Investigating Boundary State Characteristics Of Fewbody System

The nuclei11Li,14Be and17B are pronounced halo-structures which have two loosely bound valence neutrons. These nuclei are Borromean, i.e. while they are bound and there is only one bound state, they are considered as three-body system, with on bound states in the binary subsystems. We restrict this thesis to bound state properties and our procedures emphasize on the variational approach. Based on the three-body model, with the two-body phenomenological potential, such as Yukawa potential or exponential potential, our variational computation reproduce the binding energy and such halo characteristics as the abnormally large matter r.m.s. radius and give one analytical expression for the halo neutron distribution of matter density. All the results we get are accordant with the experimental data.For two-body system, there are two cases, the non-relative and the relative. With regard to the non-relative case, we discussed the numerical approach to solve Schrodinger equation directly, for the reason that there are only several potentials which can be solved analytically. This approach is also very useful in the three-body system, because in our three-body model, the interactions between the binary subsytems are described by phenomenological potentials, all the parameters of which must be fitted with ex-periment data. And this approach will play an important role in this process. For the relative case, we found certain systems that could be analytically studied, such as the Dirac oscillator and three-dimensional non-harmonic oscillator potential1/2r2+A/2r2For the former some analytical expressions of the matrix elements for dynamical operators are obtained and their behaviour is discussed in details. For the later, the s-wave bound solutions of both Dirac equation and Klein-Gordon equation are given when the scalar potential is equal to the vector potential. For QCD, what we discussed are about the Nambu-Jona-Lasinio model and the Dyson-Schwinger equation. The former is reviewed in its flavor SU(2) versions applied to quarks. The dynamical generation of quark masses is demonstrated as a feature of chiral symmetry breaking. For the later, it is shown on general ground that there exist two qualitatively distinct solutions for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the Nambu-Goldstone phase and the other one corresponds to the Wigner phase in the chiral limit. Additionally, we propose a general method for calculation the partition function of QCD at finite chemical potential. It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant. From this a criterion for the phase transition between the Nambu and the Wigner phase is obtained.