{
  "abstract": "We present two efficient shell-model approaches for calculating nuclear matrix elements (NMEs) for two-neutrino double-beta ($2νββ$) decay and two-neutrino double-electron capture ($2ν$ECEC), based on the Lanczos strength-function and block-Lanczos techniques. The dual-sided Lanczos strength-function (DLSF) and block-Lanczos strength-function (BLSF) methods avoid the explicit calculation of a complete set of exact intermediate $1^+$ eigenstates and yield fully converged NMEs with a relatively small number of iterations starting from Gamow--Teller (GT) doorway states. Both methods simultaneously preserve the total GT strengths associated with the initial and final nuclei. We benchmark the methods for $^{48}$Ca in the $fp$ shell and apply them to candidates in different mass regions, including $^{58}$Ni, $^{76}$Ge, and $^{130}$Te. For $^{48}$Ca, a calculation allowing cross-shell excitations of up to $2\\hbarω$ in the $sdpf$ model space yields a $2νββ$ NME closer to the experimental estimate than the result obtained in the $fp$ shell. For $^{58}$Ni, we present, to our knowledge, the first shell-model calculation of the $2νβ^+$EC/$2ν$ECEC NME. Comparison with the current experimental upper limit on the NME indicates the need for a more sensitive measurement of the $2νβ^+$EC half-life. As an independent validation, the energy-denominator-free sums obtained with the proposed methods are compared with the corresponding double-GT matrix elements calculated directly between the initial and final ground states. Their agreement demonstrates that the methods correctly recover the complete energy-denominator-free intermediate-state sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02382",
  "author_total": 4,
  "authors": [
    {
      "name": "Deepak Patel"
    },
    {
      "name": "Anil Kumar"
    },
    {
      "name": "Noritaka Shimizu"
    },
    {
      "name": "Yutaka Utsuno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zkaq74qdkhyy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02382",
  "fulltext_url": null,
  "id": "7zkaq74qdkhyy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02382",
  "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-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zkaq74qdkhyy.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02382"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Evaluation of $2νββ$ decay nuclear matrix elements using Lanczos techniques preserving Gamow-Teller strengths from both parent and daughter nuclei",
  "title_text": "Evaluation of 2νββ decay nuclear matrix elements using Lanczos techniques preserving Gamow-Teller strengths from both parent and daughter nuclei",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/7zkaq74qdkhyy",
  "venue": "arXiv",
  "versions": []
}