Abstract:
Transition probabilities of the ground-state bands in $\gamma$-soft nuclei are studied for the first time using the triaxial projected shell model approach. It is observed that the angular-momentum dependence of the transition quadrupole moment $Q_t$ is related to the triaxial deformation of the nuclear mean-field potential. The introduction of the $\gamma$-degree of freedom in the shell model basis is shown to have a little influence on the {\it constant} behavior of the low-spin $Q_t$ in a well-deformed nucleus. However, the {\it increasing} collectivity with spin for the low-spin states in a $\gamma$-soft nucleus can only be explained by considering the triaxial mean-field deformation.

Abstract:
Chiral rotation observed in $^{128}$Cs is studied using the newly developed microscopic triaxial projected shell model (TPSM) approach. The observed energy levels and the electromagnetic transition probabilities of the nearly degenerate chiral dipole bands in this isotope are well reproduced by the present model. This demonstrates the broad applicability of the TPSM approach, based on a schematic interaction and angular-momentum projection technique, to explain a variety of low- and high-spin phenomena in triaxial rotating nuclei.

Abstract:
Recent experimental data have demonstrated that $^{76}$Ge may be a rare example of a nucleus exhibiting rigid $\gamma$-deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and $\gamma$-vibrational bands in $^{76}$Ge, a rigid-triaxial deformation parameter $\gamma\approx 30^\circ$ is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published results from the spherical shell model. The occurrence of a $\gamma\gamma$-band in $^{76}$Ge is predicted with the bandhead at an excitation energy of $ \sim$ 2.5 MeV. We have also performed TPSM study for the neighboring Ge- and Se-isotopes and the distinct $\gamma$-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states.

Abstract:
We present a fully quantum-mechanical, microscopic, unified treatment of ground-state band and multi-phonon $\gamma$-vibrational bands using shell model diagonalization with the triaxial projected shell model. The results agree very well with data on the g- and $\gamma$-band spectra in $^{156-170}$Er, as well as with recently measured $4^+$ 2-phonon $\gamma$-bandhead energies in $^{166}$Er and $^{168}$Er. Multi-phonon $\gamma$-excitation energies are predicted.

Abstract:
We expand the triaxial projected shell model basis to include triaxially-deformed multi-quasiparticle states. This allows us to study the yrast and gamma-vibrational bands up to high spins for both gamma-soft and well-deformed nuclei. As the first application, a systematic study of the high-spin states in Er-isotopes is performed. The calculated yrast and gamma-bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-gamma phonon where current data are still sparse. It is observed that gamma-bands for neutron-deficient isotopes of 156Er and 158Er are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.

Abstract:
The Triaxial Projected Shell Model (TPSM) has been successful in providing a microscopic description of the energies of multi-phonon vibrational bands in deformed nuclei. We report here on an extension of the TPSM to allow, for the first time, calculations of B(E2) values connecting gamma- and gamma-gamma-vibrational bands and the ground state band. The method is applied to 166,168Er. It is shown that most of the existing B(E2) data can be reproduced rather well, thus strongly supporting the classification of these states as gamma-vibrational states. However, significant differences between the data and the calculation are seen in those B(E2) values which involve odd-spin states of the gamma-band. Understanding these discrepancies requires accurate experimental measurements and perhaps further improvements of the TPSM.

Abstract:
Nuclear magnetic dipole properties of ground bands and gamma-vibrational bands are studied for the first time using the triaxial projected shell model approach. The study is carried out for the Dy and Er isotopic chains, ranging from transitional to well-deformed region. It is found that the g-factor ratio of the 2^+ state in ground bands to that of gamma-bands, r=g(2^+, gamma-vib)/g(2^+, ground), varies along an isotopic chain. With the gamma-deformations, which best reproduce the energy levels for both bands, we obtain a qualitative agreement with the experimental data. This result thus suggests that study of the ratio may provide an important information on the triaxial deformation of a nuclear system. The angular-momentum dependence of the ground band g-factor on the triaxial deformation is also investigated.

Abstract:
The Projected Shell Model is a shell model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking $^{160}Dy$ as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many $J^\pi = 0^+, 1^+, 4^+$ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the Projected Shell Model is a model essentially with no free parameters.

Abstract:
A systematic study of the yrast-band structure for the proton-rich, even-even mass-80 nuclei is carried out using projected shell model approach. We describe the the energy spectra, transition quadrupole moments and gyromagnetic factors. The observed variations in energy spectra and transition quadrupole moments in this mass region are discussed in terms of the configuration mixing of the projected deformed Nilsson states as a function of shell filling.

Abstract:
the study of nuclear isomer properties is a current research focus. to describe isomers, we present a method based on the projected shell model. two kinds of isomers, k-isomers and shape isomers, are discussed. for the k-isomer treatment, k-mixing is properly implemented in the model. it is found however that in order to describe the strong k-violation more efficiently, it may be necessary to further introduce triaxiality into the shell model basis. to treat shape isomers, a scheme is outlined which allows mixing those configurations belonging to different shapes.