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34 2. Theoretical background
2
LS-coupling. L = i , S = s i , J = L + S.
−1/2 0 6/2 6/2
7 S 3
core hole
m J of
Table 2.3.: Photoemission final states of Eu ns
shells couple via exchange coupling with the
s ∗ m L m S final state term symbol 8 S J open shell.
+1/2 0 8/2 8/2
9 S 4
In the final state of the photoionized core (we consider 4f 6 also as “core”), the term symbol
shows the angular momentum F. This is due to Hund’s second rule, which lets L be maximal
under the precondition of 6 parallel spins in 4f 6 . Thus, the Eu 4f core final states consist
of the 7 F J multiplet with m J =0,...,6. 117 The splitting between the spin–orbit states of different
J is approximately 0.1 eV, and therefore one observes an unresolved single peak in
high-energy photoemission spectroscopy. Beyond this simple model, electronic correlation
effects may be included by the model proposed by Gunnarsson and Schönhammer, 118 which
includes an interplay of strong intra-atomic Coulomb correlations between 4f electrons and
predicts hybridization of the 4f states with the conduction states. The ground and excited
states can be then described by a mixing of several 4f configurations. For details on 4f correlations
in EuO, we may refer to literature. 40,119,120
LS-coupling. L = i , S = s i , J = L + S.
n − 1
m J of
spins m L m S final state
+ 6 2 3 3 6
2 3 5
1 3 4
0 3 3
−1 3 2
−2 3 1
−3 3 0
Table 2.4.: Photoemission final states of Eu 4f shells in LScoupling.
In this work, we consider the 4f orbitals as
core-level shell.