Centre-of-mass effects on the hydrogen atom in a magnetic field

With a canonical transformation, the Hamiltonian of a neutral system of charged particles in a homogeneous magnetic field is transformed into the sum of an internal Hamiltonian, a CM kinetic energy operator and a term coupling the internal and CM motions. When the magnetic quantum number m of a hydrogen atom state differs from zero, its binding energy is qualitatively affected by the existence of a transverse motion, even a very small one. The number of bound states with a given m not=0 becomes finite and vanishes beyond a critical magnetic field. For any m, the binding energies are reduced by a transverse collective energy which is conveniently expressed as a function of an effective mass. Several effective masses are calculated with a second-order perturbation method in the strong-field region.