Theoretical study of the parity and time reversal violating interaction in solids

A new theoretical approach to study the properties in solids, which are sensitive to a change of densities of the valence electrons in atomic cores (hyperfine structure constants, parameters of space parity (P) and time reversal (T) violation interaction, etc.) is proposed and implemented. It uses the two-step concept of calculation of such properties which was implemented earlier for the case of molecules [Progr.\ Theor.\ Chem.\ Phys. B 15, 253 (2006)]. The approach is applied to evaluate the parameter $X$ describing electronic density gradient on the Pb nucleus that is required to interpret the proposed experiment on PbTiO$_3$ crystal [PRA, 72, 034501 (2005)] to search for the Schiff moment of the $^{207}$Pb nucleus because of its high sensitivity to the corresponding P,T-violating interactions. For comparison the $X$ parameter has also been calculated on the Pb nucleus for the $^1\Sigma^+$ state of $^{207}$PbO molecule using the same density functionals as those utilized in PbTiO$_3$ studies. The relativistic coupled-clusters approach with single, double and perturbative triple cluster amplitudes, applicable to a few atom systems and providing high accuracy for $X$, is also applied to the PbO case to estimate the accuracy of density functional studies.