Green's-function approach to the hyperfine problem in atoms and molecules

To avoid the shortcomings of conventional methods such as the symmetry dilemma and the subtraction of large numbers of roughly equal magnitude, a Green's-function method is extended to the study of hyperfine splitting in atoms and molecules. With this method the hyperfine coupling constants are calculated for the ground and excited states of the molecule by a self-consistent equation, starting from the Hartree-Fock level of a closed-shell system. In this approach the one-particle picture is retained, and it is possible to study the hyperfine problem from a different physical point of view. The theory is applied to the calculation of the ground-state and some excited-state hyperfine coupling constants of Li and C${\mathrm{H}}_3$. It is shown that those terms of the perturbation expansion which are essential to explain the constant of the atom are unessential in the case of the methyl radical and vice versa. This result is generalized. The computational effort to evaluate the coupling constants has been found to be very small.