Structure Study Of Neutron-rich Nuclei And Nuclear Isomer By Using Projected Shell Model

Due to the recent application of radioactive ion beam and advanced?detectingdevice in nuclear experiments, it becomes possible to study the structure of nuclei un-der extreme conditions. Furthermore, to study Nuclear Astrophysics which is one ofthe current frontier topics in nuclear physics, one must reveal the property of unsta-ble nuclei in the neutron-rich and proton-rich regions. Motivated by these, we applythe projected shell model (PSM) to study some neutron-rich nuclei and the relevantnuclear isomer structure.The PSM begins with deformed Nilsson single-particle states, and the pairingcorrelations are incorporated into these states by a BCS calculation. Thus the Nilsson-BCS calculation defines a deformed quasiparticle (qp) basis on which the PSM isbased. Then angular-momentum projection is carried out on those multi-qp states toform a projected basis. Finally a two-body shell model Hamiltonian is diagonalized inthis projected space, from which we get the eigenvalues and wave functions. The PSMhas some advantages such as the use of a small configuration space, fast computationprocess, and wide application domain. It can be applied to most deformed nucleiincluding even-even, odd-mass, and odd-odd nuclei.The theoretical studies in this thesis have a close connection with the current nu-clear physical experiments. We perform PSM calculations for neutron-rich nuclei inthe mass A = 60 and 160 region up to high spins (I = 20 ). In the A = 60 massregion, we study systematically the structure of Cr and Fe isotopes with neutron num-ber from 30 to 44. Discussions focus on the character of the yrast spectra, momentsof inertia, and electromagnetic properties (B(E2), g-factor). By including the neutrong9/2 orbital in our calculation, we successfully interpret the irregularities found in theyrast spectra and B(E2) values. Our study reveals a soft property near the ground state of N?40 isotopes and predicts low-lying high-K isomeric band in 66,68Fe. For theodd-mass neutron-rich Cr, the nature of the 9/2+ isomeric state and the associated ro-tational band are interpreted to have a main component of the K = 1/2[440] Nilssonstate with prolate deformation. In the A = 160 mass region, the strongly-deformedneutron-rich, even–even Nd and Sm isotopes with neutron number from 94 to 100 andthe odd-mass 159Sm (as a representative example for the odd-mass isotopes) are stud-ied. We present the ground band and side band energies for each isotope studied inthis mass region. The emphasis is given to rotational bands based on various negative-parity 2-qp isomers. Our calculations further predict several proton 2-qp and neutron2-qp isomeric bands. Meantime, new bands in 159Sm based on neutron 1-qp are alsopredicted.The systemic calculations for these nuclei are carried out for the first time in PSM.A nearly perfect agreement between the PSM calculations and experiment indicatesthat the PSM is suitable for description of unstable nuclei, which extends greatly theapplication domain of the PSM in the nuclear structure study.