Abstract
The formulae of Redmond are used to construct expressions for the fractional parentage coefficients relating the configurations
l
3
and
l
2
. The explicit occurrence of godparent states is avoided for the quartet states of
f
3
and also for a sequence of doublet states. The latter are defined by the set of quantum numbers
f
3
WUSLJJ
2
, where
W
and
U
are irreducible representations of the groups
R
7
and
G
2
. Matrix elements of the type (
f
3
WUSL
||
U
k
||
f
3
W'U'SL'
), where
U
k
is the sum of the three irreducible tensor operators
u
k
corresponding to the three
f
electrons, are tabulated for
k
= 2, 4 and 6 and for all values of
W, U, S
and
L
.
Reference12 articles.
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3. Edm onds A. R . 1957 Angular momentum in quantum mechanics. P rinceton U niversity Press.
4. Proc. Roy;Edm A. R .;Soc. A,1952
5. Proc. Roy;Iliott J .;Soc. A,1957
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