= Rotational polarizability outside the weak-field regime
The quadratic <rotational Stark effect> is a small-field expansion, rather than a response law valid at every field. For a polar linear <rigid rotor> with rotational constant $B$ in <energy> units and permanent <electric dipole moment> $p$, a static field $\mathcal E$ gives the <Hamiltonian operator>
$$
H=B\frac{\mathbf J^2}{\hbar^2}-p\mathcal E\cos\theta.
$$
The dimensionless ratio $p\mathcal E/B$ measures competition between rotation and orientation. Once it is not small, the field mixes many field-free <angular momentum eigenstates>, so diagonalizing the fixed-<magnetic quantum number> matrix replaces a truncated second-order correction. Increasing the basis cutoff tests numerical convergence.
For a differentiable nondegenerate eigenvalue $E_\alpha(\mathcal E)$, the <Hellmann–Feynman theorem> gives the mean dipole component $-dE_\alpha/d\mathcal E=p\langle\cos\theta\rangle$. Its magnitude cannot exceed $p$. Continuing the weak-field linear induced-dipole formula indefinitely would violate this bound. Strongly oriented low-lying <pendular states> instead describe restricted angular motion about the field direction.<Spatial orientation of molecules in strong electric fields and evidence for pendular states by Bretislav Friedrich and Dudley R. Herschbach>[abstract: rotational cooling, orientation and pendular states]{ref}
Back to article page
