Nucleon-pair Correlations In Low-lying States Of Atomic Nuclei

For low-energy phenomena, atomic nuclei are regarded as complex quantum many-body systems consisting of protons and neutrons. In studies of nuclear structure, nuclear physicists predict and explain experimental data based on various models of fundamental building blocks(i.e., protons and neutrons) plus effective interactions; nuclear physicists also wish to achieve a deep understanding of simple patterns and regularities from the complexity of atomic nuclei. The traditional studies of nuclear physics have focused on the structure, reaction and decay modes of relatively stable nuclei. In the last decade, with new-generation facilities of radioactive beams, the study of extremely proton-rich and neutronrich nuclei is realizable, and becomes the new frontier in nuclear physics.The nuclear shell model(SM for short) is the most successful microscopic model in nuclear structure. Yet the SM configuration space is too huge to handle heavy nuclei, and thus truncations of the SM space are indispensable.The nucleon-pair approximation of the shell model(NPA for short) is among one of these approaches. As the interaction between nucleons are attractive and short-range, nucleon-pair configurations are favored. If one chooses the pair configurations with lowest energies, the low-lying states of atomic nuclei which have a huge dimension in the SM configuration can be well represented by a much smaller model space constructed by correlated nucleon pairs. In this thesis we study two issues in nuclear structure theory. The first is proton-neutron pair correlations in atomic nuclei within the framework of the NPA, and the second is proton-neutron interaction connected with predictions of nuclear masses, with the details as below.In the first chapter we present a brief introduction to the background of nuclear physics and current status of nuclear structure studies, including the theoretical framework of the SM and the history of the NPA. Starting from the attraction and short-range feature of nuclear force, we explain why the nucleon pairs with spin zero and spin two are dominant in low-lying states of atomic nuclei, and why the proton-neutron pairs are important if valence protons and neutrons are in the same orbits. We also explain the relevance of nuclear masses(or binding energies) in nuclear physics, as well as in nuclear astrophysics, stellar nucleosynthesis, particle physics, neutrino physics, and metrology.In the second chapter we study proton-neutron pair approximations. We derive Wick theorem for coupled fermion operators with isospin symmetry, and develop the NPA with isospin symmetry, together with a computer code in FORTRAN language. We make use of this approach and perform systematic studies of low-lying states for N = Z nuclei. The NPA with isospin symmetry provides us with a proper platform to study proton-neutron pair correlations. Based on this model, we study the quartet truncation of the SM.Within the NPA with isospin symmetry, we have studied proton-neutron pair approximations for low-lying states of N = Z nuclei with four valence nucleons and eight valence nucleons. We calculate overlaps between wave functions of the NPA space and wave functions of the full SM space. For the first time, the NPA calculations with isospin symmetry become feasible for many-j shells with effective interactions. Our calculations demonstrate that the low-lying states of N = Z even-even nuclei are well described by both isoscalar proton-neutron pair approximation and isovector pair approximation. This duality is a consequence of nonorthogonality of nucleon-pair basis. For the ground states of N = Z even-even nuclei, isovector spin-zero pair approximation is superior to isoscalar spin-one proton-neutron pair approximation.Again within the NPA with isospin symmetry, we study the quartet truncation in low-lying states of eight nucleons. Our calculations suggest that the ground state of92 Pd is well described by two quartets with both spin and isospin zero. Here the quartet is a tightly bound cluster of two protons and two neutrons,and the interaction between two quartets is very weak.Under random interactions, we study low-lying states in the framework of the fermion dynamical symmetry model(FDSM for short, which is a SD-pair approximation of the SM). Very strong linear correlations between low-lying states are found in the Mallmann plots, regardless of the ground state spin. We also find very strong correlations of electric-quadrupole transition rates. These correlations are very robust.In the third chapter we make use of nuclear masses to extract empirical proton-neutron interactions, and investigate their systematics. We find that such proton-neutron interaction of nuclei with even mass numbers is systematically stronger than that of neighboring nuclei with odd mass numbers. We apply the systematics of the proton-neutron interaction and its relation with nuclear masses to description and prediction of nuclear masses. Our mass formula is very simple,and is among the most accurate mass formulas in the market.We study proton-neutron interactions of sd-shell nuclei by using the SM with the USDB effective interaction. We find that isoscalar proton-neutron interactions of the shell model results are consistent with the empirical proton-neutron interaction. There is an additional binding in both even-even and odd-odd nuclei,originated from residual proton-neutron interactions. This additional binding is the origin of the odd-even staggering of the empirical proton-neutron interaction.Both the T = 0 part and the T = 1 part of the USDB effective interaction have contributions to the Wigner effect in the empirical proton-neutron interaction.The odd-even staggering and the Wigner effect in the empirical proton-neutron interaction are very robust with random interactions, and may be originated from underlying symmetries of quantum many-body systems.In the fourth chapter we summarize this thesis and present our view of the future studies. The NPA is a very flexible approach. Many works can be done by using the NPA with proper modifications, for instances, quartet truncations,core excitations, nuclear continuum and resonance states, effective interactions of the shell model, β decay and double-β decay.