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A series expansion of the interaction between a nucleus and its surroundingelectron distribution provides terms that are well-known in the study ofhyperfine interactions: the familiar quadrupole interaction and the lessfamiliar hexadecapole interaction. If the penetration of electrons into thenucleus is taken into account, various corrections to these multipoleinteractions appear. The best known one is a scalar correction related to theisotope shift and the isomer shift. This paper discusses a related tensorcorrection, which modifies the quadrupole interaction if electrons penetratethe nucleus: the quadrupole shift. We describe the mathematical formalism andprovide first-principles calculations of the quadrupole shift for a large setof solids. Fully relativistic calculations that explicitly take a finitenucleus into account turn out to be mandatory. Our analysis shows that thequadrupole shift becomes appreciably large for heavy elements. Implications forexperimental high-precision studies of quadrupole interactions and quadrupolemoment ratios are discussed. A literature review of other small quadrupole-likeeffects is presented as well.

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