 Stretched hyperfine Zeeman state

For electronic $J=1/2$, an extremal total projection has only one product state rather than a two-dimensional spin block. With dimensionless angular-momentum operators and nuclear Zeeman coefficient $g_I$ in Bohr-magneton units, its energy is $AI/2\pm {\mu }_{B}B(g_J/2+g_{I}I)$. Extending both signs of a two-state Breit-Rabi formula square root to each stretched projection would invent an extra state.