Absorption of atomic hydrogen in a strong magnetic field

Abstract

The photoabsorption of atomic hydrogen in a strong static magnetic field is studied. The bound states are considered in some detail, approximating the wavefunctions by a set of unperturbed, spherical hydrogenic functions and a set of simple separable functions of cylindrical symmetry. Results are presented for the energy eigenvalues of fourteen low lying states in the range of magnetic field strengths 10 ≤ B ≤ 2.35 x 10 G. The eigenfunctions corresponding to the bound states are used to obtain electric dipole transition probabilities. For strong transitions, transition probabilities in the two approximations agree at fields of 10 and 10 G. However, at 5 x 10 ≤ B≤ 2.35x10 G, the cylindrical basis proves to give a better description of the system, producing a lower set of energy eigenvalues, and the agreement between the two sets of transition probabilities is not so good. Relativistic and spin effects are neglected here. The simple cylindrical functions are used to calculate photoionization cross sections, enabling, in the case of the pure Landau continuum, all the matrix elements occurring in these cross sections to be calculated analytically. A second, more appropriate model for the continuum, in the range of fields considered, is also used, in which the Coulomb attraction of the nucleus is considered in the plane perpendicular to the field direction. Wavefunctions and energy eigenvalues for the discrete states in this second continuum model are calculated numerically, from a two point boundary value equation. Calculations of the photoionization of the lowest even and odd parity bound states at photon energies from the (field dependent) ionization threshold to 8gamma rydbergs above it are reported, where gamma = hwc. The appropriate generalization of the Wigner threshold law is given. Resonances are found at each embedded discrete continuum level in the absence of broadening, and secondary maxima associated with the motion along the field are predicted, and confirmed in a simple model. Results for the two continuum models are compared and the differences discussed in some detail.