A Relativistic Many-Body Analysis of the Electric Dipole Moment of $^{223}$Rn

Abstract: We report the results of our {\it ab initio} relativistic many-body calculations of the electric dipole moment (EDM) $d_A$ arising from the electron-nucleus tensor-pseudotensor (T-PT) interaction, the interaction of the nuclear Schiff moment (NSM) with the atomic electrons and the electric dipole polarizability $\alpha_d$ for $^{223}$Rn. Our relativistic random-phase approximation (RPA) results are substantially larger than those of lower-order relativistic many-body perturbation theory (MBPT) and the results based on the relativistic coupled-cluster (RCC) method with single and double excitations (CCSD) are the most accurate to date for all the three properties that we have considered. We obtain $d_A = 4.85(6) \times 10^{-20} < \sigma > C_T \ |e| \ cm$ from T-PT interaction, $d_A=2.89(4) \times 10^{-17} {S/(|e|\ fm^3)}$ from NSM interaction and $\alpha_d=35.27(9) \ ea_0^3$. The former two results in combination with the measured value of $^{223}$Rn EDM, when it becomes available, could yield the best limits for the T-PT coupling constant, EDMs and chromo-EDMs of quarks and $\theta_{QCD}$ parameter, and would thereby shed light on leptoquark and supersymmetric models that predict CP violation.