Studies Of The Structure And Spectrum For Some Weakly Bound Three-body System

The studies of three-body systems have been across many fields, especially for their structure and properties which were fundamental problems in physics. Weakly-bounded three-body system has properties which have no classical analog, for example, Efimov ef-fect predicted by Vitaly Efimov since 1970. The main characteristics of the Efimov effect are that there are infinite number of weakly bound three-body states when the two-body scat-tering length a is infinite and these bound states can be characterized by the scaling relation. Efimov effect is a good example for the discrete scaling symmetry in physics. Atom diffrac-tion technique, ultracold Atomic preparation and magnetic Feshbach resonance technology development makes it possible for experimental observation of Efimov effect, meanwhile, it brings challenges to the theoretists to make the quantitative explanations on the experiments. The van der Waals trimers composed by noble gas atoms, which have strong correlation be-tween atoms, are ideal samples for the studying of quantum chaos. Based on these frontier problems of weakly-bounded three-body systems, we develop methods for calculating ac-curate values of binding energies and sizes. We carry out calculations on the structure and properties for 4He27Li, four Efimov-favored systems, Ar2Kr and Ar2Xe. The thesis focuses on the following three topics:(1) The very earliest and most promising system in which Efimov effect can be found is He3. It was not until 2015 that a experimental paper for Science identified the excited state of the 4He3 was an Efimov state. Another promising system, similarly to 4He3, is He2Li. We carry out calculations on the van der Waals trimer 4He27Li, using the slow variable dis-cretization (SVD) method combined with the discrete variable representation (DVR) basis within the frame of hyperspherical coordinates. Our results demonstrate that the system presents an excited state which shows Efimov character. Our calculations also demonstrate that the three-body parameter (3BP) is independent of the short-range details of the two-body interaction, but dependent on the value of the background scattering length.(2) Efimov-favored systems are ideal for the direct observation of multiple Efimov res-onances because of the small scaling constant. The observation of multiple Efimov reso-nances is important for directly testing Efimov scaling property. Recently, the observation of three Efimov resonances in 6Li133Cs2 by Tung et al., for the first time, have provided direct evidence of the discrete scaling property. Universal properties of Efimov states for four Efimov-favored systems,3He*87Rb2,6Li174Yb2,6Li133Cs2 and 6Li87Rb2, are investigated, using the S VD method combined with the finite-element method-discrete variable represen-tation (FEM-DVR) basis within the frame of hyperspherical coordinates. Three successive Efimov states are obtained for all the four Efimov-favored systems. The size-binding mo-mentum relation of the Efimov states are studied as well. On basis of these studies, we suggest using this size-binding momentum relation to confirm an Efimov state for the first time.(3) Based on our calculation method, the rovibrational bound levels J= 0-1 and their statistical behaviours of Ar2Kr and Ar2Xe trimer are investigated. The effect of the Axilrod-Teller potential term on the rovibrational spectra is taken into consideration as well. Based on the optimization of the B-spline basis for hyperangles, the highest hyperspherical potentials, which we coupled in our calculations, have five significant digits. The binding energies of highest rovibrational states have four significant digits. The Brody parameter is 0.68 for J=0 spectra of Ar2Kr when the the Axilrod-Teller potential is not included. After the Axilrod-Teller potential is taken into consideration, the Brody parameter becomes 1. Same trend is found in Ar2Xe. We can conclude that these two systems are fully chaotic when the Axikod-Teller potential is taken into consideration. For J=1° case, the statistical properties depends essentially on the coupling between|K|=0 and|K| = 1 subsystems.