Semiclassical Calculation of Recurrence Spectra of Rydberg Hydrogen Atom Near a Metal Surface

Using closed orbit theory, we give a clear physical picture description of the Rydberg hydrogen atom near a metal surface and calculate the Fourier transformed recurrence spectra of this system at different scaled energies below ionization threshold. The results show that with the increase of the scaled energy, the number of the closed orbit increases greatly. Some of the orbits are created by the bifurcation of the perpendicular orbit. This case is quite similar to the Rydberg atom in an electric field. When the scaled energy increases furthermore, chaotic orbits appear. This study provides a different perspective on the dynamical behavior of the Rydberg atom near a metal surface.

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in StrongExternal Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.

Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincare surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε 〈 εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε 〉 εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.

Short-ranged potential effects on the recurrence spectra of lithium M=1 atoms in parallel electric and magnetic fields

This paper presents recurrence spectra of highly excited lithium atoms with M = 1 state in parallel electric and magnetic fields at a fixed scaled energy ε = -0.03. Short-ranged potentials including ionic core potential and centrifugal barrier are taken into account. Their effects on the states and photo-absorption spectrum are analysed in detail. This demonstrates that the geometric features of classical orbits are of special importance for modulations of the spectral pattern. Thus the weak polarization as well as the reduction of correlation of electrons induced by short-ranged potentials give rise to the recurrence spectra of lithium M = 1 atoms more compact than that of the M = 0 one, which is in good agreement with the experimental prediction.

Absorption and Recurrence Spectra of Li Rydberg Atom in Perpendicular Electric and Magnetic Fields

We develop the semi-closed orbit theory from two degrees of freedom to three non-separable degrees of freedom and put forward a new model potential for the Li Rydberg atom, which reduces the study of the system to an effective one-particle problem. Using this model potential and the closed orbit theory for three degrees of freedom, we caiculate the recurrence spectra of Li Rydberg atom in perpendicular electric and magnetic fields. The closed orbits in the corresponding classicai system have also been obtained. The Fourier transformed spectra of Li atom have ailowed direct comparison between the resonance peaks and the scaied action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. Our result is in good agreement with the quantum spectra, which suggests that our calculation is correct.

Absorption and Recurrence Spectra of Nonhydrogenic Rydberg Atom Near a Metal Surface

Multielectron to theoretical treatments atoms near a metal surface are essentially more complicated than hydrogen atom with regard By using the semicalssical dosed orbit theory generalized to the multielecton atoms, we study the dynamical properties of the Rydberg lithium atom near a metal surface. The photoabsorption spectra and recurrence spectra of this system have also been calculated. Considering the effect of the ionic core potential of the Rydberg lithium atom, the number of the closed orbits increases, which leads to more peaks in the recurrence spectra than the case of hydrogen atom near a metal surface. This result shows that the core-scattered effects play an important role in nonhydrogenic atoms. This study is a new application of the closed-orbit theory and is of potential experimental interest.

Semiclassical calculation of recurrence spectra of Rydberg He_2^+ molecular ion in a magnetic field

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we have calculated the recurrence spectra of He^2＋ molecular ion in a magnetic field for different quantum defects. The Fourier transform spectra of He^2＋ molecular ion may be used to perform a direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in external fields. We find that the spectral modulations can be analysed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of the Rydberg molecule. Our results are in good agreement with the quantum results, which suggests that our method is correct.

Semiclassical Analysis of Quarter Stadium Billiards

An expansion method for stationary states is applied to obtain the eigenfunctions and the eigenenergies of the quarter stadium billiard, and its nearest energy-level spacing distribution is obtained. The histogram is consistent with the standard Wigner distribution, which indicates that the stadium billiard system is chaotic. Particular attention is paid to pursuing the quantum manifestations of such classical chaos. The correspondences between the Fourier transformation of quantum spectra and classical orbits are investigated by using the closed-orbit theory. The analytical and numerical results are in agreement with the required resolution, which corroborates that the semiclassical method provides a physically meaningful image to understand such chaotic systems.