LARGE-FIELD BEHAVIOR OF THE LOSURDO-STARK RESONANCES IN ATOMIC-HYDROGEN

The Schrödinger equation for atomic hydrogen in a large electric field F is solved by separation in parabolic coordinates. As F, the scaled field f that enters the separated equations tends to 0. Thus the large-F asymptotics depend on the small-f behavior of the separated equations, each of which in turn is equivalent to a quarticly perturbed two-dimensional anharmonic oscillator. The Bender-Wu branch cuts of the oscillator play a major role in the hydrogen asymptotics. A simple iterative algorithm permits the calculation of the branch points at which two eigenvalues coincide. We have found numerically that, as F, the separation constant 1 returns to the smaller of the unperturbed values 1(0) or 2(0). At the same time, 2 tends to the negative of the smaller value. As the real electric field F increases from 0 to, in each case that 1(0) and 2(0) are not equal, the trajectory of either f or e-if (but not both) loops around a single branch point and passes through the cut that joins the two (1(0) and 2(0)) Riemann triple sheets. All other branch cuts are avoided. No branch cuts are crossed if 1(0)=2(0). The known small-f asymptotic expansion for the discontinuity of the separation constant, in the f plane, across the negative real axis leads to a large-F asymptotic expansion for E in terms of the parabolic quantum numbers n1, n2, and m. © 1994 The American Physical Society.