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:

    ““... So it’s plain to be discerned
    That the shades of holy men
    Who have failed, being weak of will,
    Pass the Door of Birth again,
    And are plagued by crowds, until
    They’ve passion to escape.””
    —William Butler Yeats (1865–1939)

    “Vigil strange I kept on the field one night;
    When you my son and my comrade dropt at my side that day,
    One look I but gave which your dear eyes return’d with a look I
    shall never forget,
    One touch of your hand to mine O boy, reach’d up as you lay on the ground,”
    —Walt Whitman (1819–1892)