Low-frequency Slivan states in the outer main belt?

Context. Spin states of several main belt asteroids have been recently found to reside in what is called the Slivan state, namely a secular spin-orbit resonance with the s(6) mode of their orbital precession in space. Aims. We examine a possibility of the Slivan states of asteroids with other than orbital s6 precession frequency. Methods. The asteroids' orbital and spin states are numerically propagated using well-tested computer codes. We select parameter space favorable for the Slivan-state capture with the s(7) frequency mode of the orbital precession. The stability of these states is numerically verified. Results. We find that asteroid (184) Dejopeja has a spin state captured in (or very nearly) the Slivan state with the s7 orbital frequency. In general, such a situation may favorably occur for low-inclination orbits in the outermost part of the main asteroid belt. We expect these states to be common among the Themis family members.