The role of electron correlation in the hyperfine structure of alkali metals and alkaline earth metal monopositive ions in their ground electronic configuration is investigated using the Z-vector method in a relativistic coupled-cluster regime within the singles and doubles approximation. The systematic effects of core-correlating functions, polarization of core electrons, and high-lying virtual functions on core electrons correlation are studied. The study reveals that the core-correlating function plays a significant role in core polarization and thus is very important for precise calculation of the wave function near the nuclear region. The inner-core electrons (1s-2p) require very high virtual energy functions for proper correlation. Therefore, the all-electron correlation treatment and the inclusion of higher-energy virtual functions are the key factors for precise calculation of the hyperfine structure constant of atoms. Our calculated values are in excellent agreement with the available experimental values, which also implies that the wave function produced by the Z-vector method is accurate enough for further calculation of the parity- and time-reversal symmetry-violating properties in atoms and molecules.

Foreign