High Precision Calculations For Low-lying States Of Lithium Atom

The main part of this dissertation is to solve the Schrodinger equation for the low-lying states of the atomic lithium using Rayleigh-Ritz variational method.At present, it is possible for us to obtain extremely precise solutions for the Schrodinger equation of two-electron atomic systems by using Rayleigh-Ritz varia-tional method in Hylleraas coordinates. These solutions help us understand energy level structures of two-electron atomic systems very well, such as the atomic helium. However, extending to a three-electron system, such as lithium, has been much more challenging. Nevertheless, significant advances have been made along this line in the past two decades, partly due to rapid development of computer technology that pro-vides a powerful tool for solving large-scale variational problems with high precision. This dissertation endeavours in both the longitudinal and transverse directions for im-proving accuracy of variational results of the Schrodinger equation for low-lying states of lithium in Hylleraas coordinates. In the longitudinal direction, we developed parallel computer programs, which helped us overcome the time-consuming problem for large basis sets. We can now be able to enlarge the size of variational basis set up to 30,000 terms. We calculated the 2S,3S, and 2P states of lithium at this scale and found that the result for the 2S state was very precise, i.e. the variational energy is accurate to 14 significant figures. But, for the 3S and 2P states the results were not so precise. We further made endeavours along the transverse direction to improve the results for the 3S and 2P states, namely, to modify the method of constructing variational basis sets. For S states, since the total angular momentum of the system is zero, we do not need to consider the coupling of angular momenta and thus the degrees of freedom of the system reduce to six. For these six degrees of freedom, we found a more efficient way of choosing basis sets and obtained new results which were far more precise than the old ones. Using this new method, the energy level for the 3S state has been cal-culated to 14 significant figures. We further extended this calculation to the 4S-9S states and obtained good convergence against the size of basis set. Our results for the energy eigenvalues and eigenfunctions of the 2S - 9S states of lithium are the most accurate to date. For non S states, the problems of angular momentum coupling and the completeness of angular functions have to be taken into consideration because of the non-zero total angular momenta of systems. Here, we considered the 2P and 3D states. In addition to the radial parts of the bases, we also improved the angular parts. The results obtained for these two states are also the most accurate to date.Additionally, we discussed the problem of completeness of the Hylleraas bases, the problem of orthogonality of wave functions between two excited states and the effect of the second spin wave function.