Transitional Structure And Binding Energies Of Medium-heavy Nuclei

With the new-generation facilities (such as RIA in USA and RIKEN-RIBF inJapan), extensive studies of structure for unstable nuclei with medium and heavymasses become one of the frontiers in nuclear physics. It is therefore one of thepurposes in this thesis to study the low-lying states of a number of heavy nuclei in atransitional region, by using the nucleon-pair approximation (NPA) of the shell model.In this thesis we first give a very brief overview of fundamental properties of in-teractions between free nucleons, and a few well known nuclear models which includethe Fermi Gas model, the liquid-drop model, the nuclear shell model, the geometricmodel, the interacting boson model,and the mean-field theory. We present a detaileddiscussion of the nucleon-pair approximation of the shell model. This approach hasbeen shown to be an efficient method in studying low-lying states for nuclei in transi-tional regions.In this thesis we perform systematic calculations of low-lying states for Ir, Pt,Au, Hg and Tl isotopes with neutron numbers between 120 and 125, within the frame-work of the SDG-pair subspaces. We employ a monopole and quadrupole pairingplus quadrupole-quadrupole-type interaction with optimized parameters, which areassumed to be constants for nuclei with the same proton number or neutron number.We calculate binding energies of the ground states, low energy level schemes, electricquadrupole and magnetic dipole moments, and E2 transition rates. Our results are rea-sonably consistent with the available experimental data as well as previous theoreticalstudies, in particular, for low-lying yrast states. We also demonstrate that low-lyingstates of nuclei studied here are usually well represented by very simple configurationsin collective nucleon-pair basis.Another purpose of this thesis is to study binding energies of nuclei with medium- heavy masses. Nuclear binding energy is of great interest not only in nuclear physicsbut also in astrophysics. There have been many other approaches prior to this thesis.Our new strategy is to study binding energies via the residual proton-neutron interac-tion. This quantity plays an important role in a wide variety of nuclear phenomena,such as configuration mixtures, development of collectivity, spherical-deformed shapetransitions. We begin with the systematics of the proton-neutron interaction betweenthe last proton and the last two neutrons, V1p?2n, and that between the last two pro-tons and the last neutron, V_2p-1n, for nuclei with mass number A 60. Their valuesare extracted by using experimental binding energies of neighboring nuclei. By usinga simple function to describe V(1p-2n) and V_2p-1n, we present new relations connect-ing the masses of neighboring nuclei. The root mean squared (rms) deviations of ourpredicted values (in keV) for even-even, even-odd, odd-even and odd-odd nuclei withn = 8, with respect to experimental data compiled in the AME2003 database, are52,69,70,86, respectively.In the appendix of this thesis, we show an interesting phenomenon exhibited innuclear database. We find that the pattern claimed by Benford's law arises in the 2003version of atomic mass evaluation.