Electronic Final States in Nuclear $β$ Decay: A Sudden-Approximation Framework

• URL: http://arxiv.org/abs/2604.23910v1
• Date: Sun, 26 Apr 2026 23:06:31 GMT
• Title: Electronic Final States in Nuclear $β$ Decay: A Sudden-Approximation Framework
• Abstract summary: Electronic final states generated by sudden changes of the Hamiltonian are studied here.<n>A $$-parametrized family $hat H()$ that continuously connects the initial and final Hamiltonians is introduced.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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