What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}

Abstract

We perform an analysis of a binding energy difference called delta V_{pn}(N,Z) =- 1/4(E(Z,N)-E(Z,N-2)-E(Z-2,N)+ E(Z-2,N-2) in the framework of a realistic nuclear model. Using the angular-momentum and particle-number projected generator coordinate method and the Skyrme interaction SLy4, we analyze the contribution brought to delta V_{pn} by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of delta V_{pn} throughout the chart of nuclei with the exception of the anomaly related to the Wigner energy along the N=Z line. The main conclusions of our analysis are that (i) the structures seen in the systematics of delta V_{pn} throughout the chart of nuclei can be easily explained combining a smooth background related to the symmetry energy and correlation energies due to deformation and collective fluctuations; (ii) the characteristic pattern of delta V_{pn} around a doubly-magic nucleus is a trivial consequence of the asymmetric definition of delta V_{pn}, and not due to a the different structure of these nuclei; (iii) delta V_{pn} does not provide a very reliable indicator for structural changes; (iv) δV_{pn} does not provide a reliable measure of the proton-neutron interaction in the nuclear EDF, neither of that between the last filled orbits, nor of the one summed over all orbits; (v) delta V_{pn} does not provide a conclusive benchmark for nuclear EDF methods that is superior or complementary to other mass filters such as two-nucleon separation energies or Q values.

19 pages and 12 figures

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• Shape coexistence in even-even nuclei: A theoretical overview
• Lightweight self-conjugate nucleus ${}^{80}$Zr
• $N=Z$ nuclei: A laboratory for neutron-proton collective mode
• Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory
• Double binding energy differences: Mean-field or pairing effect?
• Empirical pairing gaps and neutron-proton correlations
• Description and prediction of even-A nuclear masses based on residual proton-neutron interactions
• Nuclear landscape in a mapped collective Hamiltonian from covariant density functional theory
• Mass Probe of Tetrahedral Symmetry in Atomic Nuclei