Neutral two-body systems in inhomogeneous magnetic fields: the quadrupole configuration

We investigate the theoretical foundations of neutral two-body systems exposed to an inhomogeneous magnetic field. Various representations for the Hamiltonian describing the coupled centre-of-mass and internal motion are derived. For the specific case of a magnetic quadrupole field we establish the continuous and discrete symmetries and show that the energy levels of the interacting system are two-fold degenerate. We exploit the symmetries in two alternative ways and derive corresponding effective equations of motion. The first approach eliminates two of the six spatial degrees of freedom and leads to an (infinite) set of coupled channel equations for the spin and spatial degrees of freedom. The second approach introduces the projection of the total angular momentum onto the symmetry axis of the quadrupole field as a canonical momentum, thereby eliminating the corresponding cyclic angle.