时间反演不对称的投影后变分方法

发布时间：2018-03-01 13:00

本文关键词： 超越平均场投影后变分原子核结构时间反演对称性破缺　出处：《沈阳师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：原子核是一个复杂的量子多体体系,求解该体系的薛定谔方程是一个长期困扰理论家的难题。本文的工作是发展一种称之为投影后变分方法(即VAP方法)的理论,期待它能够成为求解原子核薛定谔方程的很好近似方法。首先,本文比较系统地介绍了VAP的研究背景。简单介绍了相互作用壳模型和平均场近似方法的基本思想。讨论了在原子核的研究中,这两种理论模型的优点以及在它们应用中遇到的困难。其中,相互作用壳模型是量子多体理论中比较理想的一种方法,可以全面地描述原子核的结构性质。但是这种方法在处理组态空间较大的重核体系时却遇到了困难。随着组态空间的变大,计算量会成数量级地增加。对于如此巨大的计算量,目前的计算条件还无法对其进行处理。于是,人们只能采用近似方法,引入了平均场近似理论。平均场近似方法中,比较典型的有HF和HFB近似。其中HFB方法的应用非常广泛,它可以用来计算整个核区。但是由于很多物理效应被忽略,我们无法得到好的波函数。以至于人们只能粗略地描述原子核的结构性质。基于此,人们便提出了超越平均场方法。在诸多超越平均场方法中,有一类可以通过投影的方法将平均场的对称性进行恢复,再对投影波函数进行变分,即投影后变分,简称VAP(Variation After Projection)。VAP中比较典型的一个例子是VAMPIR。作为一种壳模型的近似方法,VAMPIR的近似效果非常好。原则上这种方法具有很好的发展前景,但是VAMPIR却因为计算量较大,近几年几乎没有什么进展。本文在最新发展的理论基础上,提出一套新的有效的VAP计算方法。本文重点介绍了VAP计算中的一些细节问题,以及这一算法的特色。在前期工作中,我们将平均场的轴对称性进行破缺,但保留了时间反演对称性,这使VAP计算仅仅局限于偶偶核的偶自旋态。本文将平均场的时间反演对称性进一步破缺,并成功地将新的VAP方法应用于偶偶核,奇奇核和奇-A核的所有自旋态的晕带计算中。计算结果显示,新的VAP方法给出的近似值与壳模型给出的准确值非常接近。这充分地表明,VAP方法是一种非常有效的壳模型近似方法。由于这里只做了角动量投影,显然,角动量投影是获得良好的壳模型近似的关键。同时,在新的VAP算法中,我们首次计算了能量的二阶偏导数。这不仅能够加速收敛,还能够检验所得到的收敛能量值是否达到了真正的极小。目前的VAP方法比初期的VAP方法更加简便,计算效率更高。这对于进一步发展和完善VAP方法是个良好开端。最后,本文讨论了VAP方法未来的发展方向。我们希望能够进一步优化VAP算法,提高计算效率。并期待能够将新的VAP方法推广到重核区,以便可以更加深入地研究重核的结构性质。如果有可能,我们还希望将VAP方法推广到原子核激发态的计算中。这样可以研究更多有趣的物理问题。
[Abstract]:The nuclear is a complex quantum multi-body system, and the solution of the Schrodinger equation for this system is a problem for theorists for a long time. The work of this paper is to develop a theory called the post-projection variational method (VAP method). It is expected to be a good approximation to the nuclear Schrodinger equation. In this paper, the background of VAP is systematically introduced, and the basic ideas of interaction shell model and mean field approximation are briefly introduced. The advantages of these two theoretical models and the difficulties encountered in their application, among them, the interacting shell model is an ideal method in quantum multi-body theory. The structural properties of atomic nuclei can be described comprehensively. However, this method has encountered difficulties in dealing with heavy nuclear systems with larger configuration space. With the increase of configuration space, the amount of computation increases by an order of magnitude. Therefore, people can only adopt approximate method and introduce the theory of mean field approximation. In the method of mean field approximation, HF and HFB approximations are typical. Among them, HFB method is widely used. It can be used to calculate the entire nuclear region. But because many physical effects are ignored, we can't get good wave functions, so that one can only roughly describe the structural properties of the nucleus. The method of transcendental mean field has been put forward. Among the methods of transcendental mean field, one of them can recover the symmetry of mean field by projection method, and then change the projective wave function, that is, post-projection variation. A typical example in VAP(Variation After Projection).VAP is vamp IR.As an approximate method for shell model, the approximate effect of VAMPIR is very good. In principle, this method has a good development prospect, but VAMPIR has a large amount of computation. There has been little progress in recent years. Based on the latest development of the theory, this paper proposes a new and effective VAP calculation method. This paper mainly introduces some details of VAP computation and the characteristics of this algorithm. We break the axisymmetry of the mean field, but retain the time inversion symmetry, which limits the VAP calculation to the even spin state of the even even nucleus. In this paper, the time inversion symmetry of the mean field is further broken. The new VAP method has been successfully applied to the halo band calculation of all spin states of even and even nuclei, odd odd nuclei and odd -A nuclei. The results show that, The approximate value given by the new VAP method is very close to the exact value given by the shell model. This fully shows that the VAP method is a very effective approximate method for the shell model. Angular momentum projection is the key to obtain a good shell model approximation. At the same time, in the new VAP algorithm, we calculate the second order partial derivative of energy for the first time. The current VAP method is simpler and more efficient than the initial VAP method. This is a good start for the further development and improvement of the VAP method. In this paper, the future development of VAP method is discussed. We hope to further optimize the VAP algorithm and improve the computational efficiency. We hope that the new VAP method can be extended to the heavy kernel region. If possible, we also hope to extend the VAP method to the calculation of the excited states of the nucleus. In this way, we can study more interesting physics problems.
【学位授予单位】：沈阳师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O571

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