- Landé g-factor
In
physics , the Landé g-factor is a particular example of ag-factor , namely for anelectron with both spin andorbital angular momenta. It is named afterAlfred Landé , who first described it in 1921.In
atomic physics , it is a multiplicative term appearing in the expression for the energy levels of anatom in a weakmagnetic field . Thequantum state s ofelectron s inatomic orbital s are normallydegenerate in energy, with the degenerate states all sharing the same angular momentum. When the atom is placed in a weak magnetic field, however, the degeneracy is lifted.The factor comes about during the calculation of the first-order perturbation in the energy of an atom when a weak uniform magnetic field (that is, weak in comparison to the system's internal magnetic field) is applied to the system. Formally we can write the factor as,
:g_J= g_Lfrac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)}+g_Sfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)} :approx 1+frac{J(J+1)-L(L+1)+S(S+1)}{2J(J+1)}
:g_L = 1 , g_Sapprox 2
Here, "J" is the total electronic angular momentum, "L" is the
orbital angular momentum , and "S" is thespin angular momentum . Because "S"=1/2 for electrons, one often sees this formula written with 3/4 in place of "S"("S"+1). The quantities "gL" and "gS" are otherg-factor s of an electron.If we wish to know the g-factor for an atom with total atomic angular momentum F=I+J,
:g_F= g_Jfrac{F(F+1)-I(I+1)+J(J+1)}{2F(F+1)}+g_Ifrac{F(F+1)+I(I+1)-J(J+1)}{2F(F+1)}
:approx g_Jfrac{F(F+1)-I(I+1)+J(J+1)}{2F(F+1)}
This last approximation is justified because g_I is smaller than g_J by the ratio of the electron mass to the proton mass.
Wikimedia Foundation. 2010.