The classical centre-of-mass separation for two particles in a homogeneous magnetic field

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Abstract
The authors investigate classically the problem of the centre-of-mass separation for a two-body system with net charge in a homogeneous magnetic field. With a view to general atomic physics applications, particular attention is paid to the case where one particle is much heavier than the other. Using a series of canonical transformations they introduce constants of the motion as the new momenta and determine the conjugate coordinates. Alternative momenta involving a suggested near-constant of the motion are investigated for use with a translation-invariant internal potential. These lead to a 'near separation' in terms of two coupled particles characterised by vectors which possess a simple classical interpretation, even in the presence of an interaction potential. However they find that the coupling is not small and is not reduced when one of the particles is much heavier than the other, although the frequencies of the two motions then differ widely.

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