Properties Of The Symmetry Energy Studied By Nuclear Radioactivity

In this doctoral thesis,the properties of the symmetry energy in asymmetric nuclear matter,including the quadratic and quartic symmetry energies as well as their density slopes at the saturation density,are studied by the properties of nuclear radioactivity of unstable nuclei.The symmetry energy was initially introduced as a quantum correction energy in the Weizsacker-Bethe liquid-drop model,which was proposed to describe the binding energies of finite nuclei.Afterwards,in order to systematically study the symmetry energy,the concept of the nuclear matter was introduced,which consists of neutrons and protons with finite neutron and proton densities but infinite neutron and proton numbers.By comparing the properties of the isospin symmetric nuclear mat-ter,in which the neutron density is equal to the proton one,and those of the isospin asymmetric nuclear matter,in which the two densities are unequal,the symmetry en-ergy is found to approximately represent the difference of the energy per nucleon in them.That is to say,the symmetry energy is an evaluation of the energy cost to convert protons in symmetric nuclear matter to neutrons in asymmetric nuclear matter.Since the symmetry energy characterizes the isospin asymmetric effect in nuclear matter,it plays critical roles in not only nuclear physics but also astrophysics.For example,the symmetry energy is closely related to the nuclear masses,the structures and properties of nuclei far away from stability line and near drip lines,the mechanism of heavy-ion reactions,the structures and component of neutron stars,the masses and radii of neu-tron stars,the cooling process of neutron stars,and so on.Besides of the quadratic symmetry energy,the quartic symmetry energy can have obvious effects on the prop-erties of neutron stars as well.The quartic symmetry energy can significantly affect both the proton fraction in ?-stable neutron stars and the critical density for the direct Urca process,which leads to faster cooling of neutron stars.In addition,the quartic symmetry energy is found to be very important for the location of the inner edge of crusts and the core-crust transition density and pressure in neutron stars.So the quartic symmetry energy can also have an influence on the structure of neutron stars.Because of the very important roles of the symmetry energy played in both nuclear physics and astrophysics,it is of great significance to study the properties of the symmetry energy.The bulk of the previous work has mainly focused on the properties of the quadrat-ic symmetry energy.Though the magnitude of the quadratic symmetry energy at the saturation density has been well constrained around 30 MeV,the value of its density slope at the saturation density still remains uncertain,and much effort has been made in order to reduce its uncertainty.Relatively speaking,the quartic symmetry energy has been paid much less attention to.Due to the obvious influence of the quartic symmetry energy on neutron stars,the properties of the quartic symmetry energy have also been studied in this thesis.There are mainly two parts of the research content.In the first part,the properties of the symmetry energy are closely linked to nuclear radioactivity,such as the proton radioactivity and the heavy-cluster radioactivity.Then by applying the experimental decay energies and decay half-lives of nuclear radioactivity,both the quadratic and the quartic symmetry energies as well as their density slopes at the sat-uration density are constrained.With the obtained results,the value of the quadratic symmetry energy at the reference density pA=0.1 fm-3 is also calculated.In the second part,based on the modified Weizsacker-Bethe liquid-drop model,the formu?las of three kinds of ?--decay energies are derived to be closely related to both the quadratic and the quartic symmetry energies.Then by fitting the three kinds of ?--decay energies given in the Atomic Mass Evaluation,not only the quadratic symmetry energy coefficient is obtained,but also the quartic symmetry energy coefficient is ex-tracted.The slope parameter of the quadratic symmetry energy at the saturation density is further constrained with the obtained results.In Chapter one,the research background of the nuclear radioactivity and the sym-metry energy is mainly introduced.At first,we briefly review the history of the discov-ery of radioactivity of unstable nuclei and different models to study nuclear radioactiv-ity.Then the background of the concept of the symmetry energy proposed in the study of nuclear masses and nuclear binding energies is introduced,as well as the current status of the research about the symmetry energy in finite nuclei.Subsequently,the definition of the symmetry energy in infinite nuclear matter is given and different mod-els and approaches to study the symmetry energy in nuclear matter are also introduced.At last,the main research content and the arrangement of this doctoral thesis are given.In Chapter two,at first the relationship between the properties of the symmetry en-ergy and the nucleon single-particle potentials is derived in detail.As the same to pre-vious conclusion,the properties of the symmetry energy can be totally obtained from the information of the nucleon single-particle potentials.Then the density-dependent cluster model,which is applied to study the nuclear radioactivity,is introduced,as well as the deformed density-dependent cluster model,in which the deformation effect of the daughter nucleus is considered in the decay process.Within the density-dependent cluster model,the effects of electron screening on a-decay half-lives in different exter-nal environments are studied.Then we give a detailed introduction about how to link the symmetry energy to nuclear radioactivity through the nucleon single-particle poten-tials.The results of the proton radioactivity and the heavy-cluster radioactivity studies by the density-dependent cluster model are discussed and the values of the quadrat-ic and the quartic symmetry energies as well as their density slopes at the saturation density are also given.At last,we summarize the research content in this chapter.In Chapter three,the modified Weizsacker-Bethe liquid-drop model is firstly in-troduced.Then based on this mass formula,the expressions of three kinds of ?--decay energies Q(?-),Q(2?-),and Q(4?-)are derived in detail.The reason why these three kinds of decay energies are chosen to study the symmetry energy in finite nuclei rather than the nuclear masses is also particularly given.Furthermore,by fitting the three kinds of decay energies given in the Atomic Mass Evaluation,both the quadratic and the quartic symmetry energy coefficients are extracted.The results respectively obtained by the three kinds of decay energies are also compared with each other and discussed.With the obtained results of the quadratic symmetry energy,its slope param-eter at the saturation density is further constrained.In the final section is a summary about this chapter.In Chapter four,we give a systematic summary about this doctoral thesis.Mean-while,the problems encountered during the studies are also discussed.Finally,we present reasonable outlooks for future studies.