bei48482_FM

252 Chapter Seven

the various electrons are coupled together into a single resultant L. The spin angular mo-

menta Siare also coupled together into another single resultant S. The momenta Land

Sthen interact via the spin-orbit effect to form a total angular momentum J. This scheme,

called LS coupling,can be summarized as follows:

L Li

LScoupling S Si (7.19)

JLS

The angular momentum magnitudes L,S,Jand their zcomponents Lz,Sz, and Jzare

all quantized in the usual ways, with the respective quantum numbers L, S, J, ML,

MS,and MJ. Hence

LL(L1)

LzML

SS(S1)

SzMS

JJ(J1)

JzMJ (7.20)

Both Land MLare always integers or 0, while the other quantum numbers are half-

integral if an odd number of electrons is involved and integral or 0 if an even number

of electrons is involved. When L S, Jcan have 2S1 values; when L S, Jcan

have 2L1 values.

Figure 7.18In the presence of an external magnetic field B,the

total angular-momentum vector Jprecesses about B.

B

The atom

S

Cone traced

out by J

L

J

B B

Figure 7.17The orbital and spin angular-momentum vectors Land

Sprecess about J.

J

Cone traced out by L

Cone traced out by S

The atom

S

L

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