Quantisation of new periodic orbits for the hydrogen atom in a magnetic field

The classical Hamiltonian for an electron moving under the combined action of the Coulomb and magnetic potentials is considered, and a new class of periodic orbits for the quadratic Zeeman problem in the irregular region is found. It is suggested that these orbits pass through the origin and are just one set of different classes of periodic orbits in this region. The quantum analogs of these orbits are considered, and new level spacings near the zero-field threshold are predicted. It is suggested that these spacings should be observed in high-resolution experiments on atoms in external fields.