Abstract
A method is described for calculating matrix elements of operators in a basis in which the spin-up and spin-down spaces of an atomic
l
shell are both split into separate parts. Instead of elaborate tables of fractional parentage coefficients, only a few reduced matrix elements are required. These are tabulated for d, f, g and h electrons. The transformation coefficients relating the states in the new basis to the familiar
LS
states are given for f electrons. An operator
e
h
that separates and classifies repeating terms of the configuration h
N
(in analogy to the separation achieved by Racah for f
N
) is shown to take a simpler form if parts off diagonal with respect to
N
are added to it, thereby accounting for some puzzling coincidences in the eigenvalues of
e
n
.
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