Triplet Intervals of Beryllium and Calcium

The 3P intervals of a beryllium atom with an electron configuration 1s2 2s 2p were theoretically calculated by G. Araki. He computed the parameters involved in the interval formula using hydrogen-like radial functions except a parameter r-3. He calculated the last parameter using a self-consistent radial function. Since the principal quantum numbers of one-electron functions are small in this configuration, Slater's method is applicable in order to obtain the analytical expressions of the self-consistent functions. In this paper these analytical expressions will be obtained and the calculation of the above mentioned intervals will be repeated, by making use of them, according to the general formula of Araki. Further the calculation will be extended to the triplet 1s2 2s2 2p6 3s2 3p6 4s 4p3P of a calcium atom. In this case Slater's method can not be applied because the one-electron radial functions with large principal quantum numbers have too many nodes to determine accurately their analytical form. Therefore the calculation will be caried out by the method of numerical intergrations. It will be seen that our result is unfortunately worse than Araki's for beryllium and as for calcium the calculated intervals are far from agreeing with observed ones.