Lowest-order relativistic interaction between lattice vibrations and internal degrees of freedom of a nucleus

A moving nucleus experiences a Lorentz contraction and spin rearrangement due to relativity. A nucleus that oscillates in a molecule or solid due to vibrations will undergo minor relativistic modifications which are a result of the vibrations, indicative of a relativistic phonon-nuclear interaction. The derivation of the lowest-order interaction from the many-particle Dirac model is reviewed. The Dirac model with a realistic potential model is not covariant, which is a source of concern. The lowest-order phonon-nuclear interaction obtained from a covariant two-body Bethe–Salpeter model is found to be similar to the interaction obtained from the Dirac model, supporting the notion that the interaction is not an artifact. Matrix elements of the lowest-order interaction are expressed in terms of one-body operators, which facilitates evaluation and allows for quantitative estimates of the magnitude.