Angular momentum states for phonons and a rotationally invariant development of lattice dynamics

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Abstract
It is shown that the rotationally invariant harmonic model provides a realistic zero-order phonon bases for crystals and that it can also be used for molecules of three or more atoms (the triatomic molecule must be linear). A simple way to introduce the harmonic and anharmonic lattice potential coefficients if given for a rotationally invariant force system. It is then shown that all the phonons of this model may be organised exactly into sharp angular momentum states. The phonon angular momentum operator is given. Then the harmonic model is used to show how, in perturbation treatments of internal and external interactions, the correct tensorial transformation and symmetry properties are always obtained, whereas in the standard treatment they are usually hidden (lost?) and arbitrarily (and not necessarily correctly) imposed on the final result. It is also shown how the basis can provide a direct approach to the crystal symmetry conditions in the treatment of ion-phonon interactions and it is shown how to obtain a new simple selection rule for the direct process of ion-phonon transitions for the special values of the wavevector in the Brillouin zone. The application of this method can be expected to lead to more new results in such processes.

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