Semiclassical Theory Of Atomic And Molecular Dynamics In Strong External Fields

The development of laser theory and technique gives rise to influence on the traditional atomic and molecular physics in deeply, with the help of the short intense laser pulse experiment made preparing and probing highly excited Rydberg states in possible, and promoted, therefore, relative researches and explorations in following basic areas: the interactions between laser and particles of matter, the interference evolution of wavepacket in spatial and temporal domains, correlations of many-body theory, the spectroscopy for intense field, regular-chaos transitions and correspondence between classical mechanics and quantum mechanics, etc.As a sensitive probative tool of interaction of the fields and particles, Rydberg atoms have widely used to many fields due to the characteristics of long-lifetime, wide scattering cross section and sensitive to applied external fields. For example, atom-chip experiments that realize control and storage of the Rydberg states have opened the way to investigations at the frontier of solid state physics and atomic physics. Aside from their relative ease of use and potential as atom interferometers, they provide an ideal environment in which atomic ensemble can be integrated with, and coupled to, devices on a microcircuit. The dynamic measurement in external static fields may simulate strong effects in celestial physics subject to ultra conditions. Furthermore, physical scientists have paid more and more attention on the dynamics of Rydberg atoms and molecules in strong external fields, which have important applications in many branches of physics such as astrophysics, plasma physics and semiconductor physics not only, but also have great academic significance in many basic questions on atomic physics and quantum mechanics, for example, the diamagnetism, the quantum-classical correspondence, the ionization induced by fields, etc. For theoretical works the system of Rydberg atom in strong fields is typical example demonstrating classical-quantum correspondence and exhibiting the transition from regular motion to chaos motion. This system became one of a few available low dimensional systems for understanding quantum chaos.Since 70^th years last century the development of physics has to confront with the challenges from complicated atomic and molecular system having higher dimensional degree of freedom and strong correlation between particles. Variety of the classical method got resurgence as the full quantum treatment fails in exactly solving this problem. Closed-orbit theory is available semi-classical approach to spectrally analyze the non-integrable system with a finite resolution, because it reveals that multiple-periodic phenomena hidden in quantum transition. The calculation method can be referred to what called space region-splitting consistent and iterative approach: In atomic nucleus region wave function is calculated by quantum mechanics, such as Coulomb scattering and Core-scattering. The impacts of the external fields can be ignored respect to the Coulomb interaction of the core. In region far away from the nucleus the electron motion is along with classical trajectories, the wave functions can be built according to quasi-classical approximation. The inner and outer solutions are connected in proper position in the Coulomb region around the core. To ensure accuracy of the result, the asymptotic expand is introduced for inner solution and carried out the stationary phase approximation. This theory provides a whole new method for studying the diamagnetism of the atoms and molecules,scaling property and the energy structure of the Rydberg states.In last twenty years, the closed orbit theory has successfully used to approach to photoabsorption phenomena of some atoms and molecules from simple hydrogen atom and Lithium atom to H₂ molecule in external fields. The research method also has extended from original electron closed orbit to the photon closed orbit recent, and implemented quantum defect theory, model potential, scaled variables recurrence spectroscopy, quantum spectral function, the uniform approximation and harmonic inversion, etc. A recurrence spectrum is the Fourier transformation of the photoabsorption spectrum. Each oscillating peak in the recurrence spectrum corresponds to the contribution of one semiclassical closed orbit beginning and ending near the nucleus. Therefore, the recurrence spectrum has connected the visible signal in quantum spectra with the closed classical trajectory of the electron, and built a bridge between classical trajectories and quantum spectra.Up to now, the closed orbit theory and recurrence spectra method have got widely applications, however a general extended closed orbit theory on multi-electronic atoms still is required partly due to the fact that atoms with a heavy core behave differently from the light core and partly accounting for the fact for the photoabsorption process of the Rydberg atoms the most complex dynamics occurs in a small region near the nucleus such that must be evaluated in full quantum mechanical framework. Based on the closed orbit theory framework together with the quantum defect theory and time-independent scattering matrices theory, we calculate the recurrence spectra of diamagnetic Cs atoms at several different scaled energies near the second ionization threshold. The results reveal that the new extra peaks in spectra are attributed to the combination recurrences of semiclassical closed orbits arising from core-scattered events. This method considers the dynamic states of the Rydberg electron in the core region and long-range region and can be analytically resumed to include all orders of core-scattering automatically. With this method a convergent recurrence spectrum has been obtained. It is found that the spectral complexity depends sensitively on the scaled energy. With the increase of the scaled energy, the spectral structure changes from simple to complicate and the corresponding dynamics from regular to chaotic. Comparison of the recurrence spectra with Dando's result under the same conditions demonstrates that there exist some similarities and a few deviations each other, and furthermore, evidences the feasibility of the scattering matrix method was explained. This method can be generalized to approach the simple molecular system readily, as an example we investigate the recurrence spectra of H₂ molecules in the strong external magnetic field. The quantum resonance peaks are intimately related to the corresponding closed orbits and the new extra peaks in spectra are attributed to the combined recurrences of semiclassical closed orbits which arise from the influence of elastic scattering and inelastic scattering. It is demonstrated that the interchannel scattering and the intrachannel scattering are equivalently important.For a typical Rydberg molecule, when placed in the external field, there exist rotations and vibrations in the inner of nucleus so that electrons will experience a multichannel scattering process. The states of the Rydberg electron and nucleus will change while colliding. Comparing with H₂ molecules, the NO molecule, named as "Star molecule", is more complicate and more difficult for the academic analyze. Using the multichannel quantum-defect theory, we extend closed orbit theory to complicate molecules, and calculate the recurrence spectra of NO molecules in the strong external magnetic field. It is indicated that the contribution of core-scattering arose from the interchannel scattering and the intrachannel scattering is more crucial than the contribution in atomic systems.The thesis works include six chapters. The first chapter is summarization, which briefly introduces the trait and the progress on the atoms and molecules in strong external fields, the subject we choose and the main work we have done. The second chapter analyzes the multichannel quantum defect theory. In the third chapter, using the scattering matrix and combining the quantum defects theory with the extended closed-orbit theory, we calculate the recurrence spectra of Rydberg Cs atoms in the magnetic field. In the next chapter, we develop the scattering matrix theory from the atomic systems to the molecular systems and calculate the recurrence spectra of H₂ molecules in the strong magnetic field. In the fifth chapter, together the quantum defect theory with molecular closed-orbit theory, the recurrence spectra of NO molecules in the magnetic field are presented. As the conclusion, in the last chapter, we briefly summarize the total subject and give an outlook for the future work.