【作者】 王宇；

【导师】 郭建友； 牛中明；

【作者基本信息】 安徽大学 ， 物理学， 2020， 硕士

【摘要】 共振现象是物理学中最受关注的现象之一,这种现象已在原子,分子和核物理中被广泛地发现。奇特核的费米面接近于连续谱,因此共振态在许多奇特核结构的形成中起着非常重要的作用,如晕,巨晕,和形变晕。所以,研究单粒子共振态有助于人们理解原子核中的奇特现象与奇特结构。近年来在核物理学领域,共振态的研究越来越受到人们的关注和重视。为了研究原子核奇特结构中的共振现象,我们发展了一种新的模型方法,即在相对论平均场理论的点耦合模型(RMF-PC)下,用复动量表象(CMR)方法研究单粒子共振态。我们推导出了相关的理论公式,用Fortran软件编写了数值计算程序,从而将相对论点耦合模型中的狄拉克方程转换到动量表象中求解,获得我们所需要的共振态和束缚态。主要内容如下:一、简述了共振态在原子核奇特结构研究中的重要作用、单粒子共振态的研究方法与进展、以及近年来相对论平均场(RMF)理论的发展。由于相对论点耦合模型在描述各种核现象方面非常地成功,而且CMR方法是探究原子核单粒子共振态的一种有效方法,所以本文工作的重点是在相对论点耦合模型下,应用CMR方法去研究Dirac粒子的共振态。二、介绍了本文的理论框架。包括相对论平均场理论中的点耦合模型(RMF-PC),复动量表象(CMR)方法.并将两者结合,建立了复动量表象的相对论点耦合模型(RMF(PC)-CMR)的理论方法.用该模型方法就可以开展对原子核单粒子共振态的研究,其中还给出了该模型方法的理论公式和数值计算的细节。三、运用复动量表象的相对论点耦合模型研究了球形核120Sn的单粒子共振态。我们以120Sn原子核为例,计算其共振能量和共振宽度以及动量空间中的波函数,并将结果与其它方法的计算结果进行比较,得到了很好的一致性。尤其,本方法不仅对计算窄共振非常有效,而且也能可靠地应用于宽共振。此外,即使对于那些连续谱附近的共振态,也可以通过该方法方法准确预测出来。所以该模型方法是求解单粒子共振态的好方法。四、运用复动量表象的相对论点耦合模型系统地研究了 Sn的同位素链。通过研究球形核120Sn的单粒子共振态,说明了该模型方法是求解共振态的一种好方法。紧接着,我们以锡同位素链为例,系统地计算它们的共振能量和共振宽度,并将其与格林函数方法计算得出的结果进行比较,也得到了很好的一致性。预测的共振能量和共振宽度通常随着中子数的增加而减小,这主要是由锡同位素的不同势场引起的。此外,还计算了单粒子态的径向动量概率分布和它们在坐标空间中的密度分布。发现对于共振态而言,动量空间中的波函数呈现出较好的局域化,即是一个局域波函数,而在坐标空间中,共振态的密度在半径较大的地方有一个长尾巴。这些发现都表明了 CMR方法在研究共振态特性方面的优势。更多还原

【Abstract】 Resonance is one of the most concerned phenomena in physics,which has been widely found in atomic,molecular,and nuclear physics.The Fermi surfaces of exotic nuclei are close to the continuum,so the resonances play important roles in the formation of many exotic nuclear phenomena,such as halo,giant halo,and deformed halo.So studying the single-particle resonant states helps people understand the exotic phenomena and exotic structure in the nuclei.The study on the resonances achieved more and more attention in nuclear physics during recent years.In order to study the resonant phenomenon in the exotic structure of nuclei,we have developed a new method,namely,the complex momentum representation(CMR)method is used to study the single-particle resonant states in the relativistic point-coupling model.The related theoretical formulas are deduced,and the numerical calculation code is written with Fortran software,so that the Dirac equation in the relativistic point-coupling model is transformed into the momentum representation to obtain the resonant states and the bound states we needFirstly,the important role of resonant states in the exotic structure of nuclei,the research methods and progress of single-particle resonant states,and the development of the relativistic mean-field(RMF)theory in recent years are briefly described.Since the relativistic point-coupling model is very successful in describing various nuclear phenomena and the CMR is an efficient method for describing single-particle resonant states,so the focus of this work is to probe the resonance of Dirac particle in the relativistic point-coupling model by CMR methodSecondly,the theoretical framework of this paper is introduced.Including the point-coupling model of relativistic mean-field theory(RMF-PC),the complex momentum representation(CMR)method,and combining the two to establish the theoretical method of the relativistic point-coupling model of complex-momentum-representation method(RMF(PC)-CMR).The model method can be used to study the single-particle resonant states of the nuclei.The theoretical formula of the model method and the details of numerical calculation are also givenThirdly,the relativistic point-coupling model of complex-momentum-representation was used to study the single-particle resonant states of spherical nucleus 120Sn.We take the 120Sn nucleus as an example,the resonant energies and resonant widths,and the wave function in the momentum space are calculated,and compared the results with the calculation results of other methods.Our results get a good agreement with those of other methods.In particular,the method is not only very effective for calculating narrow resonances,but also can be reliably applied to broad resonances.In addition,the resonant states are predicted accurately with the CMR method even for those lying near the continuum threshold.Therefore,this model method is a good method for solving single-particle resonant statesLastly,the relativistic point-coupling model of complex-momentum-representation was used to systematically study the isotopic chain of nucleus Sn.By studying the single-particle resonant states of spherical nucleus 120Sn,the model method is a good method to solve the resonant states.Immediately,taking Sn isotopes as examples,the resonant energies and widths are systematically calculated and compared with those from the Green’s function method.Our results are also in excellent agreement with those of the Green’s function method The predicted resonant energies and widths generally decrease with the increase of neutron number,which are mainly induced by the different potentials of Sn isotopes.Moreover,the radial-momentum probability distributions of the single-particle states and their density distributions in the coordinate space are also calculated.Well localized wave functions are found in the momentum space for the resonant states,while the density distributions of the resonant states have long tails in the coordinate space,which indicates the advantage of CMR method in studying the properties of resonant states.更多还原