Removal of $K$-mixing in angular momentum projected nuclear wave functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913492429176832 |
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| author | Lu, Xiao Lian, Zhan-Jiang Gao, Zao-Chun |
| author_facet | Lu, Xiao Lian, Zhan-Jiang Gao, Zao-Chun |
| contents | Angular momentum projection plays a key role in studying quantum many-body systems with rotational invariance such as atomic nuclei. At a given spin $J$, one can generate $2J+1$ angular momentum projected states labeled with $-J\leq K \leq J$ from a deformed Slater determinant. Usually, a nuclear wave function with $K$-mixing can be expressed as a superposition of all these $2J+1$ projected states, where the coefficients can be obtained by solving the generalized eigenvalue equation. In this Letter, we report a new fundamental feature that the frequently discussed $K$-mixing in the angular momentum projected nuclear wave function can be safely removed. Strikingly, we found that such nuclear wave function with $K$-mixing can always be equivalently replaced by a single projected state with any given $K$. Consequently, such nuclear wave function can be significantly simplified, especially for high-spin states. This also indicates that the $K$-mixing in the angular momentum projected nuclear wave functions, adopted by many present-day nuclear models, does not carry any physical meaning, and is essentially different from that $K$-mixing caused by the Coriolis force in the cranked shell model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06521 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Removal of $K$-mixing in angular momentum projected nuclear wave functions Lu, Xiao Lian, Zhan-Jiang Gao, Zao-Chun Nuclear Theory Angular momentum projection plays a key role in studying quantum many-body systems with rotational invariance such as atomic nuclei. At a given spin $J$, one can generate $2J+1$ angular momentum projected states labeled with $-J\leq K \leq J$ from a deformed Slater determinant. Usually, a nuclear wave function with $K$-mixing can be expressed as a superposition of all these $2J+1$ projected states, where the coefficients can be obtained by solving the generalized eigenvalue equation. In this Letter, we report a new fundamental feature that the frequently discussed $K$-mixing in the angular momentum projected nuclear wave function can be safely removed. Strikingly, we found that such nuclear wave function with $K$-mixing can always be equivalently replaced by a single projected state with any given $K$. Consequently, such nuclear wave function can be significantly simplified, especially for high-spin states. This also indicates that the $K$-mixing in the angular momentum projected nuclear wave functions, adopted by many present-day nuclear models, does not carry any physical meaning, and is essentially different from that $K$-mixing caused by the Coriolis force in the cranked shell model. |
| title | Removal of $K$-mixing in angular momentum projected nuclear wave functions |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2303.06521 |