Question

Into what number of sublevels are the following terms split in a weak magnetic field:
(a)`.^(3)P_(0)`, (b) `.^(2)F_(5//2)`, (c ) `.^(4)D_(1//2)` ?

Answer 1

(a) The term `3P_(0)` does not split in weak magnetic firld as it has zero total angular momentum.
(b) The term `.^(2)F_(5//2)` will split into `2xx(5)/(2)+1=6` sublevels. The shift in each sublevel is given by
`DeltaE= -g mu_(B)M_(Ƶ)B`
where `M_(j)= -J(J-1),....,J` and `g` is the Landi factor
`g=1+((5xx7)/(4)+(1xx3)/(4)-3xx4)/(2xx(5xx7)/(4))=1+(38-48)/(70)=(6)/(7)`
(c ) In this case for the `.^(4)D_(1//2)` term
`g=1+((1xx)/(4)+(3xx5)/(4)-2xx3)/(2xx(1xx3)/(4))=1+(3+15-24)/(6)=1-1=0`
Thus the energy difference vanish and the level does not split.