Calculation of the Differential Breit–Rosenthal Effect in the 6s6p 3P1,2 States of Hg

Abstract

Studies of the hyperfine anomaly has found a renewed interest with the recent development of techniques to study the properties of long chains of unstable nuclei. By using the hyperfine structure for determining the nuclear magnetic dipole moments, the hyperfine anomaly puts a limit to the accuracy. In this paper, the differential Breit–Rosenthal effect is calculated for the 6s6p3P1,2 states in 199Hg as a function of the change in nuclear radii, using the MCDHF code, GRASP2018. The differential Breit–Rosenthal effect was found to be of the order of 0.1%fm−2, in most cases much less than the Bohr-Weisskopf effect. The results also indicate that large calculations might not be necessary, with the present accuracy of the experimental values for the hyperfine anomaly.

Table of Hyperfine Anomaly in Atomic Systems - 2023

“…This will open possibilities for systematic studies as it will become easier to compare experimental values with calculations. In addition, as was found by Heggset et al [12] the BR-effect can be calculated readily using the present GRASP code, it is still interesting to study the effect using a more realistic charge distribution for heavy nuclei [19].…”

“…It is well established that the hfa (BW-effect) attains rather similar values within the same nuclear configuration and spin as has been observed in Fr (I = 9/2), Hg (I = 13/2), Pb (I = 13/2) and Eu (I = 5/2). In these cases, the BR-effect may be on the same order as the BW-effect [12] and cannot be neglected. Since it is possible to calculate the BR-effect it is possible to assume a smaller uncertainty in the determination of the nuclear magnetic dipole moment of unstable isotopes if the hfa (BW-and BR-effect) is known in an isotope with the same nuclear configuration.…”

Calculation of the Differential Breit-Rosenthal Effect in Pb

“…where the change in charge radius can be obtained from tables [10] or isotope shift studies. This work is a continuation of the calculations of the BR-effect completed by Heggset and Persson in the 6s6p 3 P 1,2 states in Hg [11].…”

“…First, we aim to expand the data set of differential BR-effect as a function of changes in nuclear charge radius in heavy atoms, building on the results of Heggset et al [11]. Second, we seek to explore the effect of extending the configuration expansion in Multi-Configurational Dirac-Hartree-Fock (MCDHF) calculations on the BR-anomaly, as this seemed to be relatively independent on the size of the expansions in Hg [11]. This will shed light on the extent of expansions required in the calculations for other heavy atoms.…”

The hyperfine anomaly in heavy atoms and its role in precision atomic searches for new physics

“…, where A 00 is the hyperfine constant with pointlike nuclear magnetic and charge distributions. Since the nuclear charge distribution is known with relatively high accuracy, errors associated with the Breit-Rosenthal correction are typically negligible [29,53,54]. Note that radiative quantum electrodynamics (QED) corrections contribute to the hyperfine structure with comparable size to ǫ [27, 49, 55], though they are largely independent of the isotope and therefore mostly cancel in the differential hyperfine anomaly considered below.…”