The spin-orbit interaction depends on the spin orientation of the nucleons with respect to their angular momenta as well as on the derivative of the nuclear density. Eventhough this density dependence is used in all mean field model, it has never been tested yet due to the lack of data. We propose an original method to test this density dependence by comparing a 'bubble' nucleus (34Si)to a 'normal' nucleus (36S). The 34Si exhibits a central density which is depleted by a factor of two which induces a non-zero central density derivative and should change the strength of the spin orbit interaction for the inner orbits such as the p orbits (L=1). By performing (d,p) transfer reactions with 36S and 34Si beams, the p3/2 and p1/2 spin orbit splitting can be inferred for these nuclei. Depending on the models, the spin-orbit splitting varies from 7% (VlowK interaction) up to 70% (Relativistic mean field approach). Beams of 36S and 34Si, produced at the LISE spectrometer at 20A.MeV, were impinged onto a CD2 target. Tracking the beam particles was achieved using 2 xy beam tracking gas detectors. Protons emitted were detected by 4 multi-segmented Si detectors (MUST2) placed at backwards angles. Gammas issued from the excited states decay were detected in the 4 EXOGAM segmented Germanium detectors. Transfer like nuclei were identified with an ionization chamber and a plastic detector. The excitation energy spectra of the 37S and 35Si are determined up to about 7 MeV. Spectroscopic factors and energies of p and f states are derived for the first time in 35Si. The two nuclei show strong similarity for the f spin-orbit partners, whereas the p3/2 - p1/2 energy gap is reduced by 55%.
