Proton-neutron interactions in $N\approx Z$ nuclei

Proton-neutron $\mathrm{}(p-n)\mathrm{}$ interactions and their various aspects in $N\approx Z$ nuclei of $g_{9/2}$ and $f_{7/2}$ subshells are studied using a schematic model interaction with four force parameters proposed recently. It is shown that the model interaction reproduces well observed physical quantities: the double differences of binding energies, symmetry energy, Wigner energy, odd-even mass difference, and separation energy, which testifies to the reliability of the model interaction and its $p-n$ interactions. First of all, the double differences of binding energies are used for probing the $p-n$ interactions. The analysis reveals different contributions of the isoscalar and isovector $p-n$ pairing interactions to two types of double differences of binding energies, and also indicates the importance of a unique form of isoscalar $p-n$ pairing force with all J components. Next, it is shown that this p-n force is closely related to the symmetry energy and the Wigner energy. Other calculations demonstrate the significant roles of $p-n$ interactions in the odd-even mass difference and in the separation energy at $N=Z$.