| In this dissertation, we develop the cluster model for a decay and systematically calculate the a decay lifetimes, especially for heavy and superheavy nuclei; with the help of the successful model, we extract the root-mean-square (rms) nuclear charge radii of superheavy nuclei and very unstable nuclei from the experimental decay data.α decay, cluster radioactivity and proton emission are important decay modes of unstable nuclei. In principle, they are similar with each other belonging to the quantum tunneling phenomena, and investigations on them can provide rich structural informa-tion, such as the shell effect, the ground state properties, the shape coexistence, etc. Especially, the synthesis of new superheavy elements and new isotopes is a hot topic in contemporary nuclear physics, and the observation of a decay chains is the reliable tool to identify these synthesized nuclei. Hence it is quite important to theoretically investigate these radioactive decay, which is helpful for future experiments as well. Strikingly, the rms nuclear charge radius of the nucleus is one of its fundamental prop-erties. Due to the few events in the synthesis of superheavy nuclei, it is quite difficult to measure the nuclear charge radii of superheavy nuclei via the usual experimental methods. Hence we propose a new tool to obtain the nuclear radii-extracting the radii of unstable nuclei from the experimental decay data. Considering that a decay is one of the dominant decay modes of superheavy nuclei, we extract the rms nuclear charge radii of superheavy nuclei from the experimental a decay data. This is the first result on nuclear radii of superheavy nuclei based on the experimental decay data, which is of great physical importance. The main content of this dissertation is given as follows:In Chapter two, we develop the density-dependent cluster model to systematically investigate the a decay width and lifetime, and the half-lives of cluster radioactivity in heavy and medium mass nuclei, by using the modified two-potential approach. By further introducing the effect of nuclear deformation, we extend the initial model for spherical nuclei to the deformed case in order to systematically calculate a decay half-lives of heavy and superheavy nuclei. For even-even, odd-A and odd-odd nuclei, our calculated half-lives are all in good agreement with the experimental values including superheavy nuclei. Within the model, the parent nucleus of a decay is considered as a two-body system comprising a single a cluster coupled to a core nucleus. Their interac-tion potential includes attractive nuclear and long exclusive Coulomb parts, which are obtained by the double folding model plus the effective nucleon-nucleon (NN) interac-tion. In detail, the formulas of the matter or charge density distribution including in-volved parameters are derived from the high-energy electronic scattering experiments, and the microscopic effective potential correctly contains the low-density behavior of NN interaction and the NN exchange behavior. On the basis of the two-potential ap-proach, we treat the a decay process as a bound state problem and a scattering problem to give the decay width and sequently present the half-life by taking into account the a-preformation factor. We initially preform systematic investigation on the a decay half-lives of spherical or moderate deformed nuclei with N<126in the medium mass region, where the deviation of theoretical results and experimental data is generally within a mean factor of2. Subsequently, we pay special attention to the exotic a de-cay around the neutron shell closure N=126and focus on the shell effect on the a-formation, and the calculations agree well with the experiments. Given the validity of the developed model, we extend the study to cluster radioactivity and systematically calculate the half-lives of cluster emissions in the trans-lead (Z>82) region. Our cal-culated results are compared with the available experimental data, which proves that the present model is suitable for the description of cluster radioactivity as well. In the following, we make predictions on cluster emission in the trans-tin (Z>50) region, and discuss the different types of emitted clusters from trans-lead and trans-tin nuclei to some extent. We aim at not only pursuing a better agreement between theory and experiment, but also a significant understanding of the physical mechanism of a decay and cluster radioactivity.As a further step, we extend the studied subject to heavy and superheavy nuclei, which usually involve the obvious nuclear deformation. By means of the multipole expansion, we introduce the effect of nuclear deformation and develop the deformed version of nuclear decay model. We subsequently make extensive calculations on a decay half-lives of heavy and superheavy nuclei (including even-even, odd-A and odd-odd nuclei). Combined with new progress of international syntheses of superheavy nuclei like the117and118elements, we take into account another important decay mode of superheavy nuclei, i.e., spontaneous fission. After investigating the compe-tition between α decay and spontaneous fission for these heaviest nuclei, we give the corresponding half-lives and the branch ratios, which are consistent with the experi-mental data. As well, we predict decay modes and decay lifetimes of those unknown heaviest nuclei, in order to be useful for the future experiment.In Chapter three, by means of the successful decay model, we successfully ex-tract the rms nuclear charge radii of superheavy nuclei and very unstable nuclei, and the quadrupole deformation values of nuclei. Up to now, there are mainly several ex-perimental methods for measuring the rms charge radii such as electron scattering, transition energies in muonic atoms, proton elastic scattering and optical isotope shifts and so on. Although these measurements are quite useful for stable nuclei, it is quite difficult to apply these methods to superheavy nuclei and very proton-rich nuclei due to their short lifetimes. With these in mind, we obtain the nuclear radii of target nu-clei from the experimental data of α decay, cluster radioactivity and proton emission. Within the density-dependent cluster model, we can deduce the charge density distri-bution of the daughter nucleus from the experimental half-life, which finally leads to the rms charge radius of the studied nucleus. We extract the rms radii of even-even nuclei with Z=58-96, and odd-A and odd-odd nuclei with Z=65-87, and com-pare them with the corresponding measured values, which achieves a good agreement between theory and experiment. Encouraged by this, we present the rms charge radii of superheavy nuclei with Z=102-116. Moreover, we propose a three-parameter formula to calculate the nuclear radii motivated by the WKB penetration expression of α decay, and predict the rms radii of these superheavy nuclei as well. As we all know, the usual measurement for nuclear radii can not be applied to superheavy nuclei. It is of great theoretical importance that we extract the rms charge radii of nuclei in the su-perheavy regime for the first time, via the experimental a decay data. Besides, within the developed decay model, we successfully extract the rms radii of very proton-rich nuclei close to the proton dripline and light neutron-rich nuclei, respectively from the measured data of proton emission and cluster radioactivity. In the other part of this chapter, we perform systematical investigation on the shape coexistence in the Pt and Hg isotopes by using the deformed a decay model. In detail, the quadrupole deforma- tion parameters of the ground and the first exited0+states in the Pt and Hg isotopes are successfully deduced from the correspondingly experimental a decay data.At last, a summary of this dissertation and some outlooks are given in Chapter four. |
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