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Re-Evaluation of the Nuclear Magnetic Octupole Moment of ^{209}Bi

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## Abstract

**:**

**1970**, 1, 685] and ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{P}_{3/2}^{o}$ [Landman, D.A.; Lurio, A. Phys. Rev. A

**1970**, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of ${}^{209}$Bi.

## 1. Introduction

## 2. Theory

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Electronic factors of the magnetic dipole (${A}_{\mathrm{el}}$ in MHz/${\mu}_{\mathrm{N}}$) and magnetic octupole ($-C/\mathsf{\Omega}$ in kHz/(${\mu}_{\mathrm{N}}\times $b)) hyperfine interaction constants of states in the [Kr]$4{d}^{10}4{f}^{14}5{s}^{2}5{p}^{6}5{d}^{10}6{s}^{2}6{p}^{3}$ ground configuration of Bi.

Models | ${}^{4}\phantom{\rule{-0.166667em}{0ex}}{\mathit{S}}_{3/2}^{\mathit{o}}$ | ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{\mathit{D}}_{3/2}^{\mathit{o}}$ | ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{\mathit{D}}_{5/2}^{\mathit{o}}$ | ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{\mathit{P}}_{3/2}^{\mathit{o}}$ | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{A}}_{\mathrm{el}}$ | $-\mathit{C}/\mathsf{\Omega}$ | ${\mathit{A}}_{\mathrm{el}}$ | $-\mathit{C}/\mathsf{\Omega}$ | ${\mathit{A}}_{\mathrm{el}}$ | $-\mathit{C}/\mathsf{\Omega}$ | ${\mathit{A}}_{\mathrm{el}}$ | $-\mathit{C}/\mathsf{\Omega}$ | |

DHF | 41.9 | −22.5 | −530 | 14.6 | 2954 | 68.9 | 883 | −33.4 |

MR-CI | −572 | −32.4 | −1357 | 24.1 | 2691 | 83.2 | 13,245 | −41.7 |

CV${}_{3}$ | −540 | −32.9 | −1370 | 24.5 | 3017 | 84.4 | 13,427 | −42.3 |

+Breit | −554 | −32.6 | −1338 | 24.2 | 3007 | 84.3 | 13,365 | −42.2 |

${\mathsf{\Omega}}_{\mathbf{SP}}$ | This Work | Others | ||||
---|---|---|---|---|---|---|

${}^{4}\phantom{\rule{-0.166667em}{0ex}}{\mathit{S}}_{3/2}^{\mathit{o}}$ | ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{\mathit{P}}_{3/2}^{\mathit{o}}$ | Average | ${}^{4}\phantom{\rule{-0.166667em}{0ex}}{\mathit{S}}_{3/2}^{\mathit{o}}$ [24] | ${}^{2}\phantom{\rule{-0.166667em}{0ex}}{\mathit{P}}_{3/2}^{\mathit{o}}$ [25] | NS [4] | |

0.127 | 0.56 | 0.46 | 0.51(5) | 0.43 | 0.55(3) | 0.48 |

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**MDPI and ACS Style**

Li, J.; Gaigalas, G.; Bieroń, J.; Ekman, J.; Jönsson, P.; Godefroid, M.; Froese Fischer, C. Re-Evaluation of the Nuclear Magnetic Octupole Moment of ^{209}Bi. *Atoms* **2022**, *10*, 132.
https://doi.org/10.3390/atoms10040132

**AMA Style**

Li J, Gaigalas G, Bieroń J, Ekman J, Jönsson P, Godefroid M, Froese Fischer C. Re-Evaluation of the Nuclear Magnetic Octupole Moment of ^{209}Bi. *Atoms*. 2022; 10(4):132.
https://doi.org/10.3390/atoms10040132

**Chicago/Turabian Style**

Li, Jiguang, Gediminas Gaigalas, Jacek Bieroń, Jörgen Ekman, Per Jönsson, Michel Godefroid, and Charlotte Froese Fischer. 2022. "Re-Evaluation of the Nuclear Magnetic Octupole Moment of ^{209}Bi" *Atoms* 10, no. 4: 132.
https://doi.org/10.3390/atoms10040132