bei48482_FM

Many-Electron Atoms 251

J = j (j + 1)^3

h = 2 h

Jz J = j (j + 1)

(^3)
2
(^1)
2

-^1 2
-^3 2

(^3)
2
mj=
mj= –^1 2
(^1)
2
mj=
mj= –^3 2
15
2
Jz
(^1) _
2

-^1 _ 2

mj –^1 _

= 2

mj^1 _

= 2

h

h

h

h

h = h

h

h

Figure 7.16Space quantization of total angular momentum when the orbital angular momentum is l1.

Example 7.4

What are the possible orientations of Jfor the j^32 and j^12 states that correspond to l1?

Solution

For the j^32 state, Eq. (7.18) gives mj ^32 , ^12 , ^12 , ^32 . For the j ^12 state, mj ^12 , ^12 .

Figure 7.16 shows the orientations of Jrelative to the zaxis for these values of j.

The angular momenta Land Sinteract magnetically, as we saw in Sec. 7.7. If there

is no external magnetic field, the total angular momentum Jis conserved in magni-

tude and direction, and the effect of the internal torques is the precession of Land S

around the direction of their resultant J(Fig. 7.17). However, if there is an external

magnetic field Bpresent, then Jprecesses about the direction of Bwhile Land S

continue precessing about J, as in Fig. 7.18. The precession of Jabout Bis what gives

rise to the anomalous Zeeman effect, since different orientations of Jinvolve slightly

different energies in the presence of B.

LSCoupling

When more than one electron contributes orbital and spin angular momenta to the total

angular momentum Jof an atom, Jis still the vector sum of these individual momenta.

The usual pattern for all but the heaviest atoms is that the orbital angular momenta Liof

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