Radial excitations and their potential impact on Fermi -decay rates
L. Xayavong🇰🇷 · Y. Lim🇰🇷 · N. A. Smirnova🇫🇷 · Calvin W. Johnson🇺🇸
We investigate the contribution of radial excitations to Fermi -decay matrix element. To this end, exact no-core shell model calculations are performed for the mirror 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 , 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 values obtained in the shell model approach, where radial excitations are not explicitly included, are likely overestimated. Based on experimental 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 nuclear decay tends however to worsen agreement with the Standard Model.