Theoretical Study Of Cluster Structure And α-cluster Preformation Probabilities Of Nuclei

Clustering is a crucial dynamic feature of the atomic nucleus.In light nuclei,there have been plenty of investigations and progresses from both the experimental and theoretical aspects.However,the knowledge of the clustering in heavy nuclei is still very limited.In this dissertation,the binary cluster model（BCN）is developed to provide a suitable and global description of the nuclear cluster structure in heavy and superheavy nuclei evidenced by the experimental data.On the other hand,in previous studies of cluster model and states,the uncertainty analysis appears to be missing,which is in turn very important when extending towards unknown region.The Monte Carlo resampling method is therefore combined with the experimental rotational bands of typical nuclei,in order to make a comprehensive evaluation on the uncertainty of the present model.The present study is then extended to more possible cluster states in heavy nuclei.Based on the above determined alpha-core potential,the alpha preformation factor is then extracted to be systematically compared with the interaction energy between valence nucleons.This is aimed at the insight into the effect of the valence nucleon correlation on the surface clustering of heavy nuclei.The behavior of alpha decay energy is analyzed in the valence correlation scheme（VCS）at last.The main content of this dissertation is given as follows:In Chapter II,seven typical alpha-core-type nuclei,namely ²⁰Ne,^44,52Ti,⁶⁰Zn,⁹⁴Mo,¹³⁶Te,and ²¹²Po,are selected as the sample group.Based on the nonparametric bootstrap method with the M=10⁵ times resampling,the probability distributions of the involved parameters in the effective nuclear potential are obtained plus the correlation analysis between these parameters.The ground state rotational bands of sample nuclei are then produced with the corresponding error bars.Besides,the electromagnetic transition reduced probability B（E2）and the root-mean-square（rms）radii are calculated as well.These theoretical results are all found to be in excellent agreement with the experimental values.Encouraged by this,given that the double magic nucleus is still chosen as the core,the involved clusters in the rotational states are extended to more heavier isotopes of helium,beryllium,carbon,nitrogen,and oxygen.In this sense,the possible cluster states of heavy nuclei are proposed,well reproducing the measured rotational bands.Analogous to the heavy particle decay in superheavy nuclei,we predict the cluster states in superheavy nuclei with the residual core ²⁰⁸Pb,which is compatible with the only available energy of 2⁺in ²⁸²Cn.In Chapter III,within the nuclear potential determined by the cluster structure,the alpha decay width of even-even nuclei are calculated to extract the alpha preformation factor from the experimental data.By assuming the role played by the valence nucleon correlation in the clustering process,we systematically analyze the similarity between the alpha preformation probability and the neutron-neutron（proton-proton）plus the neutron-proton pairing correlation in different major shell regions,which provides an initial physical picture about the clustering at the surface of the nuclei.In Chapter IV,the alpha decay energy,as the mass difference,not only determines the decay half-life,but also carries rich structural information.Considering that the VCS is an effective method in describing the structural evolution,the alpha decay energy is plotted versus the VCS factor by dividing into different（half）shell regions,leading to an obvious linear relationship between the decay energy and the numbers of valence nucleons.During this,another shell closure seems to be expected beyond the N=126closed shell.By combing with other theoretical predictions,the N=152 neutron shell is supposed to be a possible shell,as companied by improved accuracy of the aforementioned systematics of alpha decay energies.The validity of the present relationship of decay energies is approved in the VCS on the basis of the BW nuclear mass formula.