# Fine Structure of Positronium

1. Jul 25, 2014

### "pi"mp

Hi all,
I'm trying to compute the effect that a magnetic field has on the singlet and triplet states of positronium. I know that the positron has a charge and magnetic moment opposite that of the electron, so I'm tempted to write the interaction as:

$$\vec{B} \cdot (\vec{M}_{1}+\vec{M}_{2})= \mu B(S_{1z}-S_{2z})$$

where the minus sign comes about thanks to what I mentioned above. However, when I write out the singlet and doublet states in the $|s_{1}=s_{2}=\frac{1}{2} s_{1z}\, \, s_{2z} \rangle$ basis, I get that the above interaction does not split the energy levels...at least to first order.

Did I do something wrong? If not, do I need to try 2nd order perturbation theory?
Thanks :)

2. Jul 25, 2014