Classical beta spectra calculations are briefly described, highlighting the usualassumptions and limitations. To go beyond these usual assumptions, the numericalresolution of the Dirac equation for the atomic and beta electrons is necessary. Thisallowed us to determine the parameters λi involved in the theoretical shapefactors exactly. A systematic comparison between theoretical and experimental shapefactors led us to disqualify the usual λi = 1 assumption for all forbiddentransitions. The usual ξ-approximation was proved to be incorrect fornumerous first forbidden non-unique transitions, and for all higherorder non-uniquetransitions. A more accurate screening correction was defined and the atomic exchangeeffect 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, arewell reproduced in our calculations. The exchange effect was demonstrated to have a greatinfluence on the spectral shape within this energy range.
