Hartree Computation of the Internal Diamagnetic Field for Atoms

For an atom or monatomic ion in a magnetic field $H$ there will be an induced shielding field $H^{\prime }\mathrm{}\left(0\right)\mathrm{}$ at the the nucleus given by $H^{\prime }\mathrm{}\left(0\right)=\left(\frac{\mathrm{eH}}{3m{c}^2}\right)v\left(0\right)\mathrm{}$ where $v\left(0\right)\mathrm{}$ is the electrostatic potential produced at the nucleus by the atomic electrons. Using the Thomas-Fermi model, Lamb put this expression into a calculable form. However, in modern nuclear induction and resonance absorption experiments it is important to have a more precise knowledge of the magnitude of this shielding field. In this paper computed values of $v\left(0\right)\mathrm{}$ are given for all atoms and singly charged ions which have been treated by the Hartree or Hartree-Fock approximations to the self-consistent field method. By interpolation a list of $\frac{H^{\prime }\mathrm{}\left(0\right)\mathrm{}}{H}$ values for all neutral atoms is given. Although it is impossible to check the accuracy of these values experimentally it is estimated from other evidence that they can be trusted to within five percent. An exception must be made, however, for the heaviest atoms where the relativity effect becomes appreciable, amounting to an estimated six percent correction to $\frac{H^{\prime }\mathrm{}\left(0\right)\mathrm{}}{H}$ for $Z=92\mathrm{}$. Finally, the usefulness of accurate values of the atomic shielding field in analyzing the total shielding field in molecules is discussed.