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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.13013 |
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| _version_ | 1866912127323734016 |
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| author | Zhang, Yu-Shan Dang, Wei Wang, Kai Tang, Yong-Bo |
| author_facet | Zhang, Yu-Shan Dang, Wei Wang, Kai Tang, Yong-Bo |
| contents | Using relativistic multiconfiguration Dirac-Hartree-Fock method, we calculate the hyperfine-structure properties of the $2s2p$ $^3\!P_{J}$ state in $^9$Be. The hyperfine-structure properties encompass first-order hyperfine-structure parameters, as well as second-order and third-order corrections arising from the hyperfine mixing of different $2s2p$ $^3\!P_{J}$ levels. Based on our theoretical results, we reanalyze the previously reported measurement of the hyperfine interval for the $2s2p$ $^3\!P$ state in $^9$Be [A. G. Blachman and A. Lurio, Phys. Rev. 153, 164(1967)], yielding updated hyperfine-structure constants. Our results show that the hyperfine-structure constant $B$ of $2s2p$ $^3\!P_{1}$ is notably sensitive to second-order correction. Conversely, accurately determining the hyperfine-structure constant $B$ of $2s2p$ $^3\!P_{2}$ necessitates consideration of the hyperfine-structure constant $C$ in the first-order hyperfine interaction equation. The updated hyperfine-structure constant $B$ of the $2s2p$ $^3\!P_{2}$ state is found to be $1.4542(67)$~MHz, which is approximately $1.7\%$ larger than the previous value of $1.427(9)$~MHz.
By combining our theoretical results with the updated hyperfine-structure constant for the $2s2p$ $^3\!P_{2}$ state, we extract the electric quadrupole moment $Q$ of $^9$Be nucleus to be $0.05320(50)$~b. This value is consistent with the most recent determination using the few-body precision calculation method. Additional, we also discuss the reasons for the discrepancy between the $Q$ values obtained through few-body and previous many-body calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting the hyperfine interval for the $2s2p$ $^3\!P_{J}$ state in $^9$Be Zhang, Yu-Shan Dang, Wei Wang, Kai Tang, Yong-Bo Atomic Physics Using relativistic multiconfiguration Dirac-Hartree-Fock method, we calculate the hyperfine-structure properties of the $2s2p$ $^3\!P_{J}$ state in $^9$Be. The hyperfine-structure properties encompass first-order hyperfine-structure parameters, as well as second-order and third-order corrections arising from the hyperfine mixing of different $2s2p$ $^3\!P_{J}$ levels. Based on our theoretical results, we reanalyze the previously reported measurement of the hyperfine interval for the $2s2p$ $^3\!P$ state in $^9$Be [A. G. Blachman and A. Lurio, Phys. Rev. 153, 164(1967)], yielding updated hyperfine-structure constants. Our results show that the hyperfine-structure constant $B$ of $2s2p$ $^3\!P_{1}$ is notably sensitive to second-order correction. Conversely, accurately determining the hyperfine-structure constant $B$ of $2s2p$ $^3\!P_{2}$ necessitates consideration of the hyperfine-structure constant $C$ in the first-order hyperfine interaction equation. The updated hyperfine-structure constant $B$ of the $2s2p$ $^3\!P_{2}$ state is found to be $1.4542(67)$~MHz, which is approximately $1.7\%$ larger than the previous value of $1.427(9)$~MHz. By combining our theoretical results with the updated hyperfine-structure constant for the $2s2p$ $^3\!P_{2}$ state, we extract the electric quadrupole moment $Q$ of $^9$Be nucleus to be $0.05320(50)$~b. This value is consistent with the most recent determination using the few-body precision calculation method. Additional, we also discuss the reasons for the discrepancy between the $Q$ values obtained through few-body and previous many-body calculations. |
| title | Revisiting the hyperfine interval for the $2s2p$ $^3\!P_{J}$ state in $^9$Be |
| topic | Atomic Physics |
| url | https://arxiv.org/abs/2411.13013 |