Triaxial Potential Impact Of The Single-particle Wave Function And The Cranked Shell Model Variational Before Angular Momentum Projection Calculation

In the first part of the thesis , the eigen-value equation of a single particle moving in a triaxial deformed potential is solved with two kinds of basis. One basis space is the single j particle orbit, another is single shell N orbits. The representation transformations are carried for the first case in order to see clearly the links between the symmetries of the potential and the eigen wave function. The explanation is made for the characteristics of the wave functions in the second basis space.In the second part of the thesis, the connections between the matrix elements of angular momentum projection operator and the CG coefficients are provided by taking the simplest product wave function of two, and six particles as examples. The properties of the matrix elements of the angular momentum projection operator, the coincidence between the CG coefficients and integration methods are discussed. The advantages and the disadvantages of the two methods are analyzed. Then the angular momentum projection is performed for the basis of a six-particle system of the original cranking shell model. The diagrams of K structure for certain angular momentums versus cranking frequencies in the eigen-functions are plotted after solving the generalized eigen-value equations. The figures are compared with the original cranking shell model results. The differences between them are analyzed..At last, the internal essential relations of the two seemingly independent parts are pointed .