 Dipole moment from a rotational Stark doublet

For $J=0\to 1$, the $m=0$ and $|m|=1$ frequency shifts are $4(pE{)}^2/(15Bh)$ and $7(pE{)}^2/(60Bh)$. Their difference is $3(pE{)}^2/(20Bh)$, so $p=(h/E)\sqrt{(20/3)(B/h)\Delta \nu }$. The common lower-state shift cancels from the splitting but not from either absolute transition frequency.