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:

    “In that open field
    If you do not come too close, if you do not come too close,
    On a summer midnight, you can hear the music
    Of the weak pipe and the little drum
    And see them dancing around the bonfire
    The association of man and woman
    In daunsinge, signifying matrimonie....”
    —T.S. (Thomas Stearns)

    “... there are no chains so galling as the chains of ignorance—no fetters so binding as those that bind the soul, and exclude it from the vast field of useful and scientific knowledge. O, had I received the advantages of early education, my ideas would, ere now, have expanded far and wide; but, alas! I possess nothing but moral capability—no teachings but the teachings of the Holy Spirit.”
    —Maria Stewart (1803–1879)