Uncovering the mechanism of chiral three-nucleon force in driving spin-orbit splitting
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909256261828608 |
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| author | Fukui, Tokuro De Gregorio, Giovanni Gargano, Angela |
| author_facet | Fukui, Tokuro De Gregorio, Giovanni Gargano, Angela |
| contents | The three-nucleon force (3NF) is crucial in shaping the shell structure of atomic nuclei, particularly impacting the enhancement of spin-orbit (SO) splitting, especially in nuclei with significant deviations from stability. Despite its importance, the specific mechanisms driving this enhancement remain unclear. In this study, we introduce a decomposition scheme based on the rank of irreducible tensors forming the 3NF, derived from chiral effective field theory at next-to-next-to-leading order, to elucidate their influence on SO splitting. Within the shell-model framework, our analysis reveals that the rank-1 component of the 3NF is the primary factor enlarging the energy gap between the $0p_{3/2}$ and $0p_{1/2}$ single-particle levels in $p$-shell nuclei, while the rank-2 component makes a subdominant contribution. Since the rank-1 component originates exclusively from the $2π$-exchange 3NF, our finding will not depend on the choice of the low-energy constants of contact terms. We also remark on the antisymmetry of the rank-1 3NF, which can affect the quantum entanglement of spin states. This study lays the groundwork for further exploration into this field toward a microscopic understanding of the 3NF impact on the nuclear shell structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uncovering the mechanism of chiral three-nucleon force in driving spin-orbit splitting Fukui, Tokuro De Gregorio, Giovanni Gargano, Angela Nuclear Theory Nuclear Experiment The three-nucleon force (3NF) is crucial in shaping the shell structure of atomic nuclei, particularly impacting the enhancement of spin-orbit (SO) splitting, especially in nuclei with significant deviations from stability. Despite its importance, the specific mechanisms driving this enhancement remain unclear. In this study, we introduce a decomposition scheme based on the rank of irreducible tensors forming the 3NF, derived from chiral effective field theory at next-to-next-to-leading order, to elucidate their influence on SO splitting. Within the shell-model framework, our analysis reveals that the rank-1 component of the 3NF is the primary factor enlarging the energy gap between the $0p_{3/2}$ and $0p_{1/2}$ single-particle levels in $p$-shell nuclei, while the rank-2 component makes a subdominant contribution. Since the rank-1 component originates exclusively from the $2π$-exchange 3NF, our finding will not depend on the choice of the low-energy constants of contact terms. We also remark on the antisymmetry of the rank-1 3NF, which can affect the quantum entanglement of spin states. This study lays the groundwork for further exploration into this field toward a microscopic understanding of the 3NF impact on the nuclear shell structure. |
| title | Uncovering the mechanism of chiral three-nucleon force in driving spin-orbit splitting |
| topic | Nuclear Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2404.02007 |