Investigation On ?-preformation Factor In ? Decay

The content of this dissertation is mainly focused on an important physical quantity in the cluster model of a decay-a-preformation factor(also noted as "P?" in brief).?-preformation factor is the quantity that describes the probability of an ? cluster forming inside an atomic nucleus,which also reflects the weight of ?-cluster configurations in the wavefunction for the initial state of the ? emitter.In the early stage of study on ? de-cay,the Pa factor was usually treated to be unity by assuming that the a cluster already exists inside the nucleus.This simple hypothesis leads to a certain degree of deviation between the predicted ?-decay widths and the experimental values.It was then that scientists realized the a cluster inside nucleus only exists with some possibility,and hence the question on the formation probability of a cluster was raised.Afterward,in the calculation of a-decay half-lives,as to different kinds(even-even/odd-A/odd-odd)of nuclei,the Pa factor was approximated by a constant that does not vary with the nucleon number.This simplified treatment for Pa reduces the deviation to some extent.However,a constant P? factor cannot reflect the difference in nuclear struc-ture as to different nuclei,which makes the deviation still fluctuate within a factor of 2?3.For the ? emitters around the nuclear shell closure,the deviation is especially significant.On the other hand,because the Pa factor is closely related to the wave-functions of the initial and final states of the parent nucleus,it is considered that P?carries the major structural information of a decay and serves as an important input as to nuclear structure in a-decay theories.It was indicated in numerous research that a-preformation factor shares in-depth correlations with other nuclear structural prop-erties,such as shell effect,nuclear deformation,isospin asymmetry,and the thickness of neutron or proton skin,etc.Hence,a precise evaluation of a-preformation factor would be not only beneficial to improving the half-life predictions.Meanwhile,from the evolution of the preformation factors,one can also obtain the information that is associated with other important structural properties,making the Pa factor to be an indicator for the studies of other nuclear structural properties.This dissertation contains two parts of research content.In the first part,through analyzing the correlation energies between the surface nucleons from the perspective of nuclear binding energy,we successfully introduce the contribution of unpaired nu-cleons into the cluster formation model(CFM)and make the model work for all kinds(even-even/odd-A/odd-odd)of nuclei in Pa calculation.Based on our generalization,we systematically investigate the P? evolution of medium and heavy nuclei,and dis-cuss its correlations with the associated nuclear structural properties.In the second part,combining the latest results of studies on ?-cluster structure in heavy nuclei,we introduce,as a first attempt,the nuclear medium effect into the double-folding model for ? decay,which enables the microscopic ?-nucleus potential to incorporate more structural details contained in the decay process.In addition,the resulting influences on a-nucleus potential,?-decay half-life,and a-preformation factor due to the intro-duced medium effect are carefully studied.Some meaningful results are obtained.Chapter one is mainly an introduction to the background of researches on a-preformation factor.First,starting from the microscopic theory of ? decay,we will present the microscopic definition of ?-preformation factor and introduce the micro-scopic calculations of a-preformation factors as well as the main conclusions reached by these studies.Second,we will give an introduction to the semiempirical approach for Pa evaluation,that is,to extract the P? factor from the ratio between the theoretical and experimental ?-decay half-lives.Because the semiempirical approach is frequent-ly used in many researches,we will give a detailed introduction to their major results,especially,the nuclear structural information shown in the variation of preformation factor with the nucleon numbers.In the third subsection,we will introduce the latest researches on a-clustering in heavy nuclei,and the relation between these researches and the a-preformation factor will be discussed.Lastly,we will explain the aim of our researches and the content arrangement of this dissertation.In Chapter two,we make some generalization to the CFM which is used for Pa evaluation,and then systematically study the evolution of P? factors for medium and heavy nuclei.The CFM is a phenomenological model proposed by Ahmed et al.in re-cent years.Based on simple quantum mechanical approximations,the model provides an approach that enables one to calculate the P? factor by using nuclear binding energy.It is indicated that,with the formation energy of the ? cluster and the total energy of the clustering system extracted from the nuclear binding energies,the a-preformation probability can be approximately described by the ratio of these two energy values.However,the expressions given by the original model are only valid for even-even nu-clei.As an attempt to generalize the model,we analyze the extraction process of the formation energy of the a cluster.By introducing the contribution of unpaired nucleons into the formation energy,we successfully extend the CFM to odd-A and odd-odd nu-clei.Within our generalization,the formulas proposed for P? evaluation are expressed on the basis of nucleon/cluster separation energies.In comparison with the work by Ahmed et al.,the mathematical formalism of the expressions given in our study is more simple and symmetrical,in which the physical insight also becomes more transparent.In order to examine the reliability of the generalization,we systematically calculate the P? factors for different kinds of nuclei in medium-and heavy-mass regions and compare the resluts with previous studies.It is found that,after our generalization the model is not only capable to yield reasonable P? factors in magnitude,but also suc-cessfully reproduces the critical features in the evolution of preformation factors with nucleon numbers.In particular,evident shell effects are observed from the behavior of P? factors around the N = 126 and Z = 82 shell closure,which is in accordance with the characteristics predicted by previous microscopic and semiempirical studies.In Chapter three,through considering the nuclear medium effect on the ? cluster during the decay process,we improve the microscopic double-folding model for a de-cay and investigate the resulting impact on both ?-decay half-lives and Pa factors.Due to the influence of nuclear mean field and the Pauli blocking effect,the ? cluster inside an nucleus is different from the free ? particle-the former is usually larger in size and radius.When the ? cluster penetrates the Coulomb potential barrier,the size of the a cluster also varies with the decreasing density of the surrounding nuclear medi-um.It is suggested in relevant many-body calculations that the a cluster at one-fifth of the nuclear saturation density is about 20%larger in radius than the a particle in vacuo.This medium effect,however,is not explicitly considered in the conventional double-folding a-nucleus potential.Therefore,we improve the double-folding mod-el by introducing the density-dependence on the daughter nucleus into the a-cluster density distribution.Based on existing research,we determine the formalism of this density-dependence and obtain an improved ?-nucleus potential which can embody the nuclear medium effect.Through comparing the improved double-folding potential with the conventional one,we find the introduced medium effect slightly depresses the?-nucleus potential at the nuclear surface,while the variation of the inner geometry of the potential is more evident.To further investigate the influence of this medium effec-t,the half-lives and the corresponding Pa factors of even-even spherical ? emitter are calculated respectively by using the original and the improved potentials.It is found that the improved potential which included the medium effect can well reproduce the experimental half-lives,leading to a more reasonable Pa factors in magnitude.In the last chapter,we make a systematical summary of the aforementioned re-searches and present an reasonable outlook for future studies.