What can be learned from binding energy differences about nuclear structure: The example ofδVpn

Abstract

We perform an analysis of a binding energy difference called $\ensuremath{\delta}{V}_{\mathit{pn}}(N,Z)\ensuremath{\equiv}\ensuremath{-}\frac{1}{4}[E(Z,N)\ensuremath{-}E(Z,N\ensuremath{-}2)\ensuremath{-}E(Z\ensuremath{-}2,N)+E(Z\ensuremath{-}2,N\ensuremath{-}2)]$ in the framework of a realistic nuclear model. It has been suggested that $\ensuremath{\delta}{V}_{\mathit{pn}}$ values provide a sensitive probe of nuclear structure, and it has been put forward as a primary motivation for the measurement of specific nuclear masses. Using the angular momentum and particle-number projected generator coordinate method and the Skyrme interaction SLy4, we analyze the contribution brought to $\ensuremath{\delta}{V}_{\mathit{pn}}$ by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of $\ensuremath{\delta}{V}_{\mathit{pn}}$ 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 of $\ensuremath{\delta}{V}_{\mathit{pn}}$, which are at variance with its standard interpretation, are that (i) the structures seen in the systematics of $\ensuremath{\delta}{V}_{\mathit{pn}}$ 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 $\ensuremath{\delta}{V}_{\mathit{pn}}$ having a much larger size for nuclei that add only particles or only holes to a doubly magic nucleus than for nuclei that add particles for one nucleon species and holes for the other is a trivial consequence of the asymmetric definition of $\ensuremath{\delta}{V}_{\mathit{pn}}$ and not due to a the different structure of these nuclei, (iii) $\ensuremath{\delta}{V}_{\mathit{pn}}$ does not provide a very reliable indicator for structural changes, (iv)$\ensuremath{\delta}{V}_{\mathit{pn}}$ does not provide a reliable measure of the proton-neutron interaction in the nuclear energy density functional (EDF) or of that between the last filled orbits or of the one summed over all orbits, and (v) $\ensuremath{\delta}{V}_{\mathit{pn}}$ 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.