Adding nuclear spin doubles the degeneracy.

Hyperfine splittings are of order .

The first term is spin angular momentum of the nucleus. For S-wave electrons only the last term is nonzero. This is the contact term.

The is 4-fold degenerate with the hyperfine considerations. This is split into 3 and 1 by the hyperfine structure. Which corresponds to and . This is really the first excited state of Hyrdorgen.

for l 0 states, the fine structure are coupled . To calculate must decouple , and recouple , . This gives:

.m

source psfile jl@crush.caltech.edu index