Adding nuclear spin doubles the degeneracy.

Hyperfine splittings are of order tex2html_wrap158 .

tex2html_wrap159

tex2html_wrap160

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.

tex2html_wrap161

The tex2html_wrap162 is 4-fold degenerate with the hyperfine considerations. This is split into 3 and 1 by the hyperfine structure. tex2html_wrap163 Which corresponds to tex2html_wrap164 and tex2html_wrap165 . This is really the first excited state of Hyrdorgen.

for l tex2html_wrap166 0 states, the fine structure are coupled tex2html_wrap167 . To calculate tex2html_wrap168 must decouple tex2html_wrap169 , tex2html_wrap170 and recouple tex2html_wrap170 , tex2html_wrap172 . This gives:

tex2html_wrap173 .m




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