  Because of its inherent 2-D character, the eigenvalue equation for the
hindered rotation around a normal cation site of an off-center impurity
nearest-neighboring an F center is the well-known Mathieu equation. We present
an overview of literature data on Mathieu's periodic functions providing exact
solutions to the Li+ reorientational problem. We compare them with bottom-well
approximating solutions by harmonic-oscillator functions at an effective
vibrational frequency renormalized by both first- and third- order
electron-mode coupling. We finally discuss the in-plane inversion
polarizability of an off-center impurity assumed to form a dipole-dipole
coupling with a nearby F center.
