Radial excitations and their potential impact on Fermi $β$-decay rates
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909624124309504 |
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| author | Xayavong, L. Lim, Y. Smirnova, N. A. Johnson, Calvin W. |
| author_facet | Xayavong, L. Lim, Y. Smirnova, N. A. Johnson, Calvin W. |
| contents | We investigate the contribution of radial excitations to Fermi $β$-decay matrix element. To this end, exact no-core shell model calculations are performed for the mirror $β$ decay of tritium, where full convergence can be achieved on an ordinary computer. The differences between the isospin-mixing correction values obtained in the full and in a restricted model spaces are matched to the radial overlap correction term, analogous to that required in the shell-model approach, where the configuration space is extremely limited. We examine this complementary correction term using a nonorthogonal harmonic-oscillator basis, generated by slightly differentiating the oscillator frequencies between the initial and final nuclei, while all desirable properties, including translational invariance, are still preserved. For $N_{\rm max}\le8$, we find that the radial excitation contribution is negative, with a typical magnitude of approximately 10\,\% to 20\,\% of the radial diagonal contribution. This effect becomes more pronounced as the model space increases. Therefore, the $δ_{C2}$ values obtained in the shell model approach, where radial excitations are not explicitly included, are likely overestimated. Based on experimental $ft$ data and the corrective terms adopted in the survey by Hardy and Towner [Phys. Rev. C {\bf 102}, 045501 (2020)], we show that the incorporation of radial excitations for the superallowed $0^+\rightarrow0^+$ nuclear $β$ decay tends however to worsen agreement with the Standard Model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Radial excitations and their potential impact on Fermi $β$-decay rates Xayavong, L. Lim, Y. Smirnova, N. A. Johnson, Calvin W. Nuclear Theory Nuclear Experiment We investigate the contribution of radial excitations to Fermi $β$-decay matrix element. To this end, exact no-core shell model calculations are performed for the mirror $β$ decay of tritium, where full convergence can be achieved on an ordinary computer. The differences between the isospin-mixing correction values obtained in the full and in a restricted model spaces are matched to the radial overlap correction term, analogous to that required in the shell-model approach, where the configuration space is extremely limited. We examine this complementary correction term using a nonorthogonal harmonic-oscillator basis, generated by slightly differentiating the oscillator frequencies between the initial and final nuclei, while all desirable properties, including translational invariance, are still preserved. For $N_{\rm max}\le8$, we find that the radial excitation contribution is negative, with a typical magnitude of approximately 10\,\% to 20\,\% of the radial diagonal contribution. This effect becomes more pronounced as the model space increases. Therefore, the $δ_{C2}$ values obtained in the shell model approach, where radial excitations are not explicitly included, are likely overestimated. Based on experimental $ft$ data and the corrective terms adopted in the survey by Hardy and Towner [Phys. Rev. C {\bf 102}, 045501 (2020)], we show that the incorporation of radial excitations for the superallowed $0^+\rightarrow0^+$ nuclear $β$ decay tends however to worsen agreement with the Standard Model. |
| title | Radial excitations and their potential impact on Fermi $β$-decay rates |
| topic | Nuclear Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2505.20587 |