Studies Of Nuclear Structure For The Ground And Low-lying States

Nuclear structure is an important field in nuclear physics.It studies the energy level schemes of ground and low-lying excited states,electromagnetic transitions,?decay,?decay and exotic decay modes.In this thesis we study two issues of nuclear structure physics.One is the systematics of nuclear structure,including the description and prediction of nuclear masses,?decay energies and nuclear charge radii.The other is the theoretical study of the nuclear shell model,including the dimension problem of identical particles in a single-j shell and numerical study of low-lying states for N=80 isotones in terms of the nucleon-pair approximation of the shell model.Nuclear mass?or binding energy?is a fundamental quantity of an atomic nucleus.The study of nuclear mass is essential not only to nuclear physics but also to astrophysics.Up to 2016,more than 3000 nuclides are found in nature or synthesized in laboratories,among which about 2500 nuclides are compiled with ex-perimental mass values.According to theoretical studies,there exist 8000 to 10000 bound nuclides in nature.Therefore experimental results for most nuclides far from stability line are unknown,and one has to resort to theoretical predictions.As well known that one of the important problems in physics?among“The 11Greatest Unanswered Questions of Physics”?is how the heavy elements in the universe were synthesized,and the masses of heavy neutron-rich nuclei are key inputs in such issue.Unfortunately,experimental measure-ments of most these nuclei are not accessible in the foreseeable future.Furthermore,the study of unknown nuclear masses not only expands our territory of nuclear chart,but also is important to understand many-body problem based on strong interaction.Therefore the description and prediction of nuclear masses is one of frontiers which have attracted much attention in the nuclear physics society.The current theoretical studies of nuclear masses can be generally classified into two categories,one is called the global and the other is the local.In this thesis we generalized the Garvey-Kelson mass relations and studied the systematic deviations of these formulas.For medium and heavy nuclei we achieved optimal channels of these local mass relations.We studied the relation between mass differences of corresponding mirror nuclei and Coulomb energies which yields an accurate relation of nuclear masses in light mass region,and predicted masses of some proton-rich nuclei.Based on our studies of the Garvey-Kelson mass relations,we obtained interesting results of?decay energies.We constructed local relations of?decay energies,and predicted some?decay energies of heavy and superheavy nuclei.As a byproduct,we extended our study to the predictive power of the empirical re-lations of nuclear charge radii,and provided a new approach to estimate whether a nucleus has proton-halo structure.Study of low-lying states in terms of the nuclear shell model is one of the central problems in nuclear structure theory.In this thesis we studied two problems related to the shell model.The first is the dimension-ality of the shell model configuration space.As we know,the shell model Hamiltonian respects the rotation invariance,and the total angular momentum for given state of a nucleus is a good quantum number.The construction of linearly independent basis states with given angular momentum?spin?of many-particle con-figurations is fundamental in the shell model theory.Usually it is useful to know the number of states with given spin for given configuration in advance.Analytical study of this dimension of a single-j shell is a complicated mathematical problem.As this dimension looks very irregular,it is very interesting to construct recursive formulas.In this thesis we obtained and proved recursive formulas between the number of states for n and n-1 identical particles with given spin for the first time.As an application of our recursive formu-las,we investigated the analytical results of the dimension for three and five identical particles.The second problem is the study of the low-lying states within the nucleon-pair approximation of the shell model.The shell model space becomes gigantic for medium and heavy nuclei,thus truncation of configuration space is indispensable.The nucleon-pair approximation of the shell model makes use of collective nucleon pairs as the building blocks of wave functions.This method has been proved to be an efficient and reliable approach of the shell model space truncation.In this thesis we studied the low-lying states of N=80 isotones with mass number A?130.There have been many theoretical and experimental studies of even-even nuclei in this region,and one of the main reasons is that these nuclei exhibit rich patterns such as the so-called back-bending phenomenon and the?unstable feature.The nucleon-pair approximation with only S and D pairs?spin equals 0 and 2?for low-lying states in the A?130 region reasonably describes the ground states,the yrast 2⁺,4⁺states and some of the non-yrast states of even-even nuclei with neutron number ranging from 72to 80.In addition to conventional SD nucleon pairs,here we considered collective pairs with higher spin and non-collective spin-ten neutron hole pairs,as well as neutron negative parity collective pairs.In such con-structed configurations,we studied low-lying energy levels of these isotones,with detailed analysis of wave functions for some selected states.Our calculated results demonstrated that,for¹³²Te and¹³⁴Xe,the yrast4⁺and 6⁺states are dominated by proton excitation,and the yrast 8⁺and 10⁺states by neutron excitation.Negative parity 4₁^--7₁^-states in¹³²Te,¹³⁴Xe,¹³⁶Ba and¹³⁸Ce are explained in terms of neutron excitation.Based on our calculations,we were able to predict a number of B?E2?values and g factors for low-lying states of these isotones.