Fine Structure
The atomic spectra fine structure is a result of the coupling between the orbital angular momentum L of the outer electron and its spin angular momentum S. The total electron angular momentum is J = L + S. The J quantum number must be between | L - S |
J L + S.
This uses the convention that the magnitude of J is
(J(J+1))
and the eigenvalue of Jz is Mj.
For ground state cesium L=0 and S=½ so J=½.
For the first excited state
L=1 (D line) so J=½ (D1) or 3/2 (D2).
These transition are written
6s2S½=>6p2P½ and
6s2S½=>6p2P3/2
where the first number is the principal quantum number of the outer electron,
the superscript is 2S+1,
the letter refers to L (S (L=0), P (L=1), D, etc.),
and the subscript gives the value of J.
The Na D doublet at 589.00 nm and 589.59 nm is an example of
the fine structure. The difference is between the
3p2P½ (589.59 nm) and
3p2P3/2(589.00 nm) transition to the
3s2S½ states.
Hyperfine Structure
The hyperfine structure is the result of the coupling of J with the total nuclear angular momentum I. The total atomic angular momentum F is then given by F = J + I and can take on values | J - I | F J + I.
For ground state cesium J=½ and I=7/2 so
F=3 or F=4. For the D1
excited state J=½ so F=3 or F=4 again.
For the D2 excited state F=2, 3, 4, or 5.
Cycling between
the F=4 and F=5 D2 transition is a stable resonance (no branching to other
states), whereas for the D1 transition this doesn't happen.
Apparently, the hyperfine structure can also refer to
splitting due to isotope shift.Specifically, the hyperfine structure splitting is due to the interaction of the magnetic-dipole, electric quadrupole, etc., moments of the nucleus with the electromagnetic field produce by the electrons at the nucleus. It is thus of order 1/1837 less than the fine structure. Although possible to measure using gratings, perhaps more commonly used is a multiple beam interferometer with the Fabry-Perot being most common.