量子多体问题至今无法用量子力学进行精确求解，是物理学研究的热点之一。原子离子多电子高激发态能级结构研究是量子多体问题研究的一个组成部分，对认识电子关联效应具有重要意义。本文计划从理论计算和实验研究两个方面对原子离子的高激发态能级结构进行研究。我们将相对论性多通道量子亏损理论（RMCT）应用到复杂离子双电子体系，对La+离子里德堡态和自电离里德堡态的能级结构进行了研究。我们发现对于阈下的La+离子里德堡系列，电子关联效应较小，仅考虑“冻结实”近似的影响就可以得到较高的精度。而对于镶嵌在La+离子里德堡态中的“干扰态”，即收敛到更高阈值的La+自电离里德堡系列，基于“冻结实”近似的计算结果不能较好解释实验数据，说明激发电子对离子实的影响而引起的电子-电子关联效应（动态极化效应）较为重要。我们在计算中考虑了最主要的动态极化效应之后，“干扰态”计算精度都有提高，部分有数量级上的提高。在此基础上，我们进一步将计算拓展到La+第一电离阈以上，由此很好地标识了实验光谱的La+自电离里德堡系列。进一步我们将RMCT方法应用到复杂原子三电子体系，采用RMCT方法对Sc原子自电离里德堡态能级结构进行了研究。虽然Sc原子的能级结构复杂，但是Sc原子自电离里德堡态的计算结果表示，3d4s(1D)nd 2D5/2和3d4s(1D)nf 2F7/2系列计算中仅考虑“冻结实”近似，其实验与理论计算的量子数亏损之差即可小于6%，3d4s(1D)np 2P1/2系列在考虑简单的偶极动态极化效应后也可以达到6%。由此可见，RMCT方法可通过较少的计算努力获得大量精度较高的能级数据。在对原子离子高激发态能级结构实验和理论研究的基础上，结合国际上近年来获得快速发展的激光冷却和囚禁技术，我们将研究拓展到冷里德堡气体和超冷等离子体。我们在目前国际研究进展的基础上，在冷里德堡气体和超冷等离子体的结构和动力学参数，以及在不同条件下它们随时间演化的规律方面，提出拟研究的物理问题和实验研究方法。在实验系统的研制方面，完成了实验装置的总体设计，进行了实验系统的搭建。
As quantum many-body issues could not be solved precisely by quantum mechanics, the investigation is a significant subject of modern physics research. The highly excited states of atoms and ions have been one of the quantum problems which are intensely studied, and many useful information for understanding electron correlation effects have been provided. The electronic structures of highly excited atoms and ions are studied both theoretically and experimentally.The RMCT (relativistic multichannel theory) is applied on complex quasi-two electron system, and the energy levels of La+ Rydberg series and La+ autoionization Rydberg series via two intermediate states (Xe)5d6d 1P1 and (Xe)5d6d 3F2 are calculated by MQDT in the framework of RMCT. Firstly, by considering only the dissociation channels which are related to the two lowest ionization thresholds of La+, i.e., (Xe)5d3/2 2D3/2 and (Xe)5d5/2 2D5/2, in calculating the electronic structures below the threshold of (Xe)5d3/2 2D3/2. The La+ Rydberg series agree well with the experimental levels, while the energy levels of some La+ autionization Rydberg series converging to (Xe)5d5/2 2D5/2, i.e., so called perturbing states deviate from the experimental results far beyond the experimental errors. Secondly, by considering the electron-electron correlation effects caused by dynamical polarizations, a better agreement with the experimental data is obtained for the calculated energy levels, which shows the overall effects of electron correlation. Thirdly, the calculaton is extended to the autoionization spectra, and the complete La+ autionization Rydberg series are calculated and assigned.The RMCT method is applied on complex quasi-three electron system further, and the Sc autoionization Rydberg series are calculated with RMCT. Although the energy levels of Sc are very complex, it is found that the errors between experimental quantum defects and theoretical values of Sc autoionization Rydberg series 3d4s(1D)nd 2D5/2 and 3d4s(1D)nf 2F7/2 could generally be less than 6% under the frozen core approximation (FCA), and those of 3d4s(1D)np 2P1/2 series could be refined in 6% with only considering the simplest dipole dynamic polarization effect. It is demonstrated that RMCT could be used to obtain large amount of data about electronic structures with high precision at the expense of limited computation efforts.The laser cooling and trapping method, which was developed in recent years, the study of the electronic structures of highly excited atoms and ions was extended to ultracold regime. On the basis of international research progress, some proprosals of exploring the structures, dynamics, and evolution in different external conditions of cold Rydberg gas and ultracold plasmas are presented. The design of experimental setup for cold Rydberg gas and ultracold plasmas is accomplished and most of the system is constructed and tested.
