Properties Of Atomic Nuclei At Ground State And Low-lying States

In this thesis I study a number of issues on ground and low-lying states of atomic nuclei,including the description of nuclear masses,empirical relations of nuclear charge radii,regular structure of sd boson systems under random interactions,and the nuclear Gamow-Teller transitions in terms of the nucleon pair approximation of the shell model,and so on.Nuclear masses and charge radii are both basic physical quantities.Nuclear masses are key inputs in nuclear astrophysics,while nuclear charge radii describe the dimensions of nuclei.Theoretical models of nuclear masses and charge radii can be simply classified into three categories.Macroscopic models fit all experi-mental data?more than 3000 mass data and about 1000 charge radii data?with simple formulas.Microscopic models calculate nuclear masses and charge radii with mean-field methods.Macro-microscopic models modify macroscopic empir-ical formulas,based on microscopic considerations of local nuclear structure on the nuclear chart.Nuclear pairing energy is very important in nuclear mass models.Its physics is the pairing of like nucleons,i.e.,the energy of two neutrons or protons get a minimum when their angular momentums couple to zero.It is already observed that,neutron number influences proton pairing energy,and proton number influ-ences neutron pairing energy.In Chapter 2 of this thesis we investigate deviations of different nuclear mass models against experimental data,and find odd-even staggering in them.Thus we suggest simple formulas to correct these deviations.We also introduce simple local formulas to describe experimental nuclear charge radii.In N,Z?8 nuclei,these formulas achieve an accuracy of 0.0084fm.Phenomenological modeling is the basic methodology of nuclear structure theory.Observables are calculated with“basic constituents+interactions”.Those interactions come from renormalized nucleon-nucleon interactions?via nucleon-nucleon scattering experiments?.However,when the input interaction-s are Gaussian random variables,regularities in the output results can not be attributed to interactions,but to“configuration space”and“interaction form”constructed with basic constituents?in shell model they are protons and neu-trons?,and these are properties of the model itself.So numerical experiments of random interactions help us better understand many-body models.The IBM model?interacting boson model?assumes that like nucleons couple into s bosons?J=0?and d bosons?J=2?.Based on symmetries of s bosons and d bosons,one can easily get nuclear energies and transition probabilities.The IBM model is simple,elegant and widely applied.In Chapter 3 we do numerical experiments in the IBM-1 model under random interactions,and point out linear correlations among low-lying states.These results are surprising,because the U?5?limit is the limit of d bosons,not necessarily a limit of sd boson system.We rigorously derived the probabilities of ground state spin,which is the only analytical results to now about ground state spin probabilities under random interactions.Nuclear Gamow-Teller transition is a kind of beta decay,and is a very impor-tant weak process.In big bang nucleo-synthesis,nuclear beta decay and neutrino physics,Gamow-Teller transition is one of the most important reactions.The Nuclear Shell Model gives reasonably good results of low-lying states.However,in heavy nuclei,because of explosive dimensions of the basis space,the Nuclear Shell Model can not consider spin-orbit partners?e.g.0h11/2 and 0h9/2?.For example in the 50-82 shell,the Nuclear Shell Model can not include 0h_9/2.In Gamow-Teller transition,the transition operator is a“spin-isospin-flip”opera-tor,so it changes the spin and isospin of a nucleon,but not the orbit quantum number.So spin-orbit partners are very important.The nucleon pair approxima-tion can effectively truncate the configuration space,thus includes more orbits,including spin-orbit partners,and is promising for application to calculations of Gamow-Teller transitions between low-lying states of heavy nuclei.In Chapter4 we apply the Nucleon Pair Approximation to calculations of Gamow-Teller transitions.Numerical results of⁴⁸Ca is consistent with those of large-scale shell model results in pf shell,and paves way for further applications in heavy nuclei in the future.