- Ions in Magnetic Fields and in Quantum Wells

Energy levels of two-dimensional D^ - centers (or H^- ions) and of three-dimensional D^- centers in bulk and in quantum wells with rigid walls are calculated. For the two-dimensional case, asymptotically exact wave functions and energies in the limit of infinite magnetic fields are obtained. Exactly four bound states are found. The two -dimensional discrete states that are unbound take part in the absorption of radiation of the D^ - center; their role is briefly discussed. For the three-dimensional D^- center in bulk and in the quantum well, the lowest-lying M = 0 (s-like), M = -1 (p-like), and M = -2 (d-like) states have been calculated variationally, employing a Chandrasekar-type ansatz, over a large range of field strengths. For bulk, significant improvements over previous high field results have been made. Numerical evidence is presented for bulk and for quantum wells that the lowest M = -1 singlet state binds at high fields. It has previously been believed that this state is unbound. For the quantum well, the calculation is carried out as a function of magnetic field strength, well width, and position along the magnetic field (the z direction). All of the states are discrete. The ground state is found to change from an M = 0 singlet state to an M = -1 triplet state with increasing field and with displacement of the central positive ion from the center of the well. Threshold fields above which binding occurs are noted for some of the excited states.