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

We perform an analysis of a binding energy difference called δVpn(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. It has been suggested that δVpn 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 δVpn by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of δVpn 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 δVpn, which are at variance with its standard interpretation, are that (i) the structures seen in the systematics of δVpn 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 δVpn 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 δVpn and not due to a the different structure of these nuclei, (iii) δVpn does not provide a very reliable indicator for structural changes, (iv)δVpn 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) δVpn 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