The Study Of The Scattering Matrix Theory Of The Recurrence Spectrum Of NO In Strong External Magnetic Field

The photo-absorption phenomena of atoms and molecules in strong external fields,which is the ideal system to study and develop semiclassical theory and quantum chaosand ,at the same time, is a challenging topic for the atomic physics, have attracted muchattention in recent years. "The semiclassical closed-orbit theory "put forward by M. L.Du and J. B. Delos has been broadly applied due to its clear physical picture and tersetheoretical computational method, and is extensively used to explain that phenomena.For instance, the theory has made comprehensive study over the photo-absorptionspectrum of various atoms whose properties in external fields, for example, the stabilityof orbits, bifurcation problems, chaotic phenomena and wave packet dynamics, havebeen analyzed detailed. All show that that theory has become a link between quantumand classical theory.As for the photo-absorption of simple atoms, we may only consider a singlechannel scattering process. But for a typical Rydberg molecule, for instance, the NOmolecule studied at present, named as "Star molecule", there exist rotations andvibrations in the inner of nucleus so that electrons will experience a multichannelscattering process. The states of the Rydberg electron and nucleus will change whilecolliding. Thus, firstly, the multichannel quantum-defect and scattering matrix theorymust be incorporated to deal with that problem.In my subject, scattering matrix elements are found through incorporating themultichannel quantum-defect theory and scattering matrix theory under the extendedsemiclassical closed orbit theory, and simultaneously the potential of NO molecule issimplified using a new model. We mainly study the closed orbits of NO molecule inexternal magnetic fields and the scattering matrix in long-range.(1) Firstly we analyze the physical picture of the photo-absorption phenomena ofNO molecule in external magnetic fields.(2) We compute the potential of NO using the approximation which the potentialhas different expression in different region. We analyze the potential numericaldistribution in the inner region with the help of Gauss98 and find the biggest inscribedequipotential cross-section. In the distant region, we select a potential with sphericalsymmetry.(3) We give the Rydberg electronic Hamiltonian of NO in strong fieldsincorporating the model potential and correspondingly, the canonical equation is given.At r = 12 a.u., we also find all the closed orbits in three channels, where the scaledenergies are -0.48, -0.85, -1.49, and rotational quantum numbers N+ are 1, 3, 5respectively.(4) Extending the semiclassical closed orbits, and incorporating multichannelquantum defect theory and scattering matrix theory, we analyze the Fouriertransformation strengths of individual elements of the long range S-matrix to draw thelink between the transformation spectrum and closed orbits.This subject is divided into five chapters. The first chapter is summarization, whichbriefly presents the development history of semiclassical closed orbit theory and thedifficulty of my subject. The second chapter is devoted to the devise of the outsidepotential of NO in strong fields, and the search of closed orbits of three channels, N+=1,3,5 with the tool of the canonical equation. The third chapter analyzes themultichannel quantum defect theory. The fourth chapter is the use of scattering matrixtheory in NO of strong external magnetic field, we mainly discuss the relationshipbetween the long range scattering matrix and closed orbits. As the conclusion, in the lastchapter, we briefly summarize the total subject and give some advice for the futurework.