Atomic Regime in Which the Magnetic Interaction Dominates the Coulomb Interaction for Highly Excited States of Hydrogen

Abstract

The atomic regime in which the interaction of the electron with an external magnetic field dominates the Coulomb interaction with the nucleus, relevant to pulsars, can be realized at laboratory magnetic fields for discrete autoionized states of hydrogen, at energies above the ionization limit. Approximate wave functions, energy levels, and electric dipole transition probabilities are presented for hydrogen, and an atomic beam absorption spectroscopy experiment at 50 kG is proposed to study this new regime.Recent astrophysical evidence indicates the existence of intense magnetic fields B of the order of 1018 G (1 G = 10-i T, tesla) on pulsars (1), and in this connection* the behavior of atoms has been discussed theoretically (2-11). From the atomic physics viewpoint these intense magnetic fields provide a new atomic regime in which the magnetic interaction dominates the Coulomb interaction. For example, the energy spectrum of hydrogen in an intense magnetic field is that of an electron in the magnetic field perturbed by the relatively small Coulomb interaction. This regime is achieved for the ground state of hydrogen for B of order 5 X 109 G, at which value the cyclotron radius is less than the Bohr radius. It would be interesting to study this new atomic regime in the laboratory. At any value of the magnetic field this regime is realized, e.g., for hydrogen, in a state of sufficiently high excitation (12-17).The nonrelativistic Schrbdinger equation for the relative motion of a hydrogen-like atom or ion in a uniform magnetic field taken along the z axis is approximately (18) For the intense magnetic field regime, the well known adiabatic approach, described initially by Schiff and Snyder (13), is applicable in which the fast motion in the plane perpendicular to the z-direction is considered separable from the relatively slow z-motion and the Coulomb interaction is neglected with regard to the perpendicular motion. The normalized eigenfunctions for the perpendicular motion of the electron in the magnetic field are (19)4'nm~pq')= 2irrc2( !+fl)! X (2 2) Llmm(p//2r22)eiO [2] in which r, -(hc/eB)'/2 is the cyclotron radius, L}'1 is the generalized Laguerre polynomial, n, = 0,1,2..., and m= 0, 4 1, -+2,.... The corresponding infinitely degenerate eigenenergies are E(°pm = (hwc/2)(2n, + JmJ + m + 1).Solutions of Eq. 1 are obtained in the formSubstitution of 4 into Eq. 1, multiplication by *pm* and integration over the p, 0 variables leads to a one-dimensional Schr6dinger equation for! P + Vn ImI(Z)jf(Z) = ef(z), [5] in which Vnpiml(Z) = -Ze2ffIcZn,,om(pO)j2(p2 + Z2) -'1/2pdpdo. [6] The discrete eigenfunctions and eigenenergies of Eq. 5 are written as fnpmna (z) and 5npmn5 where n, = 0,1,2,. orders the solutions of Eq. 5 in increasing energy and z nodes. They are infinite in number since asymptotically the leading term in Vnplml approaches -Ze2/z. There is also a continuum of solutions of Eq. 5 for e > 0, for unbounded motion along z. The discrete energy eigenvalues of Eq. 1 in the intense magnetic field regime ...