The Dynamical Properties Of Rydberg Hydrogen Atom Near A Metal Surface

The hydrogen atom is the simplest atomic system. Since both the classical andquantum behaviors of pure hydrogen atom are well known, while the properties of highlyexcited hydrogen atom in an external electromagnetic field turn out to be the best groundsfor testing and understanding the concepts of chaos. Much research work andbreakthrough about the multi-period phenomena on Rydberg hydrogen atom interactingwith time-independent and time-dependent external fields have been achieved. Thesefields include static electric field, static magnetic field, combined electric and magneticfields in parallel configuration, combined electric and magnetic fields in perpendicularconfiguration, mass anisotropy,and linearly and circularly polarized microwave fields, etal.Recently much attention is focused on the motion of Rydberg atom near a metalsurface. Because it is another important theoretical model and it could producemeasurable experimental effect. In this model the atom-wall distance d plays a criticalrole in the dynamical properties of the system. This model may cover many dynamicaleffects__ instantaneous van der Waals interaction, Zeeman-Stark effects and diamagneticeffects in strong fields and so on. When the atom-surface reaction is weak perturbationtheorem may be applied, whereas for strong interplay regular and irregular motions mergewith each other and chaos appears.In this thesis, we study the dynamical properties of the hydrogen atom near ametal surface by using of the methods of phase space analysis and closed orbit theory. Themain work is given as below.(1) Firstly we introduce the theoretical model and the physical picture of theRydberg atom near a metal surface, and describe the scaled property of the system.(2)After eliminating the singularity of the Hamiltonian withcoordinate-transformation, we plot Poincarémaps. We find the dynamical characters ofthe system depend sensitively on the atom-surface distance d while using Poincarésurface of sections to describe the classical motion which is confined to athree-dimensional energy shell. Changing the value of d 's, we focus the observation onthe variation of the mode of the motion(It turns from regular, to partly regular and partlyirregular, then to chaotic.) and the alteration of the vibrational, rotational and captureareas. (3) Some periodic orbits which are vibrator, rotator, and ro-vibrator are given byusing the method of closed orbit theory so that characters of vibrational, rotational andro-vibrational areas might be testified. By analyzing the variation of Poincarémap with different values of d 's, we findthat the system is integrable and it's motion is regular when d 's value is very large. ( It iscompletely integrable if d arrives at the infinite limit. ) When we minish d 's valuethere exist a critical point dc . For d > dc , there are four regions and vibrational androtational areas intervein with each other in the Poincarésurface of section. For d < dc ,the vibrational region departs with the rotational region, regular and irregular modemerges, and only part of the system is integrable. When the value of d is smaller boththe vibrational and rotational areas becomes smaller and region around capture area wouldbe replaced by stochastic layers. When d is sufficiently small the rotational orbitsvanish while the central part of the vibrational area is still there, but its proportiondecreases. And it would be completely substituted by the stochastic layers and now thesystem is strong non-integrable. So the chaotic behaviour is embodied. This submitted work is divided into five chapters. The first chapter is theintroduction, which briefly discuss the trait and the progress on the atom near a metalsurface system. Chapter two presents the theoretical model and physical picture of thesystem and introduces the scaled properties of the system. In chapter three After...