利用改进的方势阱集团模型研究偶偶核的α衰变

Theoretical studies onαdecays of even-even nuclei with the improved square-well cluster model

方势阱集团模型是研究原子核α衰变的一个理论模型,具有形式简洁、计算方便等优点,可以较好地解释一些偶偶核的α衰变实验数据.方势阱集团模型假设不同的偶偶核具有相同的势阱深度,这只是真实α-子核相互作用的粗糙近似.我们改进了方势阱集团模型,在保留其优点的同时,进一步合理计入势阱深度对原子核质量数和质子数的依赖.利用改进的方势阱集团模型,研究了中等质量区、重核区和超重核区115个偶偶核的α衰变性质.结果显示,改进的方势阱集团模型给出的偶偶核α衰变半衰期理论值与实验值均方根偏差值为0.2223,相比方势阱集团模型下降了36%,尤其对于中等质量区N=Z=50附近的核素,由改进的方势阱集团模型计算的结果与实验值符合很好,说明改进的方势阱集团模型可以更好地解释α衰变半衰期实验数据.此外,我们还利用改进的方势阱集团模型预言了重核区与超重核区一些未知核素的α衰变半衰期,相关理论结果对偶偶核α衰变的实验和理论研究具有一定的参考价值.

αdecay 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 forα-decay researches.Gamow,Gurney,and Condon proposed the first theoretical model to explainαdecay 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 ofαdecay.They provide preliminary descriptions ofαdecays in medium-mass and heavy nuclei.Square-well cluster model is an important model forαdecay studies.It has several valuable advantages and gives a good description of the experimentalα-decay half-lives of some even-even nuclei.It assumes that the effective potential betweenαcluster and daughter nucleus is given by the square well+the Coulomb potential at the surface.The Pauli blocking betweenαcluster and daughter nucleus is simulated by the Wildermuth condition,which prevents theαcluster from occupying the orbits inside the daughter nucleus.The theoreticalα-decay half-lives are given by the WKB approximation.One of the shortcomings of the square-well cluster model is that differentα-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 theoreticalα-decay half-lives are calculated by the WKB approximation.The free parameters in the improved square-well cluster model are determined by fitting the experimentalα-decay half-lives of the medium-mass,heavy,and superheavy even-even nuclei,respectively.We then study systematicallyαdecays 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 theoreticalα-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 theoreticalα-decay half-life of288 Fl 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 protonnumber dependence of the square-well depth.These results could be useful for experimental and theoretical studies ofαdecays.