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:

    “What the unpenetrating world call Humanity, is often no more than a weak mind pitying itself.”
    —Samuel Richardson (1689–1761)

    “The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
    —Willard Van Orman Quine (b. 1908)