Exchange correction for allowed β decay

AbstraktAbstract

We investigate the exchange effect between the final atom's bound electrons and those emitted in the allowed beta decay of the initial nucleus. The electron wave functions are obtained with the Dirac-Hartree-Fock-Slater self-consistent method, and we ensure the orthogonality between the continuum and bound electron states, in the potential of the final atom, by modifying the last iteration of the self-consistent method. We show that orthogonality plays an essential role in calculating the exchange correction. After imposing the orthogonality, we found considerable differences in magnitude and energy dependence compared to previous results. We argue that our findings can solve the mismatch between the previous predictions and experimental measurements in the low-energy region of the beta spectrum. First, we calculate the exchange effect for the low-energy beta transitions in 14C, 45Ca, 63Ni, and 241Pu, recently investigated in the literature. Next, we compute the total exchange correction for a large number of beta emitters with Z from 1 to 102. From the systematic study, we found that for ultralow energy, i.e., 5 eV, the Z dependence of the total exchange effect is affected by s1/2 and p1/2 orbitals closure. We also show that the contributions from orbitals higher than the 2s1/2 orbital are essential for correctly calculating the total effect, especially for low energies and heavy beta emitters. Finally, we provide an analytical expression of the total exchange correction for each atomic number for easy implementation in experimental investigations.

We investigate the exchange effect between the final atom's bound electrons and those emitted in the allowed beta decay of the initial nucleus. The electron wave functions are obtained with the Dirac-Hartree-Fock-Slater self-consistent method, and we ensure the orthogonality between the continuum and bound electron states, in the potential of the final atom, by modifying the last iteration of the self-consistent method. We show that orthogonality plays an essential role in calculating the exchange correction. After imposing the orthogonality, we found considerable differences in magnitude and energy dependence compared to previous results. We argue that our findings can solve the mismatch between the previous predictions and experimental measurements in the low-energy region of the beta spectrum. First, we calculate the exchange effect for the low-energy beta transitions in 14C, 45Ca, 63Ni, and 241Pu, recently investigated in the literature. Next, we compute the total exchange correction for a large number of beta emitters with Z from 1 to 102. From the systematic study, we found that for ultralow energy, i.e., 5 eV, the Z dependence of the total exchange effect is affected by s1/2 and p1/2 orbitals closure. We also show that the contributions from orbitals higher than the 2s1/2 orbital are essential for correctly calculating the total effect, especially for low energies and heavy beta emitters. Finally, we provide an analytical expression of the total exchange correction for each atomic number for easy implementation in experimental investigations.