Abstract
Three-dimensional “regular” quasi-Landau resonances, recently discovered experimentally in the Balmer spectrum of the highly excited hydrogen atom around the ionization limit in external static homogeneous magnetic fields, are investigated theoretically by extending previous classical trajectory calculations to semi-classically. Employing the EBK-method for multidimensional non-separable systems, closed trajectories of the excited electron with the proton as origin are quantized by numerical quadrature of the two-dimensional EBK-integral in cylindrical coordinates. The results are resonances with quantum numbersn=1, 2,... for each closed classical trajectory as functions of both the excitation energyE and field strengthB. The calculations include in particular also the classically chaotic region around the ionization limit with experimentally accessible fields, just the region which has so far defied exact quantum mechanical solution. Based on simple physical arguments for the motion of the highly excited electron, an analytic relation is derived for the (E, B)-dependence of the regular three-dimensional resonances which fits quantitatively the numerical EBK-results.
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