Analysis Of The Tensor Forces In The Shell Model Hamiltonian

The Shell Model(SM) is one of the most fundamental theories in the nuclear physics. It has been very successful in describing various properties of the low-lying states in the light and medium nuclei, such as the binding energies, the spectroscopy, the transition properties, etc. The key to the success of the SM is the excellent choice of the Hamiltonians. However, an effective Hamiltonian, which provides good saturation properties and good spectroscopy, seems very difficult to be built from a realistic nuclear force.Instead, it is usually built in other ways, such as fitting the experimental data. Those Hamiltonians may include the most important information of the complex nuclear system. Therefore, to deeply understand the interacting system of the nucleus, it is necessary to study the structure of the SM Hamiltonians via analyzing the contributions of various tensor forces. Meanwhile, this analysis also provides an important guidance when one builds a new SM Hamiltonian. A shell model Hamiltonian usually includes one body term and n-body interactions. The two-body interaction is the most often used one, and can be separated into monopole part Hm and multipole part HM. Hm is responsible for the bulk properties, such as binding energies and shell gaps, while HM provides good spectroscopy. To investigate the structure of the Hamiltonian, the HM part of some realistic Shell Model Hamiltonians, USD, KB3G and GXPF1A, have been transformed from the normal representation to the particle-hole representation by using the known formulation.It is well known that HM is dominated by the pairing and the quadrupole interactions. Therefore, the modeling with pairing plus quadrupole forces has been very successful in describing various properties of nuclei, especially, for the deformed ones. A typical example is the Projected Shell Model(PSM), which provides a good description of rotational bands. Other types of tensor forces such as the Gamow-Teller force, octupole and hexadecapole interactions are also important parts of the shell model Hamiltonian. However, the coupled tensor forces, such as [rιY1,(?)σ]λand [ι(?)σ]λin the shell model Hamiltonian have not yet been analyzed. The analyses seem necessary because some coupled-tensor forces have already been found to play important roles in the study of the strength function. In this thesis, the multipole term was separated from the SM Hamiltonian and various spherical tensor forces were compared with the known realistic SM Hamiltonians (USD, GXPF1A, FPD6). It has been shown that some coupled-tensor forces, such as [r2Y2(?)σ]1, also give certain important contributions to the shell model Hamiltonian.