Motional Stark term

As a consequence of the collective motion of the neutral system across the homogeneous magnetic field, a motional Stark term with a constant electric field arises. This Stark term inherently couples the center of mass and internal degrees of freedom and hence any change of the internal dynamics leaves its fingerprints on the dynamics of the center of mass. In particular the transition from regularity to chaos in the classical dynamics of the internal motion is accompanied in the center of mass motion by a transition from bounded oscillations to an unbounded diffusional motion. Since these observations are based on classical dynamics, it is a priori not clear whether the observed classical diffusion will survive quantization. From both the theoretical as well as experimental point of view a challenging question is therefore whether quantum interference effects will lead to a suppression of the diffusional motion, i.e. to quantum localization, or not. 

The latter term is gauge independent, i.e. does not contain the vector potential, and, therefore, fully deserves the interpretation of an additional potential term for the internal motion with the kinetic energy at Eq. (6). Apart from the constant the potential contains two coordinate dependent parts. The term linear in the coordinates — ] (K x B)r consists of two Stark terms one which is due to the external electric field E and a second one which is a motional Stark... 

The first term of (3.289) represents a translational Stark effect. A molecule with a permanent dipole moment experiences a moving magnetic field as an electric field and hence shows an interaction the term could equally well be interpreted as a Zeeman effect. The second term represents the nuclear rotation and vibration Zeeman interactions we shall deal with this more fully below. The fourth term gives the interaction of the field with the orbital motion of the electrons and its small polarisation correction. The other terms are probably not important but are retained to preserve the gauge invariance of the Hamiltonian. For an ionic species (q 0) we have the additional translational term... 

The purpose of the present communication is to resolve this contradiction. From the analogy with Kramers work on the Stark effect, it seemed probable that the discrepancy was due to the omission on Jones part of considering the relativity terms in the motion of the electron. For this reason the problem was studied in its completeness, taking into account the effect produced by the relativistic chauge of mass, as well as the effect due to the presence of the electric field. 

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