Proton-Neutron Pairing in N=Z Nuclei within the Quark-Meson-Coupling Energy Density Functional

Abstract

We investigate the impact of isovector and isoscalar proton-neutron pairing correlations on the ground-state properties of even-even N=Z nuclei with mass numbers between A=16 and A=120. Nuclear mean fields are generated using the quark-meson coupling (QMC) energy density functional, while pairing correlations are treated within the quartet condensation model (QCM). Ground-state energies are obtained from axially deformed, self-consistent QMC+QCM calculations employing a zero-range pairing interaction with a density-dependent term derived consistently within the QMC framework. We show that proton-neutron pairing provides a significant contribution to the binding energies of N=Z nuclei, leading to improved agreement with experimental data.

Figures (15)

• Figure 1: Density dependence of the interaction (12) compared to the force (13) for the parameters shown in the figure.
• Figure 2: Off-diagonal matrix elements of the isovector (12) and isoscalar (14) pairing interactions in $^{64}$Ge, calculated with the scalling factors $s=1.5$ and $w=1.6$. Triangles indicate the matrix elements associated with states near the Fermi level, which play a dominant role. The quantity $I_{ij}$ (with $j > i$) denotes the pair indices corresponding to $V_{ij}$, where $i$ and $j$ run from 1 to 10.
• Figure 3: Average pairing gaps (18) for various scaling factors $s$, compared with OEMD (17) for oxygen, calcium, and tin isotopes.
• Figure 4: Binding-energy residuals of $sd$-shell nuclei obtained within various approximations indicated in the figure.
• Figure 5: Pairing energies for the sd-shell nuclei. For each nucleus, the results are displayed (from right to left) for QCM, QCM1 and, when available, BCS.