Double binding energy differences: Mean-field or pairing effect?

In this paper we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction $V_{pn}$ thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the $V_{pn}$ in even-even nuclei with $N\neq Z$ are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the $V_{pn}$ for even-even $N=Z$ nuclei and for the adjacent odd-$A$ nuclei with one neutron or proton being subtracted.