Handbook of Magnetic Measurements

Fundamentals of Magnetic Measurements 55

where

J j=

∑

i

i

j is a total angular moment vector

The total angular moment is also quantized and

its projection onto the direction z is multiple of hˉ .

Figure2.92 presents the vector addition of total angu-

lar and spin vectors—note that magnetic moment is

proportional to L + 2S.

J l s J j l s= + = = +

∑ ∑ ∑ ∑

i i i i

or ( )

(2.160)

In the rst method (Russel–Saunders coupling), rst we

determine the total L and S vectors and then the sum of

them. In the second method ( j–j coupling), we determine

values of j

i

vectors and then we are summing them. The

results of both methods can