Nucleon Pair Approximation And Random Interaction

Nuclei are complex systems consisting of nucleons, neutrons and protons. Nuclear physicshas been one of the main subjects among many branches of modern science,since Chadwickdiscovered neutron in1932. With the help of new radioactive-beam facilities internationally (e.g.,RIA and RIBF, etc), nuclear physics enter a new era.In1949, Mayer and Jensen developed the nuclear shell model. The nuclear shell model hasbeen the most important framework to study nuclear structure from a microscopic perspective.However, the configuration space of this model is too huge to deal with. Thus one has to re-sort to various truncation schemes. The nucleon pair approximation is an efficient and convenientapproach towards that goal. In this thesis we study a number of aspects of the nucleon pair approx-imation, including validity of such truncations and applications of this approach to low-lying statesof heavy nuclei. We also study general features of nuclear structure with random interactions bythis approach.In Chapter1, we introduce some fundamentals of atomic nuclei, the shell model, the short-range feature of nuclear force. We explain why the pairing phenomenon arises from the short-rangecorrelation in nuclear interaction, why spin-zero and spin-two pairs are dominant configurations inlow-lying states of medium-heavy nuclei. We also discuss the importance to study robustness ofgeneric features in low-lying states of atomic nuclei. The origin of simplicity exhibited in complexnuclei is one of the main challenges in nuclear and astrophysics. Random interactions provide uswith a powerful approach to study such simplicity.In Chapter2, we study the nucleon pair approximation of the shell model in a few contexts.The first is validity of pair approximation. We consider not only a phenomenological shell-modelhamiltonian but also effective shell-model hamiltonian (GXPF1A), not only even-even but alsoodd-mass nuclei, not only semi-magic but also open-shell systems. Our systematic studies demon-strate that the nucleon pair approximation is indeed able to reproduce very well the shell modelresults, although the gigantic shell model space is substantially truncated to a very small nucleon-pair subspace. Second, we apply the pair approximation to systematic studies of low-lying statesof nuclei with mass number A～200, with a separable phenomenological shell model hamilto-nian. Our calculations describe well the low-lying states of these nuclei. We also discussed theso-called multiplets which are nothing but a weak-coupling between the even-even core and the unpaired valence nucleon for some of these states. Third, we apply the nucleon pair approximationto studies of shape transition from spherical to axially deformed nuclei in the even Ce isotopes,proton-neutron pairing on backbend in48Cr, and IÏ€=8isomer in¹²⁸Xe.In Chapter3, we explain our studies of nuclear structure in the presence of random interac-tions. We explain the observation that semi-magic nuclei favor low-seniority if their single-particlesplittings are artificially enlarged. For the random sd (spin zero and two) boson system, we pointout that the low-lying states of such system favors a few novel collective motions due to s or dboson condensations, in addition to the well-know vibration and rotation. We analyze our resultsin terms of both wave functions and corresponding interactions among the random ensemble.As for future developments of the above works, we would like to mention two points as fol-lows:(1) Consideration of the isospin symmetry both in the nucleon-pair basis and the hamiltonian,(2) Application of the pair approximation to β-decay problem.