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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 paperdoi:10.1103/physreva.81.032507 fatcat:rk2il6lzdvdavfzfbi5xarh7da