径向激发及其对费米β衰变速率的潜在影响
Radial excitations and their potential impact on Fermi $β$-decay rates
AI总结：
本文研究径向激发对费米β衰变的影响，通过无芯壳模型计算发现其贡献为负且随模型空间增大而增强，导致壳模型δ_C2值被高估，但纳入后反而恶化与标准模型的一致性。
摘要：
我们研究了径向激发对费米β衰变矩阵元的贡献。为此，对氚的镜像β衰变进行了精确的无芯壳模型计算，在普通计算机上即可实现完全收敛。在完整模型空间和受限模型空间中获得的同位旋混合修正值之间的差异，与径向重叠修正项相匹配，类似于壳模型方法中所需的修正项，其中构型空间极其有限。我们使用非正交谐振子基来检验这一互补修正项，该基通过在初始核和末态核之间略微区分谐振子频率而产生，同时所有理想性质（包括平移不变性）仍然保持。对于N_max≤8，我们发现径向激发贡献为负，典型幅度约为径向对角贡献的10%至20%。随着模型空间的增大，这种效应变得更加显著。因此，在壳模型方法中获得的δ_C2值（其中未明确包含径向激发）可能被高估。基于实验ft数据和Hardy与Towner [Phys. Rev. C 102, 045501 (2020)]调查中采用的修正项，我们表明，对于超允许0^+→0^+核β衰变，纳入径向激发倾向于恶化与标准模型的一致性。
英文摘要：
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.
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