{
  "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 $\\rb\\rightarrow\\sr$ 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 $^{90}$Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38200",
  "author_total": 1,
  "authors": [
    {
      "name": "Yangping Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0h6j0tpv9bee.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38200",
  "fulltext_url": null,
  "id": "b0h6j0tpv9bee",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38200",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nucl-ex"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3106|Nuclear physics research studies"
    ]
  ],
  "openalex": "W7215068194",
  "pdf_url": "https://arxiv.org/pdf/2609.38200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0h6j0tpv9bee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.38200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38200"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-ex",
      "subfield": "nuclear"
    }
  ],
  "title": "$β$-Oslo and Shape analyses with unresolved parent-state mixtures",
  "title_text": "β-Oslo and Shape analyses with unresolved parent-state mixtures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/b0h6j0tpv9bee",
  "venue": "arXiv",
  "versions": []
}