Development And Application Of The Projected Shell Model For Nuclear Structure And Nuclear Astrophysics

Atomic nucleus presents us a natural laboratory to study microscopic quan-tum many-body problems as well as macroscopic evolution of cosmos.Recent years,with the rapid development of the new generation of?-detecting devices and radioactive-beam facilities,it has been a frontier for nuclear structure and nuclear astrophysics to investigate structures and decays of nuclei at extreme conditions,such as extremes of isospin,angular momentum etc.Angular momentum projected theory is one of the microscopic models that could describe the above nuclear properties.The projected shell model?PSM?,after being developed and applied for about twenty years,has been testified to be able to give a successful description of nuclear quasiparticle?qp?excitations?e.g.,high-K isomers etc.?and collective excitation?such as high spin physics,low-lying?-vibration states etc.?.The PSM start with a deformed Nilsson+BCS qp basis,and then recovers the broken symmetries by projection techniques and mixes different configurations by diagonalizing the system Hamiltonian,nuclear properties like spectra,wave functions,electro-magnetic transitions etc.could be obtained finally.In this thesis,we developed the PSM theory in two ways,and applied the developments on problems in nuclear structure and nuclear astrophysics,respec-tively.On one hand,by efficiently calculating the rotated matrix elements among different qp configurations by the Pfaffian algorithm,the configuration space of the PSM?for even-even nuclei?is expanded to include up to 10-qp states for both positive and negative parities for the first time.This enriched tremendously the physics problems that the model can describe,such as the structural changes,loss of collectivity,quantum chaos?such as the rotational damping in high-spin,high-lying states of deformed nuclei?etc.of nuclei at very high spins??50?.It is shown that the higher-order qp states play indispensable roles in describing these problems.Moreover,the pairing interaction in the Hamiltonian is found to play important roles in the quantum-chaos phenomenon of nuclear systems.On the other hand,we developed the PSM to study Gamow-Teller tran-sitions among odd-mass nuclei,including adding the separable Gamow-Teller interaction into the original model Hamiltonian as well as calculating the matrix elements in the projected basis and including up to 7-qp states in the model space by the Pfaffian algorithms etc.This presents us a shell-model method to study electron captures?EC?and?-decays of?heavy deformed?odd-mass nuclei.EC??-decay?plays crucial roles in simulating core-collapse supernova?rapid neutron capture process i.e.,r-process?,where theoretical predictions are relied on.We calculated the B?GT⁺?and B?GT^-?of EC and?^--decay for⁵⁹Co and¹⁵³Nd,respectively.Good reproduction is found between calculations and the data.In addition,strong B?GT^-?from nuclear excited states are predicted,which may be important for r-process nucleosynthesis due to the thermal population of excited states in stellar environments with high temperatures and high densities.