Research On Nuclear Structure Models And Rotational Spectral Theory

This thesis firstly introduces some nuclear structure models and their application. Then, Three methods of diagonalization in quantum mechanics and calculation of shell model are discussed. Lastly, the relation of the parameters of Bohr-Mottelson rotational spectra formula is researched and a new ralation is pointed out.Firstly , we introduce shell model, collective movement model, particle-rotor model and project shell model. As special topic, cranking shell model, BCS method of pairing force, spin assignment of rotational spectra and inertia analysis and new development of identical bands are also discussed.In quantum mechanics, diagonalization is the process of extracting eigenvalue and eigenstate of mechanical quantity. The thesis classifies the diagonalization as three sorts, namely diagonalization in own representation, diagonalization in other representation and computational method. The level scheme of spin-orbit coupling shell model is calculated. Using computational method, Nilsson diagram is given which is very important in researching nuclear structure, and wave function of some levels was also given.Lastly, using four-parameter Bohr-Mottelson formula, some ground rotational bands of even-even nuclei is analyzed. The nuclei includes superdeformed(SD) nuclei in A-150 190 regions and normal deformed(ND) nuclei in actinide and rare-earth. The parameters obtained by the least-square fitting deviate from the relations derived from ab formula, abc formula and Harris formula, but are closer to relations deduced from ab formula and abc formula. Additionally, the relations to parameters of SD bands are similar to those of ND bands. Based on researching the relation of the parameters of Bohr-Mottelson rotational spectra formula from two-parameter Harris formula, in this thesis three-parameter Harris formula is ralation of the parameters of Bohr-Mottelson rotational used and a new spectra formula is cited. By use of four-parameter expansion, the calculation results of superdeformed (SD) bands of even-even nuclei in A-60, 80, 130, 140, 150, 190 regions and normal deformed (ND) bands of nuclei in actinide and rare-earth are analyzed , and the relation of the parameters is discussed. Comparatively, the new relation and Harris formula are consistent with experiment. In the end, the rotational spectra is also analyzed by drawing comparison between some rotational spectra formula fittings, finding that ab formula fits better in with the nuclear than the other formulas.