Semiclassical Theory Of The Recurrence Spectra Of Multi-Electron Atoms And Molecules In Strong External Fields

The strong resonance structures of the photoabsorption spectra of high Rydberg atoms and molecules in strong electric and magnetic fields have attracted much interest, they have been proven to be typical examples for studying the semiclassical theory and quantum chaos. At present, many international theoretical researchers and experimental groups are studying the complex spectra of the atoms and molecules in external fields. Among them, the "closed orbit theory" put forward by M.L.Du and J.B.Delos takes the lead. Due to its clear physical picture and wide applications, it has been extensively used to explain the oscillating phenomena of the complex spectra of the highly excited Rydberg atoms and molecules in external fields and become an important link to connect the classical and quantum theory. At the same time, 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 and has acquired great achievement.At the end of 80 decade, with the presentation of the semiclassical closed orbittheory, it has made a full study for the photodetachment oscillating character of H~-, which is an important theoretical and experimental model system in parallel electric and magnetic fields , crossed electric and magnetic fields and fields with arbitrary orientations. It has also been applied to describe the photo-excitation and wave packet dynamics of some simple systems such as hydrogen atom and Lithium atom in electric and magnetic fields. Not only the validity of the closed orbit theory has been fully confirmed, but some methods such as recurrence spectroscopy and energy statistics have been developed. Recurrence spectra is the Fourier transformation of the photoabsorption spectra. Because the photoabsorption spectra obey the scaling property, after a transformation of the photoabsorption spectra versus time, a series of sharp peaks have been appeared, each oscillating peak corresponds to the contribution of one semiclassical closed orbit. Therefore, the recurrence spectra have connected the visible signal in quantum spectra with the classical motion of the electron, it has been applied to study the complex spectra from the Rydberg state to positive energy region. In the past decades, closed orbit theory and recurrence spectra method have got widely applications and the theory itself have made ceaseless improvement and development. Comparing to the hydrogen atom , when we use the semiclassicalclosed orbit theory to compute the recurrence spectra of multi-electronic atoms and molecules in strong external fields, new difficulties appear: (1) Because of the effect of core scattering, the number of the closed orbits increases very rapidly, and most of the orbits are unstable, besides, there are various combination between different orbits called combination orbits, which makes the problem much more complicated; (2) The existence of shadow effect, which includes two aspects: on the one hand, it decreases the amplitude of the recurrence, reducing the oscillating strength of the core scattering; on the other hand, when the orbit passes the ionic core, due to the existence of the diffraction effect, some new orbits which couldn't appear in the primitive orbit and the combination orbit of the hydrogen atom would appear. In addition, at some values of the scaled energy, the bifurcation effect is significant The closed orbit theory doesn't suit near the bifurcation point, so it is necessary to improve and extend the theory. At the same time, as for the molecule, due to its many nuclei and many ionization threshold, it is essential to combine the closed orbit theory with the multichannel quantum defect theory.According to the above problems, we have mainly done the following work: 1 ^ By using the semiclassical closed orbit theory and the region-splitting consistent and iterative method, we have calculated the recurrence spectra of Rydberg Helium atom in parallel electric and magnetic fields and the recurrence spectra of the Lithium atom in the perpendicular electric and magnetic fields. Our results are as follows:(a) When we search the closed orbits, in order to remove the Coulomb singularity of the classical motion of Hamiltonian, we implement the Kustaanheimo-Stiefel transformation, which transforms the system form a three-dimensional space to a four-dimensional one. After such transformation, the singularity near the origin has been removed. The elimination of the Coulomb singularity makes the numerical calculation very stable and each orbit can be launched from the origin, thus improving the computing precision.(b) We use a new model potential. For the Rydberg atoms, the effect of the atomic core acting on the excited electron can be modeled by a model potential. In the previous studies, they consider that the potential acting on the excited electron is a Coulomb attraction potential modified by a short-ranged model potential, but neglect the exchange potential between the electrons due to the spin action. But when M.Keeler and T.J.Morgan studied the effect of the electron exchange on therecurrence spectra experimentally, they have already observed its influence. In our calculation, we consider this influence and put forward a new model potential. We bring forward a method for studying the application of the Pauli exclusion principle in the dynamics of the semiclassical theory and the Rydberg system. The calculation results show when we consider the electron exchange influence, there are more peaks appeared in the recurrence spectra, which are caused by the combination orbits of the hydrogenic orbit and the core scattered orbit.