Evolution of the nuclear spin-orbit splitting explored via the ³²Si<i>(d,p)</i>³³Si reaction using SOLARIS

The spin-orbit splitting between neutron 1p orbitals at 33Si has been deduced using the single-neutron-adding (d,p) reaction in inverse kinematics with a beam of 32Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1p-shell orbitals is systematically studied using the present and existing data in the isotonic chains of = 17, 19, and 21. In each case, a smooth decrease in the separation of the - orbitals is seen as the respective p-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region