On the Evaluation of Electric Quadrupole Moments from Experimental Hyperfine Interaction Constants

A general discussion of the procedure for the evaluation of quadrupole moments from experimental hyperfine interaction constants is given. Comparison has been performed between ab initio calculations and semiempirical methods in which a mean value of r -3 is obtained from the experimental magnetic hyperfine structure. Results are given for boron, fluorine, aluminium and chlorine. The semiempirical mean values of r -3 derived from the magnetic hyperfine structure are shown to include higher-order perturbations in the orbital and spin-dipole terms. If one uses these ⟨ r -3 ⟩ values and corrects them for the quadrupole polarization with the factors given by Sternheimer a rather good agreement is obtained with the ⟨ r -3 ⟩ q values calculated with the "polarization" wavefunction by Schaefer et al. for boron and fluorine. For boron there is a difference of about eight per cent to the Bethe-Goldstone calculations performed by Nesbet. For aluminium and chlorine the semiempirical r -3 values are in rather good agreement with results obtained with orbital-polarized Hartree-Fock (OPHF) wavefunctions.