from this research an ideal subject for the next STFC grant application, and provides a key opportunity for high-impact publications.  B. Cederwall, et al., Nature 469, 68 (2011)  A. Márquez Romero, J. Dobaczewski, and A. Pastore, arXiv:1812.03927
Applications deadlne - 31st May 2019 or until a suitable candidate is found.