Precise Determination of Electric Dipole Polarizabilities of Sr Clock States Using Linear-Response and Equation-of-Motion Relativistic Coupled-Cluster Methods

We present accurate values of the electric dipole polarizabilities ($α$) of the ground and excited states of Sr using four-component relativistic coupled-cluster (RCC) theory within the linear-response (LR) and equation-of-motion (EOM) frameworks. We first investigated accuracy of the ground-state polarizability using the LR-RCC method in both spherical and Cartesian coordinate representations. Upon obtaining consistent results for the ground state, we determine the polarizabilities of the excited states using the EOM-RCC method within the finite-field approach. The uncertainties in our results are assessed by examining the completeness of the basis set, higher-order relativistic corrections, and contributions from higher-level excitation configurations beyond the truncation in our RCC method. We also discuss various procedures for extrapolating contributions to the complete basis set limit and examine their respective limitations. Our calculated ground-state polarizability is found to be inconsistent with the latest atomic calculation, but agrees with other calculations and experimental value. Using the differential $α$ value from the EOM-RCC method, we estimate the fractional black-body-radiation-induced frequency shift of the Sr $^{1}$S_{0}$$\rightarrow$$^{3}P$_{0}$ clock transition to be $-5.40\times10^{-15}$.

Source: arXiv:2610.31232v1 - http://arxiv.org/abs/2610.31232v1 PDF: https://arxiv.org/pdf/2610.31232v1 Original Link: http://arxiv.org/abs/2610.31232v1