Consistent calculation of the screening and exchange effects in allowed β^- transitions

The atomic exchange effect has previously been demonstrated to have a great influence at low energy on the ²⁴¹Pu β^- transition. The screening effect has been given as a possible explanation for a remaining discrepancy. Improved calculations have been made to consistently evaluate these two atomic effects, compared here to the recent high-precision measurements of ²⁴¹Pu and ⁶³Ni β spectra. In this paper a screening correction has been defined to account for the spatial extension of the electron wave functions. Excellent overall agreement of about 1% from 500 eV to the end-point energy has been obtained for both β spectra, which demonstrates that a rather simple β decay model for allowed transitions, including atomic effects within an independent-particle model, is sufficient to describe well the current most precise measurements. (authors)