Electron penetration in the nucleus and its effect on the quadrupole interaction

A series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known one is a scalar correction related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well

Quadrupole moments of Cd and Zn nuclei: When solid-state, molecular, atomic, and nuclear theory meet

The nuclear quadrupole moment $(Q)$ of the $5/2^+$ isomeric state of $^{111}$Cd, of particular importance to the interpretation of Perturbed Angular Correlation experiments in condensed matter, was determined by combining existing PAC data with high-level ab initio (CCSD(T)) calculations for Cd-dimethyl and hybrid density functional theory for metallic Cd. A revised value of $Q =.641(25)\text{ b}$ is found, much reduced from earlier estimates. Using the new result together with the values for other Cd isotopes from atomic data, also recently revised, the trend of $Q$ for the $11/2^−$ states in Cd is in perfect agreement with new nuclear covariant density functional theory calculations. Similar theoretical work for metallic Zn and the ZnS molecule, combined with atomic calculations, also results in an equivalent reduction for the reference value of the $^{67} \text{Zn} 5/2^−$ ground-state quadrupole moment to $Q=.125(5)\text{ b}$