Few Questions. Scattering Calculations

The Resonanting group method (RGM) is first proposed in 1937 by J.A. Wheeler. It has been used widely to study the structure of nuclei, nuclear scattering and reaction problems. In this method, the wave function of the nucleus is composed of the internal wave functions of ea,ch clusters and the relative motion wave function between clusters. Starting from the Schrodinger equation and integrating the internal coordinates of the clusters, the integro-differential equation which is satisfied by relative motion wave func-tion can be obtained. In this way. we don't need to deal with the multi-body problem, which is transfered to one-body problem. However, due to the requirements of antisym-metry of identical particles, the calculation of the integral kernel is rather complex, which brings almost insurmountable difficulties.To make the calculation tractable, the generating coordinates are introduced. The relative motion wave function is expanded by known functions, for example, the Gaussian functions. Then the RGM equation is reduced to a set of linear algebraic equations. The generating coordinates method (GCM) has been widely used in the nuclear physics and achieved a lot of success. Because the RGM wave function is expanded by other functions, the results obtained from GCM may depend on the number and the properties of functions used. For example, when the relative motion wavefunction is expanded by Gaussians with different centers, we need to check the stablization of the results by varying the distance between two adjacent Gaussians. But the numerical instabilities will appear when the distance between two Gaussians are too small. So it is interesting to explore the method to solve the RGM equation directly in hadron physics. In the present work, we proposed a new numerical method:iterating Numerov algorithrn to solve directly the RGM equation. The method is applied to nucleon-nucleon scattering phase shift (IJ=01) calculation in the framework of Isgur-Karl quark model.The study of dibaryons is an important subject. On the one hand, it is a new structure of matter. On the other hand, the freedom of the system will be enlarged accompanying with the increase of the particle number. For example, we have new color structures here. The investigation of the dibaryon can also make further test of quark model which have successfully described the properties of hardons. Therefore, the study of dibaryons will supply a wider realm for us to understand and even test QCD.Since the first theoretical prediction of H dibaryon by Jaffe in 1977,several dibaryon states such as d', d*,NΩ,ΩΩand so on have been proposed. Unfortunately there is no any convincing evidence in experiments to demonstrate the existence of the dibaryon so far. By using the chiral quark model and the quark delocalization color screening model (QDCSM), the possible dibaryon candidates AA andΩΩare studied within the framework of resonating group method(RGM). Here, the RGM equation is solved by the widely-used method Gaussian Expansion Method. The intermediate-range mechanisms of the two models are totally different. In the chiral quark model, the intermediate-range attraction is offered by theσmeson exchange, while quark delocalization and color screening mechanism governs the intermediate-range attraction in the QDCSM. In the strong interaction, the two dibaryons have no decay channels, However we can study their behaviors by calculating the phase shifts for AA andΩΩscattering in the low-energy regions. The results show that no bound states can be formed in two model for AA andΩΩstates..