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 higherorder 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.