In this review we study the level of accuracy of the electronic wave functions which is necessary to describe properly the atomic effects during nuclear β-decay. In the case of the β − -decay in the Li atom into Be + ion we compare the numerical values of the transition probabilities from the S, P , D low-lying states of the initial atom and final ion calculated using both Hylleraas-Configuration Interaction (Hy-CI) and Configuration Interaction (CI) with Slater orbitals wave functions. In addition using the CI method the transition probabilities from F , G, H and I low-lying states have been calculated. The average of the absolute deviation of the transition probabilities distribution for low-lying S states is < 0.15%, for P states < 0.5%, and larger for D-and higher energy states.The numerical results demonstrate that for low-lying states the atomic effect parameters in β-decay can be calculated with sufficient accuracy using CI wave functions constructed with Slater orbitals. This result opens a new avenue for the accurate calculation of atomic effects during the β-decay in heavier atoms and molecules. *