發(fā)布時(shí)間：2018-03-01 13:00

  本文關(guān)鍵詞： 超越平均場(chǎng) 投影后變分 原子核結(jié)構(gòu) 時(shí)間反演對(duì)稱性破缺　出處：《沈陽(yáng)師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：原子核是一個(gè)復(fù)雜的量子多體體系,求解該體系的薛定諤方程是一個(gè)長(zhǎng)期困擾理論家的難題。本文的工作是發(fā)展一種稱之為投影后變分方法(即VAP方法)的理論,期待它能夠成為求解原子核薛定諤方程的很好近似方法。首先,本文比較系統(tǒng)地介紹了VAP的研究背景。簡(jiǎn)單介紹了相互作用殼模型和平均場(chǎng)近似方法的基本思想。討論了在原子核的研究中,這兩種理論模型的優(yōu)點(diǎn)以及在它們應(yīng)用中遇到的困難。其中,相互作用殼模型是量子多體理論中比較理想的一種方法,可以全面地描述原子核的結(jié)構(gòu)性質(zhì)。但是這種方法在處理組態(tài)空間較大的重核體系時(shí)卻遇到了困難。隨著組態(tài)空間的變大,計(jì)算量會(huì)成數(shù)量級(jí)地增加。對(duì)于如此巨大的計(jì)算量,目前的計(jì)算條件還無(wú)法對(duì)其進(jìn)行處理。于是,人們只能采用近似方法,引入了平均場(chǎng)近似理論。平均場(chǎng)近似方法中,比較典型的有HF和HFB近似。其中HFB方法的應(yīng)用非常廣泛,它可以用來(lái)計(jì)算整個(gè)核區(qū)。但是由于很多物理效應(yīng)被忽略,我們無(wú)法得到好的波函數(shù)。以至于人們只能粗略地描述原子核的結(jié)構(gòu)性質(zhì)�；诖�,人們便提出了超越平均場(chǎng)方法。在諸多超越平均場(chǎng)方法中,有一類可以通過(guò)投影的方法將平均場(chǎng)的對(duì)稱性進(jìn)行恢復(fù),再對(duì)投影波函數(shù)進(jìn)行變分,即投影后變分,簡(jiǎn)稱VAP(Variation After Projection)。VAP中比較典型的一個(gè)例子是VAMPIR。作為一種殼模型的近似方法,VAMPIR的近似效果非常好。原則上這種方法具有很好的發(fā)展前景,但是VAMPIR卻因?yàn)橛?jì)算量較大,近幾年幾乎沒(méi)有什么進(jìn)展。本文在最新發(fā)展的理論基礎(chǔ)上,提出一套新的有效的VAP計(jì)算方法。本文重點(diǎn)介紹了VAP計(jì)算中的一些細(xì)節(jié)問(wèn)題,以及這一算法的特色。在前期工作中,我們將平均場(chǎng)的軸對(duì)稱性進(jìn)行破缺,但保留了時(shí)間反演對(duì)稱性,這使VAP計(jì)算僅僅局限于偶偶核的偶自旋態(tài)。本文將平均場(chǎng)的時(shí)間反演對(duì)稱性進(jìn)一步破缺,并成功地將新的VAP方法應(yīng)用于偶偶核,奇奇核和奇-A核的所有自旋態(tài)的暈帶計(jì)算中。計(jì)算結(jié)果顯示,新的VAP方法給出的近似值與殼模型給出的準(zhǔn)確值非常接近。這充分地表明,VAP方法是一種非常有效的殼模型近似方法。由于這里只做了角動(dòng)量投影,顯然,角動(dòng)量投影是獲得良好的殼模型近似的關(guān)鍵。同時(shí),在新的VAP算法中,我們首次計(jì)算了能量的二階偏導(dǎo)數(shù)。這不僅能夠加速收斂,還能夠檢驗(yàn)所得到的收斂能量值是否達(dá)到了真正的極小。目前的VAP方法比初期的VAP方法更加簡(jiǎn)便,計(jì)算效率更高。這對(duì)于進(jìn)一步發(fā)展和完善VAP方法是個(gè)良好開(kāi)端。最后,本文討論了VAP方法未來(lái)的發(fā)展方向。我們希望能夠進(jìn)一步優(yōu)化VAP算法,提高計(jì)算效率。并期待能夠?qū)⑿碌腣AP方法推廣到重核區(qū),以便可以更加深入地研究重核的結(jié)構(gòu)性質(zhì)。如果有可能,我們還希望將VAP方法推廣到原子核激發(fā)態(tài)的計(jì)算中。這樣可以研究更多有趣的物理問(wèn)題。
[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.
【學(xué)位授予單位】：沈陽(yáng)師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O571

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本文編號(hào)：1552018