Relativistic One-Electron Calculations of Shielded Atomic Hyperfine Constants

Core shielding effects in atomic hyperfine structure are examined within the framework of relativistic electron theory in the Hartree-Fock-Slater approximation. Expressions are developed for shielding factors pertaining to electric and magnetic hyperfine constants of arbitrary order. Known values of the nuclear magnetic moments for alkali and halogen atoms are used to obtain theoretical predictions of the dipole hyperfine constant "$a$" with shielding effects included. These theoretical values of $a$ are then compared with experiment as a test of the atomic model. Experimental values of the quadrupole and octupole hyperfine constants "$b$" and "$c$" for various halogen atoms are analyzed using the model to give revised values for nuclear quadrupole moments, as well as new values for octupole moments of Cl, Br, and I, including screening corrections.