Zeeman Effect - Weak Field (Zeeman Effect)

Weak Field (Zeeman Effect)

If the spin-orbit interaction dominates over the effect of the external magnetic field, and are not separately conserved, only the total angular momentum is. The spin and orbital angular momentum vectors can be thought of as precessing about the (fixed) total angular momentum vector . The (time-)"averaged" spin vector is then the projection of the spin onto the direction of :

and for the (time-)"averaged" orbital vector:

Thus,

Using and squaring both sides, we get

and: using and squaring both sides, we get

Combining everything and taking, we obtain the magnetic potential energy of the atom in the applied external magnetic field,

\begin{align} V_M &= \mu_B B m_j \left\\ &= \mu_B B m_j \left, \\ &= \mu_B B m_j g_j \end{align}

where the quantity in square brackets is the Landé g-factor gJ of the atom ( and ) and is the z-component of the total angular momentum. For a single electron above filled shells and, the Landé g-factor can be simplified into:

Read more about this topic:  Zeeman Effect

Famous quotes containing the words weak and/or field:

    “The weak have one weapon: the errors of those who think they are strong.”
    —Georges Bidault (1899–1983)

    “... no young colored person in the United States today can truthfully offer as an excuse for lack of ambition or aspiration that members of his race have accomplished so little, he is discouraged from attempting anything himself. For there is scarcely a field of human endeavor which colored people have been allowed to enter in which there is not at least one worthy representative.”
    —Mary Church Terrell (1863–1954)