Rotationsmoden

Rotationsmoden, or rotational modes, are collective excitations associated with rotation about an axis in a physical system. They appear in molecular, nuclear, and solid-state contexts and are distinguished from ordinary vibrational modes by involving orientation rather than changes in internal geometry.

In molecular physics, a nonlinear molecule has three rotational degrees of freedom and a linear molecule has two. In the rigid-rotor model the rotational energies are quantized. For a nonlinear rotor the energies depend on the total angular momentum, while for linear molecules E_J = ħ^2 J(J+1)/(2I). Transitions typically follow ΔJ = ±1.

In nuclear physics, deformed nuclei exhibit rotational bands. The level sequence often follows E(I) ≈ ħ^2/2I I(I+1), with I the angular momentum. Gamma-ray transitions connect band members and reveal the moment of inertia and deformation.

In condensed matter and materials science, rotational or torsional modes occur when parts of a structure rotate relative to one another, as in molecular crystals, polymers, or metal-organic frameworks. These modes can couple to lattice vibrations and affect thermal, mechanical, and spectroscopic properties.

Observations are made with spectroscopy, neutron scattering, or Raman and infrared methods, and theoretical treatments use normal-mode analysis that separates rotational coordinates from internal vibrations. Rotationsmoden are thus a tool for probing structure and dynamics.