Angular Momentum- and Particle Number-Projections from Cranking HFB Self-Consistent Solution

Due to recent great progress in the experimental techniques of in-beam γ-ray spec-troscopy, a great number of precise data have become available on nuclear levels and transition rates over a wide nuclear mass range. In order to interpret the nuclear dynamics behind these data from a unified point of view, one needs an appropriate theoretical framework which is able to relate given nuclear interactions to observable quantities with required accuracy. Furthermore, the numerical analysis based upon such a scheme must be practicable on the contemporary fast electronic computer systems. Thus, (1) the formalism along the line of this thought must be fully microscopic and able to derive the cooperative properties such as nuclear deformation as a result of the symmetry-conserving microscopic interactions. The nuclear deformation is to be self-consistently determined from correlating single-particle motion obeying interactions among single-particle degrees of freedom, and therefore the presumption of the deformed field must be eliminated from the theoretical framework. (2) The formalism must be quantum-mechanical and the admixture like semi-classical picture must be eliminated, because whole observable nuclear properties are in principle specified with a. set of quantum numbers. Though classical concept such as rotational frequency is frequently used, it corresponds to energy difference between two levels specified with quantum numbers and the terminology is provisional.