Energies and spectroscopic factors of the first $7/2^-$, $3/2^-$, $1/2^-$ and $5/2^-$ states in the $^{ 35}$Si$_{ 21}$ nucleus were determined by means of the (d,p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the $^{ 35}$Si and $^{ 37}$S isotones, a reduction of the $p_{ 3/2} - p_{ 1/2}$ spin-orbit splitting by about 25% is proposed, while the $f_{ 7/2} -f_{ 5/2}$ spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the 2-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei.
Categories: nucl-ex