Degeneracies Among Terms of a Configuration of Equivalent Electrons

If the radial integrals occurring in the term formulae for a configuration $l^z$ assume certain integer ratios given in Table III all elements of the energy matrix become low multiples of a common value. As a consequence high degeneracies are seen to occur. The reason for this behavior is proved to be the existence of an identity [Eq. (6)] concerning sums of products of three integrals of spherical harmonics. The regularity mentioned may serve in the approximate allocation of energy levels or as a check for exact energy formulae. Ostrofsky's formulae for $d^4$ were found to be incorrect in this way. The correct formulae are given in §2.