Investigation Of The ?-decay Properties Of Unstable Nuclei In The Nuclear Shell Model

Nuclear ?-decay is one of the most important decay modes for nuclei.Among the three thousands nuclei which have already been discovered by experiments,?-decay is the main decay mode for more than two thousands of them.?-decay is mediated by the weak interaction.As the ?-decay half-life is determined by properties of parent and daughter nuclei,the weak,strong,and Coulomb interactions are all involved in its calculations.Study of the ?-decay process is of great importance for us to understand the weak and strong interactions,and find new forms for the effective nucleon-nucleon interactions.The ?-decay half-life is of great importance in both nuclear physics and nuclear astrophysics.The nuclear ?-decay half-life is strongly influenced by its Q-value and the wave functions of parent and daughter nuclei.Research on ?-decay has helped to give us a better understanding of nuclear structures.Besides,in astrophysics,the synthesis of nuclei and the evolution of the abundance of elements in stars greatly relay on the ?-decay properties of nuclei far from the stability line.Investigations about the ?-decay properties of unstable nuclei help us understand the origin and evolution of elements.In this dissertation we systematically study the ?-decay properties of nuclei in some mass regions under the framework of nuclear shell model.Nuclear shell model is one of the reliable and accurate models for nuclear struc-ture.This model is originated from the model of Mayer and Jensen and developed to the modern nuclear shell model.Select a proper shell model space and an effective interaction,which is produced through either theory or fitting of the experimental re-sults,and make use of the strict diagonalization code we are capable of carrying out large scheme shell model calculations.Shell model calculations are capable of yield-ing the energy,wave function,angular momentum,parity,magnetic moment,?-decay strength,?-decay rate,and many other physical quantities of nuclei.As large scheme diagonalization is carried out,the calculated results of these quantities are relatively accurate.In this dissertation we calculate the ?-decay information of nuclei in some mass regions from shell model approach,get some interesting results which are consist with the experimental data,and predict the ?-decay half-lives of some unknown nuclei.The content of this dissertation is given as follows:At the beginning of the introduction,a brief review to nuclear shell model is made which contains its history,theoretical framework,and basic ideas.After that,the the-ory of the allowed and the first-forbidden ?-decays is introduced together with their detailed formulas.At the end of the introduction,formulas about the ?-decay quench-ing factor,which modifies the calculated ?-decay matrix-elements and improves the agreements,are given.In chapter 2,the allowed ?--decay properties of neutron rich unstable nuclei with charge number Z=9-13 are investigated from shell model approach.Some nuclei in this region have been found to have intruder configurations in their ground and low excitation states.This property has great influence on the nuclear ?-decay half-lives,which has been confirmed by experiments.Theoretical results of Q-values,half-lives,excitation energies,log ft values,branching fractions,and ?-delayed neutron emission probabilities are systematically discussed and compared with experimental data.The quenching factors are also evaluated and discussed.Good agreements between theo-retical ?-decay half-lives and experiments are reached.The ratios between theoretical?-decay half-lives and experimental data are within the range of 2±2.Based on our reliable calculations,we also predict the ?-decay properties of some nuclei,which can be observed by future experiments.The ?-decay properties of Li,Be,B,C,and N isotopes are investigated from the shell model approach,and compared with the ex-perimental data.Among those nuclei,the 11Be nucleus is well known for its anomaly ground state J?=1/2+.The calculated results yield the J? of ground state 11Be correctly and the agreements for low excitation states are consistent.In chapter 3,the ?-decay properties of ground states and isomers of Z=50 Sn isotopes are investigated under the frame work of the nuclear shell model.It is noted that ?-decays of Sn isomers have rarely been calculated.Thus,study the ?-decays of Sn isomers is of great importance.It is experimentally known that the first-forbidden transitions make significant contributions to the??-decays of some Sn isotopes.Thus,contributions from both the allowed and the first-forbidden transitions are considered.We write new codes based on the computer program NuShel1X,which are capable of calculating the first-forbidden ?-decay matrix-elements and phase space factors numer-ically.Theoretical results of ?-decay half-lives and Q-values are systematically studied and good agreements between theory and experiment are reached.The ?-decay half-lives and Q-values are predicted for some Sn nuclei,which can be helpful to future experiments.The calculated results of ?-decay half-lives and ?-decay Q-values also show that the neutron number N=50 and N=82 are magic numbers for unstable isotopes around Sn(Z ? 50).In the last chapter,we summarize our previous work and outlooks of our future plan are given.