In the anomalous Zeeman effect, the external magnetic field is much weaker than the internal field seen by the electron as a result of its orbital motion. In the vector model the vectors L and S precess rapidly around J because of the internal field and J precesses slowly around the external field. The energy splitting is found by first calculating the component of the magnetic moment μ_J in the direction of J and then finding the component of μ_z in the direction of B.

(a) Show that μ_J = μ. J/J can be written

(b) From J² = (L+S) . (L+S) show that S.L = 1/2 (J² - L² -S²). 

(c) Substitute your result in part (b) into that of part (a) to obtain

(d) Multiply your result by J_z /J to obtain

Transcribed Image Text:

Hј = Ив ћ h.l -(L² + 2$² + 3S.L)