Evaluation of 2νββ decay nuclear matrix elements using Lanczos techniques preserving Gamow-Teller strengths from both parent and daughter nuclei
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 (2νECEC), 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 48Ca in the fp shell and apply them to candidates in different mass regions, including 58Ni, 76Ge, and 130Te. For 48Ca, a calculation allowing cross-shell excitations of up to 2ℏω in the sdpf model space yields a 2νββ NME closer to the experimental estimate than the result obtained in the fp shell. For 58Ni, we present, to our knowledge, the first shell-model calculation of the 2νβ+EC/2νECEC 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.
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BibTeX
@misc{patel2026evaluation,
title = {{Evaluation of $2νββ$ decay nuclear matrix elements using Lanczos techniques preserving Gamow-Teller strengths from both parent and daughter nuclei}},
author = {Deepak Patel and Anil Kumar and Noritaka Shimizu and Yutaka Utsuno},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02382},
eprint = {2611.02382},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02382},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evaluation of 2νββ decay nuclear matrix elements using Lanczos techniques preserving Gamow-Teller strengths from both parent and daughter nuclei
AU - Deepak Patel
AU - Anil Kumar
AU - Noritaka Shimizu
AU - Yutaka Utsuno
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02382
UR - https://arxiv.org/abs/2611.02382
AB - 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 (2νECEC), 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 ^48Ca in the fp shell and apply them to candidates in different mass regions, including ^58Ni, ^76Ge, and ^130Te. For ^48Ca, a calculation allowing cross-shell excitations of up to 2ℏω in the sdpf model space yields a 2νββ NME closer to the experimental estimate than the result obtained in the fp shell. For ^58Ni, we present, to our knowledge, the first shell-model calculation of the 2νβ^+EC/2νECEC 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.
ER -