Electronic Final States in Nuclear $β$ Decay: A Sudden-Approximation Framework
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911625245622272 |
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| author | D'yakonov, G. V. |
| author_facet | D'yakonov, G. V. |
| contents | Electronic final states generated by sudden changes of the Hamiltonian are studied here, with emphasis on nuclear charge variation in $β$ decay. A $λ$-parametrized family $\hat H(λ)$ that continuously connects the initial and final Hamiltonians, so that the electronic response can be represented as a continuous deformation in Hilbert space, is introduced. Within the sudden approximation, transition amplitudes are written as overlaps between eigenstates of distinct Hamiltonians. To relate non-orthogonal one-electron basis sets in a stable way, the paper uses a practical transport scheme based on overlap metrics and truncated singular value decomposition (SVD). This mapping is interpreted as a discrete counterpart of continuous transport along the $λ$ path. The formalism is first developed for the one-electron case, where analytic structure and selection rules are made explicit, and then generalized to many-electron systems via nonorthogonal determinant overlap expressions. The resulting formulation gives transition probabilities in bound and continuum channels in a way that is both numerically stable and easy to interpret. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Electronic Final States in Nuclear $β$ Decay: A Sudden-Approximation Framework D'yakonov, G. V. Chemical Physics Quantum Physics Electronic final states generated by sudden changes of the Hamiltonian are studied here, with emphasis on nuclear charge variation in $β$ decay. A $λ$-parametrized family $\hat H(λ)$ that continuously connects the initial and final Hamiltonians, so that the electronic response can be represented as a continuous deformation in Hilbert space, is introduced. Within the sudden approximation, transition amplitudes are written as overlaps between eigenstates of distinct Hamiltonians. To relate non-orthogonal one-electron basis sets in a stable way, the paper uses a practical transport scheme based on overlap metrics and truncated singular value decomposition (SVD). This mapping is interpreted as a discrete counterpart of continuous transport along the $λ$ path. The formalism is first developed for the one-electron case, where analytic structure and selection rules are made explicit, and then generalized to many-electron systems via nonorthogonal determinant overlap expressions. The resulting formulation gives transition probabilities in bound and continuum channels in a way that is both numerically stable and easy to interpret. |
| title | Electronic Final States in Nuclear $β$ Decay: A Sudden-Approximation Framework |
| topic | Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2604.23910 |