Recurrence Spectra Of Rydberg Hydrogen Atom Near A Metal Surface

Last a few years, the photo-absorption phenomena of highly excited atoms in strong external fields has attracted much interests and investigation. Largely because these non-separable quantum systems turn classically chaotic as they approach the ionization limit. The semiclassical closed-orbit theory has been extensively applied to explain the phenomena due to its clear physical picture and wide availability. It has already become an important link between classical theory and quantum world, as well as a powerful tool to study quantum chaos.For the simplest system, the hydrogen atom, much researching works of the multi-period phenomena in the photoabsorption process by interacting with time-independent and time-dependent external fields have been achieved, which fall into the quantum and classical aspects. Some of the external fields are: static electric field, static magnetic field, combined electric and magnetic fields in parallel configuration, combined electric and magnetic fields in perpendicular configuration, mass anisotropy,and linearly and circularly polarized microwave fields. Recently much attention is focused on the system of Rydberg atom near a metal surface. In this model the metal surface acts for the external field and the distance d between the metal surface and the hydrogen atom plays a critical role in the dynamical properties of the system. When the distance d is large, their interaction is weak, so perturbation theorem may be applied. Whereas for strong interplay, regular and irregular motions merge with each other and chaos appear. With the varying of the metal-surface distance, the system can cover many dynamical effects-- instantaneous van der Waals interaction, Zeeman-Stark effects, diamagnetic effects in strong fields and so on.In this thesis, we study how the dynamics of the hydrogen atom near a metal surface vary with the atom-surface distance using the closed orbit theory for the first time. And, withal, we calculate the recurrence spectra at a constant scaled energy.(1) Firstly we introduce the theoretical model of hydrogen atom near a metal surface, derive its Hamiltonian,introduce the scaling rule, make a semi-parabolic transformation to remove the Coulomb singularity and describe its physical picture under the scheme of the closed-orbit theory.(2) We introduce the EBKM theorem and density of states theory simply, then represent the physical idea of the closed-orbit theory. Finally we display the formula of average oscillating density based upon the theory. In order to solve the dependence of the orbits on the energy, we apply the concept of the recurrence spectroscopy.(3) According to the classical canonical equation, we find all the steady closed orbits and consequently calculate the recurrence spectra. It demonstrates that the critical distance d c is the critical point. Here the number of the orbits is the most. Whereas in the region d > dc the number of the orbits gets lesser and lesser, this also does for d < dc. In the vicinity of d c, with the distance of d =1800, namelyε=?1.44, the effects of the movement of the electron and the orbits is most like that in electric field plus a parallel weak static magnetic field. Thereby we calculate the recurrence spectra of the hydrogen atom in a electric field with the scaled energy range fromε=?2.0 toε=?0.8, then compare them with the spectra of the hydrogen near a metal surface. It shows that they have the best correspondences whenε=?1.4.The thesis works include five chapters. The first chapter is summarization, which briefly introduces the background and the development of the closed-orbit theory. We also describe the trait and progress on the hydrogen atom near a metal surface in this passage. Chapter two presents the theoretical model and physical picture of the system and explains the scaled properties of the system. In chapter three, we reconsider the closed-orbit theory and its form at present. Chapter four is our calculation. In this section, we first calculate the closed orbits of the hydrogen atom near a metal surface, analyze then the varying of the orbits along with the atom-surface distances. We find that when d =1800, the movement of the electron is analogous to the applied static electric field plus a parallel weak static magnetic field. In evidence we calculate the recurrence spectra of the hydrogen atom in a electric field, and compare it with the spectra of the hydrogen near a metal surface. It is shown that there is a consonance between them when their scaled energy approaches to each other. As the conclusion, in the last chapter, we briefly summarize the total subject and give an expectation for the future work.