Calculation of the volume dependence of the electron density at the nucleus for the elements Li through Am. Relationship of this volume dependence to the hyperfine field for the elements dissolved in a ferromagnetic host

We have calculated the volume derivative of the electron density at the nucleus, ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$, in a self-consistent model of Dirac, Kohn, Sham, Hartree, Wigner, and Seitz for the elements $3\le Z\le 95$. These calculated ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$ show a systematic oscillatory behavior with atomic number $Z$ which is in qualitative agreement with available experimental high-pressure data. Also, as a function of $Z$, ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$ shows much similarity to $H_{\mathrm{hf}}\mathrm{}(Z,X)\mathrm{}$, the measured hyperfine field for an element $Z$ in dilute solution in a ferromagnetic host $X$, for example, in Fe, Co, or Ni. For the $s-p$ elements as solutes, this similarity may be described approximately in terms of Wigner-Seitz models for both ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$ and $H_{\mathrm{hf}}\mathrm{}(Z,X)\mathrm{}$. The Wigner-Seitz model which we use to describe $H_{\mathrm{hf}}\mathrm{}(Z,X)\mathrm{}$ is that due to Daniel and Friedel. These calculated $H_{\mathrm{hf}}\mathrm{}(Z,X)\mathrm{}$ are compared with experiment and with ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$. The similarity between $H_{\mathrm{hf}}\mathrm{}(Z,X)\mathrm{}$ and ${\gamma }_V\mathrm{}\left(Z\right)\mathrm{}$ is associated with a relationship between the magnetic susceptibility and the compressibility of the electron gas of the solid as viewed from the solute nuclei.