Study Of Neutron-rich Cd Isotopes Within The Nucleon-pair Approximation

Atomic nuclei are complex quantum many-body systems consisting of protons and neutrons.The nuclear shell model is one of the most accurate microscopic theoretical models to describe low-lying states of atomic nuclei.However,for many nuclei the shell-model configuration space is too large to handle.In the nucleon-pair approximation,the shell-model space is efficiently truncated by adopting low-energy collective nucleon pairs.Previous results suggest that the nucleon-pair approximation is able to provide good descriptions to low-lying states of semi-magic nuclei,transitional nuclei and well-deformed nuclei.The low-lying states of unstable nuclei far from the ?-stability line is one of the hot topics in nuclear physics.In this thesis we study the low-lying states of neutronrich 122,124,126,128,130,132,134,136,138Cd within the nucleon-pair approximation of the shell model.The available experimental excitation energies and quadrupole transition probabilities for 122,124,126,128,130,132Cd are well reproduced by our calculation.Here 132Cd is the most neutron-rich nucleus with available experimental data,and we also make predictions for the low-lying states of 134,136,138Cd.According to our calculation,the B(E2;0g.s.+? 21+)values exhibit an asymmetric feature with respect to the N=82 shell closure,which is mainly due to the contributions of the proton transition matrix elements.We consider the proton or neutron quadrupole operator multiplying 1/r02 to be the quadrupole phonon,and construct the phonon state with spin I based on the lowlying yrast state with spin(?-2).We calculate the explicit overlap between the phonon state constructed so and the low-lying state with the same spin.For all eight open-shell nuclei 122,124,126,128 Cd and 132,134,136,138Cd studied here,|21+>and|41+>can be well described to be the phonon states based on |01+>and |21+>,respectively.For 122,124,126,Cd and 136,138Cd,very interestingly,the 21+ state can be well described to be both the proton phonon state and the neutron phonon state,which are constructed by coupling the proton and neutron phonons to the 01+ state,respectively.This means that the two phonon states are non-orthogonal.We present an analytic relation where the overlap between such two phonon states is related to the expectations of the proton-neutron,proton-proton and neutron-neutron quadrupole-quadrupole operators in the 01+ state.As the proton-neutron quadrupole-quadrupole interaction plays a key role in low-lying states of open-shell nuclei,the above relation implies that the proton and neutron phonon states based on the 01+ state are hardly to be orthogonal in open-shell nuclei.