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

TL;DR

This paper investigates how electron penetration into the nucleus causes a quadrupole shift, affecting hyperfine interactions, especially in heavy elements, with implications for high-precision experimental measurements.

Contribution

It introduces a tensor correction called the quadrupole shift due to electron penetration, supported by first-principles relativistic calculations across various solids.

Findings

Quadrupole shift is significant in heavy elements.

Relativistic calculations with finite nuclei are essential.

Impacts high-precision hyperfine interaction studies.

Abstract

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.