Relativistic normal coupled-cluster theory analysis of second- and third-order electric polarizabilities of Zn i

We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results, including those obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. We also give a term-by-term comparison of contributions from our CC and NCC calculations in order to show differences in the results from these two methods. Moreover, we present results from other lower-order methods to understand the role of electron correlation effects in the determination of the above quantities. A machine-learning-based scheme to generate optimized basis functions for atomic calculations is developed and applied here. From the analysis of the dipole polarizability result, the accuracy of the calculated quadrupole and third-order polarizability values is ascertained, for which no experimental values are currently available.