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:

    “He serveth the servant,
    The brave he loves amain;
    He kills the cripple and the sick,
    And straight begins again.
    For gods delight in gods,
    And thrust the weak aside;
    To him who scorns their charities,
    Their arms fly open wide.”
    —Ralph Waldo Emerson (1803–1882)

    “We need a type of theatre which not only releases the feelings, insights and impulses possible within the particular historical field of human relations in which the action takes place, but employs and encourages those thoughts and feelings which help transform the field itself.”
    —Bertolt Brecht (1898–1956)