The Darwin Term
We get a correction at the origin from the Dirac equation.
When we take the expectation value of this, we get the probability for the electron and
proton to be at the same point.
Now,
for
and
for
, so
This is the same as
term that we got for the spin orbit correction.
This actually replaces the
term in the spin-orbit correction (which should be zero)
making the formula correct!
Jim Branson
2013-04-22