Positronium Zeeman spectrum ($E_{\pm }=-A/4\pm \frac{1}{2}\sqrt{A^2+16{\mu }_B^2{B}^2}$)

For the dimensionless-spin Hamiltonian $A{\mathbf{S}}_e\cdot {\mathbf{S}}_p+2{\mu }_{B}B(S_{ez}-S_{pz})$, the two aligned-spin states remain at $A/4$. The two states of total spin projection zero mix and have the displayed energies. The parameter $4{\mu }_{B}B/A$ compares off-diagonal Zeeman mixing in the singlet-triplet basis with half the zero-field splitting. A crossover is gradual, not a level-crossing phase transition.