Calculation of beta spectral shapes

Classical beta spectra calculations are briefly described, highlighting the usual assumptions and limitations. To go beyond these usual assumptions, the numerical resolution of the Dirac equation for the atomic and beta electrons is necessary. This allowed us to determine the parameters λi involved in the theoretical shape factors exactly. A systematic comparison between theoretical and experimental shape factors led us to disqualify the usual λi = 1 assumption for all forbidden transitions. The usual ξ-approximation was proved to be incorrect for numerous first forbidden non-unique transitions, and for all higher order non-unique transitions. A more accurate screening correction was defined and the atomic exchange effect was taken into account, an effect which is always neglected in usual calculations. The beta spectra of 63Ni and 241Pu, recently measured down to very low energies, are well reproduced in our calculations. The exchange effect was demonstrated to have a great influence on the spectral shape within this energy range. (authors)