Actinide and lanthanide molecules to search for strong CP-violation

The existence of the fundamental CP-violating interactions inside the nucleus leads to the existence of the nuclear Schiff moment. The Schiff moment potential corresponds to the electric field localized inside the nucleus and directed along its spin. This field can interact with electrons of an atom and induce the permanent electric dipole moment (EDM) of the whole system. The Schiff moment and corresponding electric field are enhanced in the nuclei with the octupole deformation leading to the enhanced atomic EDM. There is also a few-order enhancement of the T,P-violating effects in molecules due to the existence of energetically close levels of opposite parity. We study the Schiff moment enhancement in the class of diatomic molecules with octupole-deformed lanthanide and actinide nuclei: $^{227}$AcF, $^{227}$AcN, $^{227}$AcO$^+$, $^{229}$ThO, $^{153}$EuO$^+$ and $^{153}$EuN. Projecting the existing experimental achievements to measure EDM in diamagnetic molecules with spherical nucleus ($^{205}$TlF) to the considered systems one can expect a very high sensitivity to the quantum chromodynamics parameter ${\bar \theta}$ and other hadronic CP-violation parameters surpassing the current best limits by several orders of magnitude. It can have a dramatic impact on the modern understanding of the nature of CP-violating fundamental interactions.