(c) Extending the closed orbit theory from the two-dimensional space into three-dimensional one, with a strong emphasis on the influence of the atomic core scattering on the recurrence spectra. Unlike the case of the parallel electric and magnetic fields, in perpendicular electric and magnetic fields, the cylindrical symmetry is destroyed, the Hamiltonian has three non-separable degrees of freedom, therefore the dynamical behavior of the corresponding systems will have a great change. Because of the simultaneous action and competitions of the electric field .. magnetic field and the nuclear coulomb potential, the region of the regular motion decreases furthermore, unlike the two-dimensional orbits in the electric field ^ magnetic field or parallel electric and magnetic fields, the closed orbits all lie in three-dimensional space. The comparison of our results with the recurrence spectra of the hydrogen atom verify the important contribution of the core scattering effect on the recurrence spectra. 2, Using the time-dependent semiclassical closed orbit theory, we calculate the recurrence spectra of the Li Rydberg atom in strong magnetic fields plus a weak oscillating electric fields and analyze the influence of the oscillating electric field on the recurrence spectra. The chief works are as follows:Developing the closed orbit theory from the time-independent systems to the time dependent systems. In the previous researches, people mostly discuss the static electric fieldn magnetic field or the coexistence of the electric and magnetic fields, but have done a little calculation on the time-dependent systems. Whereas in recent years, the character of the photoabsorption spectra of the time-dependent fields have attracted widely attention, because the time-dependent external field is widely spread in the scientific experiment and practical applications. When the atom is placed in time-dependent fields, due to the influence of the unstable field, the outgoing ang^ incoming angle ^ period and classical action will be changed greatly, adding the complexity of the problem, producing new modulation phenomena.This is the first time to calculate and analyze the recurrence spectra of the Li Rydberg atom in strong magnetic field plus a weak oscillating electric field. The results show: when there is only static external field, there exist many strong recurrence in the absorption spectra, when an oscillating electric field parallel to the external field is added, the recurrence spectra is weakened according to a complicated pattern: When the period of the radio frequency field can be compared with the period of the classical closed orbit, the recurrence will be reduced; the periodic orbits are sensitive to the periodic field, recurrences with period near integer multiples of the period of the oscillating field survive, while those that are out of resonance with the field are weakened or eliminated. These irregular phenomena are caused by the effect of the perturbation to the closed orbits and the modulation of the Bessel function to the recurrence spectra.3 > By using the semiclassical closed orbit theory, we calculate the recurrence spectra of the Rydberg H2 molecule in parallel electric and magnetic fields and make an elementary calculation and analysis to the recurrence spectra of NO molecule in the magnetic field. We have mainly done the following work:(a)Using multi-channel quantum defect theory, we extend the closed orbit theory from the atomic system to the molecular system. Comparing to a lot of the experimental spectra and theoretical calculation results, the photoabsorption spectra of the Rydberg molecules in strong external fields are attracting much attention. Until recently we have all discussed the single channel scattering process. Whereas as for a typical Rydberg molecule, when placed in external field, multi-channel scattering phenomena will appear, during the collision of the Rydberg electron with the nuclear, their quantum state will be altered. Even for the simple molecule, this phenomenon existed and must be treated by using the multi-channel quantum defect theory, (b) In order to simulate the scattering effect of the molecular core, we use a new model potential. Using this model potential, we compute the analytic expression of the model potential of the excited electron in Rydberg hydrogen molecule and NO molecule, by comparing with the previous theoretical and experimental result, we verify that the potential is correct and universal, it is suitable to all the Rydberg molecules. In the future, we will further discuss the influence of different excited electronic state and the nuclear vibration on the recurrence spectra of the Rydberg molecules.This thesis is divided into five chapters: The first chapter is introduction, which chiefly introduce the establishment and the development of the closed orbit theory generally, the subject we choose and the main work we have done. In the second chapter, we have calculated the recurrence spectra of Rydberg Helium atom in parallel electric and magnetic fields and the recurrence spectra of the Lithium atom in the perpendicular electric and magnetic fields by using the semiclassical closed orbit theory and the region-splitting consistent and iterative method, put special emphasis on the influence of the exchange potential of the electrons and the atomic core scattering on the recurrence spectra. In the next chapter, we develop the closed orbit theory from the time-independent system to the time-dependent system and calculate the recurrence spectra of the Li Rydberg atom in strong magnetic field plus a weak oscillating electric field, chiefly analyze the effect of the oscillating field on the recurrence spectra. In the fourth chapter, we present the analytic expression of the model potential of the excited electron in Rydberg molecule, using the multi-channel quantum defect theory and molecular semiclassical closed orbit theory, we calculate the recurrence spectra of the Rydberg H2 molecule in parallel electric and magnetic fields and the recurrence spectra of NO molecule in the magnetic field. In the fifth chapter, we give some important conclusions of this thesis and make a brief illustration to some problems which can be handled by semiclassical closed orbit theory. At last, we make an inspections to the challenge and the application of this theory.