On the difference between proton and neutron spin-orbit splittings in nuclei

The latest experimental data on nuclei at ¹³²Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly magic region and compare the case to that of ²⁰⁸Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean-field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches. Received: 13 February 2002 / Accepted: 20 February 2002