Theoretical studies on α decays of even-even nuclei with the improved square-well cluster model

Abstract

<p indent=0mm>α decay is one of the main decay modes of some unstable nuclei. It provides rich information on nuclear structures and is crucial for the experimental identification of new nuclides and new elements in heavy and superheavy regions. It is important to develop theoretical models for α-decay researches. Gamow, Gurney, and Condon proposed the first theoretical model to explain α decay within the framework of quantum tunneling in 1928, which is the first application of quantum mechanics in the subatomic systems. After that, several new theoretical models are proposed to get a better understanding of α decay. They provide preliminary descriptions of α decays in medium-mass and heavy nuclei. Square-well cluster model is an important model for α decay studies. It has several valuable advantages and gives a good description of the experimental α-decay half-lives of some even-even nuclei. It assumes that the effective potential between α cluster and daughter nucleus is given by the square well + the Coulomb potential at the surface. The Pauli blocking between α cluster and daughter nucleus is simulated by the Wildermuth condition, which prevents the α cluster from occupying the orbits inside the daughter nucleus. The theoretical α-decay half-lives are given by the WKB approximation. One of the shortcomings of the square-well cluster model is that different α-emitters are assumed to have exactly the same potential-well depth, which is disfavored by, e.g., the double-folding model and is an oversimplification of realistic effective potentials. In this work, we improve the square-well cluster model by taking into consideration that the depth of the square well depends on the mass number and the proton number. Such an improvement preserves, at the same time, many important merits of the original square-well cluster model. The Pauli blocking effect is simulated by the Wildermuth condition. The theoretical α-decay half-lives are calculated by the WKB approximation. The free parameters in the improved square-well cluster model are determined by fitting the experimental α-decay half-lives of the medium-mass, heavy, and superheavy even-even nuclei, respectively. We then study systematically α decays of even-even nuclei in different mass regions. The logarithmic hindrance factors and root-mean-square deviations between the experimental and theoretical results are calculated. We find that the theoretical α-decay half-lives given by the improved square-well cluster model are in better agreement with the experimental data than those given by the square-well cluster model. There are more theoretical data points agreeing with the experimental data within a factor of 1.5 in the improved square-well cluster model than the squared-well cluster model. For instance, the theoretical α-decay half-life of ²⁸⁸Fl is about three times the experimental data in the square-well cluster model, but only deviates from the experimental data by 3% in the improved square-well cluster model. This shows the advantages of the improved square-well cluster model by introducing the mass-number and proton-number dependence of the square-well depth. These results could be useful for experimental and theoretical studies of α decays.