0198506961.pdf

82 TheLS-coupling scheme

Fig. 5.2The terms of the 3p4p configu-
ration in silicon all lie about 6 eV above
the ground state. The residual electro-
static interaction leads to energy dif-
ferences of∼ 0 .2 eV between the terms,
and the fine-structure splitting is an or-
der of magnitude smaller, as indicated
for the^3 Pand^3 D terms. This structure
is well described by theLS-coupling
scheme.

6.4

6.3

6.2

6.1

6.0

5.8

5.9

Fig. 5.3The energies of terms of the
3p^2 configuration of silicon. For equiv-
alent electrons the Pauli exclusion prin-
ciple restricts the number of terms—
there are only three compared to the
six in Fig. 5.2. The lowest-energy term
is^3 P, in accordance with Hund’s rules,
and this is the ground state of silicon
atoms.

2.0

0.0

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

1.0

there are several such terms then the one with the largestLis lowest.

The lowest term in Fig. 5.3 is consistent with these rules;^6 therulesays

(^6) Hund’s rules are so commonly mis-
applied that it is worth spelling out
that they only apply to thelowest term
of theground configurationfor cases
where there is only one incomplete sub-
shell.
nothing about the ordering of the other terms (or about any of the
terms in Fig. 5.2). Configurations of equivalent electrons are especially
important since they occur in the ground configuration of elements in
the periodic table, e.g. for the 3d^6 configuration in iron, Hund’s rules
give the lowest term as^5 D (see Exercise 5.6).^7
(^7) The large total spin has important
consequences for magnetism (Blundell
2001).