Experimental study of the two-body spin-orbit force

Abstract

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.

5 pages, 3 figures, accepted for publication in Physical Review Letters