A Studying Of Bifurcations Of Classical Orbits And Spectral Analyses In High-precision

The strong resonance structures of photo-absorption spectra of high Rydberg atoms and molecules in strong external fields have attracted much interest in recent years. They have been typical examples for studying the semiclassical theory and quantum chaos. And these phenomena involve many basic questions such as high Rydberg atoms'structure, the matter diamagnetism in extreme conditions and electron correlation, etc. Semiclassical closed-orbit theory has been a powerful tool for investigating photo-absorption properties of atoms, negative ions and molecules in externally applied strong fields since it was proposed in the 1980s, due to its clear physical picture and wide availability, and has become an important link to connect the classical and quantum theory. In the past decades, the closed-orbit theory has successfully been applied to highly excited states of atom in various external fields; the validity of the closed-orbit theory has been fully confirmed.However, with the development of researches, there are two new challenges for the primary theory: The first one is because that the effect of bifurcation is obvious at some special value of the parameters, where the closed-orbit theory is failure because the wave-function would become infinite at a focus or caustic passed through the origin. The other one is for the reason of core-scattering. The number of closed-orbits increases rapidly; and most orbits are unstable and are not easily realized recognized and classified, which makes the problem more difficult to work with. So it is imperative to correct and extend the primitive closed-orbit theory due to the closed orbit theory is essentially low resolution.Pursuing above problems, we have mainly done the following work here:1. We investigate the effects of bifurcations on electron motion and then the flux distribution of photo-detached electrons of H^- in parallel electric and magnetic fields. We pay our attention particularly to the interference of electron waves far from the atomic core in configuration space. Considering the electron orbits are no longer"closed"and the system possesses axis symmetry, the electron's classical motion and the bifurcation of classical orbits can be described inρ-pρandρ-θ₀ diagrams. (hereρis the distance from the original of the observation plane, p_ρis the corresponding momentum, andθ0 is the angle between the initial outgoing direction and the z-axis, respectively.)The divergence in the wave function associated with the bifurcation of classical orbit is specified by using a semiclassical uniform approximation. We calculate the detached-electron flux distribution images on the screen using the mixed position and momentum representation for the detached-electron. It is demonstrated that the major features of the detached-electron images are rings, which can be controlled by adjusting the magnetic field. Recently several interesting articles have appeared addressing the theoretical questions of detached-electron distribution in parallel fields. A point source was used to simulate the initial detached-electron in all these works. An isotropic point-like source was used. However, the results cannot be directly applied to the photo-detachment of H ? because H ? is in an s-wave state and the detached-electron is a p-wave. It is the first time to investigate this phenomenon. What makes the current system more interesting is that the classical orbits of the photo-detached electrons bifurcate with the external parameters such as the photon energy and the magnetic field strength. The relationship between the ring patterns in the detached-electron images and the bifurcation of classical orbits is discussed usingρ-p_ρdiagrams.2. We analyze the effects of bifurcations on the recurrence spectra of Li Rydberg atom in electric field.In this thesis, we present theoretical computation by using region-splitting consistent and iterative method together with the standard model potential, of course, introducing a new scale property and a concept of an effective Planck constant ( eff ) allows us to compare our results with the experiments in the future. From our results, we can see clearly that the new strong resonance structure can be refered by the combined closed-orbits.We study the Li Rydberg atom in electric field. The condition of bifurcation and anti-bifurcation has gotten. The regions for the real orbits and ghost orbits are separately determined. Because the dispersion of the wave function in the vicinity of bifurcation, we analyze the reasons why rising bifurcation and the forms of bifurcation at a constant scaled energyε= ? 2.7, then both the core potential and the bifurcation have to be taken into account. The divergences of Li Rydberg atom's recurrence spectra in electric field are corrected by using the uniform approximations method. Our works are not only the extension but also the validation and supplement for the closed-orbit theory.3. An extended harmonic inversion method is applied to obtain highly resolved spectra of lithium atom in electric field.A powerful method for both the analysis of quantum spectrum and semiclassical orbit quantization is introduced. This method allows one to circumvent the confines of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before. It is the first time for this method to be applied to the nonhydrogen atom.This thesis is divided into six chapters. The first chapter is summarization, which chiefly introduces the development of semiclassical closed-orbit theory, includes its successful and encounters challenges. The bifurcation phenomena are analyzed in the second chapter in detail. The photodetachment electron flux is discussed in the next chapter. The region-splitting consistent iterative method is introduced in chapter 4, and the concepts of scaled law and recurrence spectra are presented. Then, we explain the phenomena of the bifurcations, where the wave function is described in scheme of the uniform approximates method so as to get correct results which include the core-scattered effects. We analyze the recurrence spectrum of Li Rydberg atom in electric field with the harmonic inversion in the chapter 5. Decimating the selected window frequencies and solving a set of nonlinear algebraic equations result in the eigenvalues that evidence corresponding quantum resonances hidden in low resolution spectra. In the last chapter we give some important conclusions of this thesis and an inspection to the challenge and the application of this theory is made.