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 are the most treacherous of us all. They come to the strong and drain them. They are bottomless. They are insatiable. They are always parched and always bitter. They are everyone’s concern and like vampires they suck our life’s blood.”
    —Bette Davis (1908–1989)

    “The birds their quire apply; airs, vernal airs,
    Breathing the smell of field and grove, attune
    The trembling leaves, while universal Pan,
    Knit with the Graces and the Hours in dance,
    Led on th’ eternal Spring.”
    —John Milton (1608–1674)