Scaled energy spectra of non-hydrogenic Rydberg atoms in a magnetic field

Abstract

We present a new method for computing the spectrum of one4ectron Rydberg states of non-hydrogenic atoms in a magnetic field, at conslant scaled energy. It is based on a variant of the R-matrix melhod allowing the computation of mmy energy levels in a single diagonalization. The results are compared with recenlly obtained high-resolution cxptrimentd spectra of the helium atom. The relation h e e n peaks observed in the Fourier transform of suled spectra and classical closed orbits is discussed. We show the existence of 'ghost' peaks not corresponding to any closed orbir and also of peaks existing only in non-hydrogenic specua, due the scattering of the electron by the ionic WE.

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

“…As mentioned above, this behaviour has been experimentally observed in the recurrence spectra of hydrogen and other Rydberg atoms in a magnetic field [9,10,11]. The dynamical interpretation of such experiments and of the results shown in Fig.…”

“…Above each peak, we have drawn the shape of the classical orbit whose period matches the recurrence time of the peak. This plot arises from quantum calculations, but recurrence spectra have been experimentally observed in hydrogen [10] as well as other species of one electron ('Rydberg') atoms [11] and molecules [12] in external fields [17]. Purely semiclassical calculations have also been undertaken, reaching an excellent agreement with experimental observations and exact quantum calculations.…”

“…First, an initial wavefuntion localized in configuration space results from an expansion of several hundred energy eigenstates ψ E k (r). Second, each of these eigenstates contains several hundred thousand components on the numerical basis, obtained from the diagonalization of very large (but sparse) Hamiltonian matrices [9,11]. Third the integration of Eq.…”

Scaled-Energy Spectroscopy of Helium and Barium Rydberg Atoms in External Fields

“…For highly-excited states this involves the diagonalization of huge energy matrices, for which special numerical techniques have been developed [8,9]. Such calculations are also possible under conditions of constant-scaled energy, so that a direct comparison with experimental data and Fourier transforms can be made.…”

“…by the occurence of lesonances at and 9.03, which are the sum of actions for orbits (2.21 and 2.80), respectively (4.42 and 4.61). The occurence of sum actions (not possible in the hydrogen atom) was for the first time observed in the spectrum [8]. The proliferation of unstable orbits as well as the more pronounced occurence of sum orbits results in less good agreement between the observed and calculated (with classical closed-orbit theory) action spectrum in the case of than in case of [11].…”