A Studying Of Combination Recurrences And Bifurcations Of Orbits In The Photoabsorption Spectra Of Rydberg Atoms

Strong resonance structures of photoabsorption spectra of atoms in external fields have attracted much interest in recent years, since they involve many basic questions such as high Rydberg atoms' structure, the matter diamagnetism in extreme conditions and electron correlation, ect. Semiclassical closed-orbit theory has been extensively used to explain the photo-absorption spectra of atoms in external fields due to its clear physical picture and wide availability. It has been proved to be a powerful tool for studying the quantum manifestations of classical chaos and a typical example for understanding the conception of chaos.In the past decades, the closed-orbit theory has successfully been applied to H" as well as to the highly excited states of the hydrogen atom in various external fields, the validity of the closed-orbit theory has been fully confirmed, and the recurrence spectroscopy, scaling property and energy statistics have also been developed. However, when take the nonhydrogen atoms into account, there are new challenges: (1) The number of closed-orbits increases rapidly because of the effect of core-scattering, and most of those are unstable and are not easily realized and classified, which makes the problem more complicate. (2) The effect of bifurcation is obvious at some value of scaled energy, where the closed-orbit theory is failure for returning waves near the core, which would become infinite as a focus or caustic passed through the origin. So it is necessary to correct and extend the primitive closed-orbit theory.In this thesis, we present theoretical computations of Li Rydberg atom in parallel electric and magnetic fields by using region-splitting consistent and iterative method together with the standard model potential, and by introducing a new scale property and a concept of an effective Planck constant, we can compare our results with the experiment in the future. From our results, we can see clearly that the new strong resonance structure can be explained by thecombined closed-orbits.To study the dispersion of the wave function in the vicinity of bifurcation, we analyze the reasons rising bifurcation and the forms of bifurcation and choose the constant scaled energy e = -2.94 , in the vicinity of this energy, many orbits are created or destroyed by the bifurcation. The divergences of Li Rydberg atom's recurrence spectra in electric field are corrected by using the uniform approximations method.In the case of Li Rydberg atom, even though for the regular motion with none of the orbits closed to its bifurcation, different from the formers' works, which are approached the nonhydrogenic atoms only in sole electric or sole magnetic field, this thesis is the first time to study the recurrence spectra in parallel electric and magnetic fields. For the effect of bifurcation, the research at present is still in the beginning stage. We are the first to use the uniform approximate method and take the effect of the core-scattering into account for calculating the recurrence spectra of Li Rydberg atom in the vicinity of the bifurcation energy. Our works are not only the extension but also the validation and supplement for the closed-orbit theory. Moreover, our results possess an important insight for experiment research and for the investigating of the systems that are more complicated, such as He andO3 systems, etc.This thesis is divided into five chapters. The first chapter is summarization, which chiefly introduces the development of semiclassical closed-orbit theory. The second chapter introduces the region-splitting method. The concepts of scaled law and recurrence spectra are presented in the third chapter. The forth chapter presents the calculating results of the recurrence spectra of Li Rydberg atom in parallel electric and magnetic fields, which displayed the important contribution of core-scattering in multi-electric atoms. In the fifth chapter, we first present the phenomena of the bifurcations, then describe the wave function near the bifurcations and use the uniform ap...