Exact Solution Of The Mean-field Plus Special Non-separable Pairing Model With Three Non-degenerate J-orbits And Its Application

The nuclear shell model is fundamental and a starting point in understanding nuclear struc-ture in low-energy regime.In this thesis,within the shell model framework,the shell model mean-field plus orbit-dependent pairing model with three non-degenerate j-orbits and its pri-mary application to the ds-shell nuclei are studied.The algebraic approach used is an extension of that used in solving the mean-field plus orbit-independent standard pairing model.In the first part of this thesis,nuclear models,especially the mean-field plus standard pair-ing model and the algebraic approach to its solution,are briefly outlined.The exact solu-tion of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits is presented,based on which the non-separable pairing model with three non-degenerate j-orbits is solved exactly with a constraint on the pairing strength parameters.A Mathematica code for numerical evaluation of the solution is compiled accordingly.The al-gebraic approach presented is a generalization of the Bethe-Richardson-Gaudin methodology in solving the orbit-independent standard pairing model.As a primary application of the non-separable pairing model,binding energies and their even-odd differences,the first pairing excitation energies,the two-neutron separation energies and their even-odd differences of 17-23O are fitted by the model and compared with the corre-sponding experimental data.It is shown that these quantities can be fit by the model rather well.Therefore,the non-separable pairing model proposed is suitable in description of low-energy structure of these ds-shell nuclei.