Impact of collective vibrations on quasiparticle states of open-shell odd-mass nuclei and possible interference with the tensor force

The energy splittings between the proton $1h_{11/2}$ and $1g_{7/2}$ states in the Sb (Z=51) isotopes and the neutron $1i_{13/2}$ and $1h_{9/2}$ states in the ${N=83}$ isotones are analyzed within relativistic quasiparticle-vibration coupling (QVC) model. Although a common viewpoint is that an effective tensor interaction is needed to reproduce these splittings, we show, for the first time, that quasiparticle-vibration coupling also improves their description considerably. The remaining differences between the experiment and the QVC calculations point to a complex scenario in which both tensor interaction and quasiparticle-vibration coupling are needed to reproduce accurately the observed energy splittings. This scenario, however, requires a considerably weaker tensor interaction as compared with the previous estimates.