Consistent calculation of the screening and exchange effects in allowedβ−transitions

Abstract

The atomic exchange effect has previously been demonstrated to have a great influence at low energy in the 241 Pu 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 241 Pu and 63 Ni β spectra. In this paper, a new 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 endpoint 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 particles model, is sufficient to describe well the current most precise measurements.

The importance of the beta spectrum calculation for accurate activity determination of 63 Ni by means of liquid scintillation counting

“…1) was found to be in excellent agreement with the experimentally determined spectrum using metallic magnetic calorimeters (Loidl et al, 2014). Another computation was carried out using a more consistent approach described by Mougeot and Bisch (2014). The electron wave functions were then calculated numerically using the same screened Coulomb potential and a new screening correction was introduced.…”

“…The analysis, however, cannot be used to judge whether the more consistent approach presented by Mougeot and Bisch (2014) is better than the previously approximated calculation (Loidl et al, 2014). The relative deviation between the mean values for the activity concentrations for spectra 2 and 3 is about 0.5%.…”

“…Spectrum 1 was calculated without any correction whilst the exchange effect was taken into account for spectrum 2 with an approximation as described by Loidl et al (2014). For spectrum 3, the screening and exchange effects were consistently accounted for as proposed by Mougeot and Bisch (2014). The low energy region is shown in Fig.…”

“…The discrepancy reported by Nähle and Kossert (2011) was confirmed when applying the same efficiency computation method. Then, the analysis was repeated with newly computed beta spectra that take the atomic screening and exchange effects into account (Mougeot and Bisch, 2014). The exchange process is a quantum effect coming from the indistinguishability of the electrons.…”

BetaShape: A new code for improved analytical calculations of beta spectra

“…In order to ensure fast calculations, the atomic exchange effect was not included as its evaluation is time-consuming [7]. In this formalism, the Fermi function includes the finite nuclear size effect as it is defined by the product of the usual Fermi function F 0 and a factor L 0 which accounts for the distortion of the electron wave function by a nonpoint-like nuclear charge…”