A non-Euclidean crystal field for f electrons

To honor the memory of Clyde A. Monison, some aspects are discussed of the two-electron crystal field that exhibits the symmetry of a regular didodeca hedron, a non-Euclidean figure in which 24 regular heptagons meet in threes at 56 vertices. The group D, which comprises the 168 elements representing the rotations that send the didodecahedron into itself, is a subgroup of t he group G(2) that Racah used for f electrons, but it is not a subgroup of SO(3). Reflections extend D to D-h. The matrix elements of four two-electro n operators scaler with respect to D-h which have been previously evaluated in f(2) and f(3) within an S0(3) basis, are studied to find some isoscalar factors involving the irreducible representations of G(2) and D,. Selectio n rules and reciprocity relations are examined, and two unexpectedly null m atrix elements of an operator scalar with respect to D but odd under reflec tion are accounted for. The effect of a perturbation possessing didodecahed ral symmetry on the energy levels of a free ion is shown in a correlation d iagram for the singlet terms of f(2). (C) 2001 Elsevier Science B.V. All ri ghts reserved.