Nuclear DFT description of proton-neutron pairing correlations

Pairing correlations play a crucial role in nuclear phenomena: their effects range from the odd-even mass staggering in nuclear structure to the phases of matter found in neutron stars. Nuclear Density Functional Theory (DFT) is a framework applicable to different systems, from few-body nuclei to nuclear matter. In this thesis, we describe pairing and its manifestation within nuclear DFT, in both infinite and finite systems.

Starting from a wavefunction combining all spin-isospin channels of a pair condensate in infinite nuclear matter, we obtain the most general density matrix and pairing tensor. Our interaction-independent analysis shows that although the different proton-neutron channels separate in the Thouless matrix, they mix in the pairing tensor and the density matrix, suggesting that the relationship between pairing tensor and pair condensate cannot be taken for granted.

In finite systems, we compute B(E2; 2+ -> 0+) of T=1 multiplets, as the dependence of E2 matrix elements on isospin projection Tz is linked to the conservation of isospin symmetry. We show that Tz=0, T=1 nuclei should be described by a coherent superposition of blocked T=1 proton-neutron pairs atop the even-even quasiparticle vacua. The computed B(E2) in doubly-blocked configurations of the odd-odd Tz=0 nuclei 70Br and 78Y—cases of experimental interest—show that, individually, they do not correspond to isospin-symmetry conservation. We analyse B(E2) rates for even-even T=1 mirror nuclei with 42 ≤ A ≤ 98, and demonstrate that collective effects are crucial for describing experimental data near the N=Z line.

We introduce a new algorithm for computing finite-range interactions in nuclear DFT for direct, exchange, and pairing channels. The new technique is based on eigendecomposition truncation and exploits properties specific to Gaussian matrix elements to accelerate DFT calculations of finite-range interactions. This procedure reduces the CPU time by ≈60-90% without sacrificing numerical precision.