Low-lying Spectrum And Quantum Phase Transition In Odd Nuclei

The nuclear low-lying spectra,can reveal rich information about nuclear structure including nuclear quantum phase transitions,evolution of shell structures,isomeric states shape coexistence and so on.In particular,the nuclear quantum phase transition?QPT?,characterized by the abrupt evolution between different ground stateshapes,is governed by the interactions of the valance nucleons.In recent years,QPT has been one of the advanced subjects in nuclear physics.For even-even nuclei,since they are relatively stable and the pattern of low-lying spectra is comparatively simple,there are amounts of investigations about these nuclei.In the whole nuclide chart,nevertheless,the number of odd-A nuclei is much more than even-even nuclei.Along with that,polarization of the even-even core driven by the odd nucleon leads to more complicated pattern of low-lying spectra.The spectroscopic properties and related interesting structures of unstable odd-A nuclei,in particular,have become the hot topics and frontiers of nuclear research.Covariant density functional theory?CDFT?can provide a self-consistent description for the nuclear properties of the whole nuclide chart and has achieved great success in nuclear physics.The framework of static nuclear mean field approximation,however,can only describe ground-state properties of nucleus.Recently,the collective Hamiltonian based on CDFT has been implemented and realized the global and self-consistent description of the spectra of even-even nuclei with quadrupole and octupole deformations.Very recently,we have extend the CDFT based collective Hamiltonian to study the low-lying spectra of odd-A nuclei by mean of the core-quasiparticle coupling?CQC?framework.The CQC model predicts excitation energies,kinematic and dynamic moments of inertia,and transition rates that are in very good agreement with experiments for deformed odd-mass nuclei ¹⁵⁷Gd and ¹⁵⁹Tb.In this thesis,We further extended the microscopic CQC model,namely to include the phonon excitation states,and apply to the following works:1)We compare the low-lying spectrum of ¹⁵⁹Tb calculated from microscopic CQC model with only the ground-state band of the core and with both the ground-state and?bands of the core,to investigate the effect of phonon excitation on low-lying spectra of odd-A nuclei;2)Microscopic signatures of nuclear ground-state shape-phase transition in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave function obtained from CQC model.As function of the physical control parameter-the number of nucleons-theoretical low-energy spectra,two-neutron separation energies,charge isotope shifts,spectroscopic quadrupole moments,and E2 reduced transition matrix elements accurately reproduce available data and exhibitmore-pronounced discontinuities at neutron number N?28?90 compared with the adjacent even-evenSm and Gd isotopes.The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which,at the critical neutron number,starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing corrections compared with the corresponding Sm isotopes;3)The CQC model is extended to include the octupole degree of freedom,and applied to study the excitation energies and electromagnetic transition rates of low-energy excitation states in ²²⁷Ac.The parity doublet in ²²⁷Ac can be reproduced quite well.