We are able to set up the full hyperfine (plus B field) problem in a general way
so that different hydrogen-like systems can be handled.
We know that as the masses become more equal, the hyperfine
interaction becomes more important.
Hyperfine and Zeeman for H, muonium, positronium
Let's define our perturbation
Here, we have three constants that are determined by the strength of the
We include the interaction of the ``nuclear'' magnetic moment with the
field, which we have so far neglected.
This is required because the positron, for example, has a magnetic moment
equal to the electron so that it could not be neglected.
Like previous hf except now we take (proton) other
term into account.