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

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 correction is a scalar term 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 (pseudoquadrupole effect, isotopologue anomaly, etc.).

Hyperfine spectrum of NaF

“…There are, however, additional considerations to take into account. Koch et al [13] have called attention to the need for calculation of a shift due to the electron penetration of the nucleus, and there is also the unexplained isotopologue anomaly that we identified in our spectrum of LiI [14], where the eQq of iodine was found to change with the change of lithium isotopes. Since we are not in a position to estimate these effects, we have not attempted to recalculate the sodium nuclear moment.…”

Communication: On the isotope anomaly of nuclear quadrupole coupling in molecules

“…6 Therefore, to facilitate its experimental detection, it was proposed 7 to use a relative quadrupole anomaly…”

“…6,7 For example, in the case of RbF, using the un-contracted quadruple-zeta (QZ) basis set of Dyall 27 for Rb and the un-contracted aug-cc-pVQZ basis 28 for F in connection with the NESC/MP2 method, V , are calculated for RbI, using the Dyall's un-contracted QZ basis set 27 for both atoms. The close agreement of these values with the estimates reported in Refs.…”

“…Although the first theoretical evaluation of in molecules yielded an extremely small effect, 5 the interest in the quadrupole anomaly and in the impact of nuclear volume on NQI was recently revived in the works of Cottenier and co-workers 6,7 who surmised that experimental observation of quadrupole anomaly can be within reach.…”

“…6,7 If there were no such a dependence, the ratio of NQCCs for different isotopes would remain the same for different compounds of the given element. As NQCCs can be measured with sufficiently high precision, 4 the dependence of the ratio (2) on the chemical environment should be detectable experimentally.…”