Total Energy Surface Based On The Projected Shell Model And Its Application

The status of study of nuclear shapes and the related current interests are introduced. More comprehensive and deep understandings for the nuclear shape symmetry and symmetry break have been achieved with developments of experimental technology and nuclear structure theory. Theories describing nuclear shapes, such as the microcosmic theory, Hartree-Fock method, and widely used energy surface methods, TRS and TES theories, and their merits and demerits are discussed briefly. It is emphasized that the further development of the theoretical model is necessary in order to describe nuclear shape more reasonably and precisely.The framework of Total Energy Surface based on the Projected shell model (PTES) is formulated in this thesis. The present method describing the highly rotating nuclei is a quantum-mechanical one, and can give the nuclear shape changes with the angular momentum, while the TRS method describes the nuclear shape varying with the rotational frequency, which is semi-classical. For the rotation of a triaxial nucleus, the assumption that the rotation is round a fixed axis in TRS is unreasonable. However, PTES method is based on the shell model where there is no concept about the fixed rotational axis. As the basis of new theory, we have also introduced in detail the Triaxial Projected Shell Model (TPSM) including multi-quasiparticle configurations mainly from four aspects: the projected method; the choice of the deformed basis; the choice of the Hamiltonian and diagonalization of eigenvalue equation. Then on the basis of the TPSM, we have formulated the framework of Total Energy Surface based on the Projected shell model (PTES), which describes the total energy surface of an nuclear state with good angular momentum and parity in the laboratorial coordinate system.We have accomplished the Fortran code of PTES and applied to calculations of the yrast band, excited bands and isomeric states in even-even nuclei in the different nuclear mass regions, A～130 and A～170, the results are in a good agreement with the experimental data. The changes of nuclear deformations and band structure with increasing angular momentum are successfully described. By a comparison with the results of TRS calculations, it is found that the PTES theory usually gives a somewhat larger triaxial deformation than TRS does, and even in some case where TRS calculation shows an axial symmetry, while PTES can give a considerable triaxial deformation. The powerful experimental support of the PTES result is the fact that the experimentalγband was observed in these nuclei. For example, for the yrast states of ¹⁷²W a triaxial deformation (γ= 15°) is obtained from the PTES calculation, while the TRS calculation results in a very smallγdeformation. However, theγband based on the ground state in ¹⁷²W was observed experimentally. This indicateγdegree of freedom for this well deformed nucleus. A possible reason for giving a lessγdeformation from the TRS method is that the assumption of a fixed rotational axis in TRS is good only for axial shape but not good for triaxial shape.We have performed calculation for the ^178m2Hf isomeric state by using PTES and analyzed the band structure of ¹⁷⁸Hf by using TPSM. The result shows that the experimentalγband based on the ground state can be well reproduced withγ= 22°. By using the sameγvalue , we predict aγband based on the ^178m2Hf(16⁺) isomeric state, its band head is 14⁺, which remains to be discoverded experimentally, and it is a hope that thisγband could be a possible bridge in realizing the way of de-excitation of the ^178m2Hf isomeric state.Some possible further developments of the PTES theory and its applications are discussed by the end of this thesis.