Effective three-particle interactions in atoms with partly filled f-shell*

Three particle forces are known to be very important in nuclear physics. In atoms such forces appear between valence electrons in the second order of many-body perturbation theory due to the exchange interaction with the core. Usually their contribution to the valence energy is very small, of the order of few inverse centimeters. However, for atoms and ions with partly filled d and f shells the overlap between valence and core electrons may be large. This leads to significant enhancement of the effective three particle interactions. In Ti II (ground configuration (GC) 3d$^2$4s) these interactions change binding energy by few hundred inverse centimeters [Berengut et al., J. Phys. B, {\bf 41}, 235702 (2008)]. In Ce I (GC 4f5d6s$^2$) these interactions contribute few thousand inverse centimeters. Three particle forces are also important for highly charged ions with low-lying f shell, such as Pr$^{9+,10+}$, Nd$^{10+,11+}$, and Sm$^{13+}$. These ions may have narrow optical transitions [Safronova et al., Phys. Rev. Lett., {\bf 113}, 030801 (2014)] and are now considered for the new generation of optical clocks.