0198506961.pdf

86 TheLS-coupling scheme

Fig. 5.8Thejj-coupling scheme. The
spin–orbit interaction energy is large
compared to theEre.(Cf.Fig.5.4for
theLS-coupling scheme.)

In summary, the conditions forLS-andjj-coupling are as follows:^12

(^12) In both of these cases we assume an
isolated configuration, i.e. that the en-
ergy separation of the different config-
urations in the central field is greater
than the perturbation produced by ei-
therEs−oorEre.
LS-coupling scheme: EreEs−o,
jj-coupling scheme: Es−oEre.

5.3 Intermediate coupling: the transition

between coupling schemes

In this section we shall look at examples of angular momentum coupling

schemes in two-electron systems. Figure 5.9 shows energy-level diagrams

of Mg and Hg and the following example looks at the structure of these

atoms.

Example 5.1

3s3p, Mg 6s6p, Hg

2.1850 3.76

2.1870 3.94

2.1911 4.40

3.5051 5.40

The table gives the energy levels, in units of 10^6 m−^1 measured from

the ground state, for the 3s3p configuration in magnesium (Z= 12) and

6s6p in mercury (Z= 80). We shall use these data to identify the levels

and assign further quantum numbers.

For an sp configuration we expect^1 Pand^3 P terms. In the case of

magnesium we see that the spacings between the three lowest levels are

2000 m−^1 and 4100 m−^1 ; these are close to the 1 to 2 ratio expected from

the interval rule for the levels withJ=0,1 and 2 that arise from the

triplet. TheLS-coupling scheme gives an accurate description because