Comment on “Recurrences without closed orbits”
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چکیده
In Ref. [1] Robicheaux and Shaw calculate quantum photoabsorption spectra of atoms in electric fields with nonzero magnetic quantum numbers, m 6= 0 and observe recurrence peaks at short actions in the Fourier transform recurrence spectra. For spectra with magnetic quantum number m = 0 these peaks can be directly interpreted as the recurrences of the “uphill” and “downhill” orbit along the electric field axis. For nonzero angular momenta the authors argue that “these two orbits are not possible, because Lz is conserved and there is a repulsive Lz/(x + y) term in the potential.” The observed features at short actions are therefore interpreted as “recurrences without closed orbits.” It is the purpose of this comment to demonstrate that the uphill and downhill orbit do not disappear to nowhere at the transition from zero to nonzero angular momentum Lz, but, by contrast, closed orbits with approximately the same short action still exist for Lz 6= 0. As will be shown, the orbits along the z axis undergo bifurcations and split into a real and a complex “ghost” orbit. The importance of ghost orbits for the photoabsorption spectra of atoms in a magnetic field has been discussed at length in [2]. For the hydrogen atom in an electric field the Hamiltonian separates in semiparabolical coordinates, μ = √ r + z, ν = √ r − z, i.e., H = Hμ + Hν with
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تاریخ انتشار 1999