β-Oslo and Shape analyses with unresolved parent-state mixtures
Abstract
An unresolved mixture of beta-decaying ground and isomeric states populates a common daughter nucleus through different excitation-energy and spin-parity distributions. A framework is developed to determine when such data admit conventional β-Oslo and Shape analyses and which quantities remain identifiable. The physical primary-γ distribution is an average of separately normalized branching kernels; the global parent fraction does not, in general, equal the fraction in an excitation-energy bin or an accepted primary-γ sample. Population invariance, Oslo factorization, and recovery of the total nuclear level density are separated. An exact log-linear compatibility test and a lower-cascade replacement identity isolate factorization and first-generation-subtraction effects. For Shape analysis, matched final-state spins and parities remove common angular-momentum factors but can retain excitation-dependent E1/M1 weights. A graph representation gives consistency conditions and exposes the information lost when only one fixed final-state separation is measured. Deterministic spin-parity-resolved cascade benchmarks reproduce the population-invariant limit and exhibit both exact factorization with an effective, rather than total, level density and small matrix residuals accompanied by appreciable shape errors. Evaluated rb→sr properties specify a relevant application, including two 2+ candidate final states and time-dependent parent mixing. The numerical examples are controlled synthetic tests, not an extraction from 90Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.
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BibTeX
@misc{shen2026βoslo,
title = {{$β$-Oslo and Shape analyses with unresolved parent-state mixtures}},
author = {Yangping Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38200},
eprint = {2609.38200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38200},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - β-Oslo and Shape analyses with unresolved parent-state mixtures
AU - Yangping Shen
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.38200
UR - https://arxiv.org/abs/2609.38200
AB - An unresolved mixture of beta-decaying ground and isomeric states populates a common daughter nucleus through different excitation-energy and spin-parity distributions. A framework is developed to determine when such data admit conventional β-Oslo and Shape analyses and which quantities remain identifiable. The physical primary-γ distribution is an average of separately normalized branching kernels; the global parent fraction does not, in general, equal the fraction in an excitation-energy bin or an accepted primary-γ sample. Population invariance, Oslo factorization, and recovery of the total nuclear level density are separated. An exact log-linear compatibility test and a lower-cascade replacement identity isolate factorization and first-generation-subtraction effects. For Shape analysis, matched final-state spins and parities remove common angular-momentum factors but can retain excitation-dependent E1/M1 weights. A graph representation gives consistency conditions and exposes the information lost when only one fixed final-state separation is measured. Deterministic spin-parity-resolved cascade benchmarks reproduce the population-invariant limit and exhibit both exact factorization with an effective, rather than total, level density and small matrix residuals accompanied by appreciable shape errors. Evaluated rb→sr properties specify a relevant application, including two 2^+ candidate final states and time-dependent parent mixing. The numerical examples are controlled synthetic tests, not an extraction from ^90Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.
ER -