Self-consistent field, with exchange, for beryllium

Except for the lightest atoms, most calculations of approximate wave functions and fields for many-electron atoms have been carried out by the method of the “self-consistent field,” of which the principle is, shortly, the determination of a set of one-electron wave functions such that each represents a stationary state of an electron in the field of the nucleus and the Schrödinger charge distribution of the electrons occupying the other wave functions of the set. This method has been found quite practicable for numerical work, even for the heaviest atoms. As so far applied, it involves three main approximations, namely, (a ) neglect of relativity and spin effects, (b ) neglect of exchange effects, and (c ) treatment of the wave function of the whole atom as built up of functions of the co-ordinates of the individual electrons only, its dependence on the mutual distances between every pair of electrons being neglected; or, in other words, each electron is replaced by a statistical average distribution, in calculating its effect on the other electrons on the atom.