類重整化群對反核子譜相對論對稱性的研究
發(fā)布時(shí)間：2018-12-23 18:57
【摘要】：相對論對稱性是核結(jié)構(gòu)理論中相當(dāng)重要的一環(huán),其起源與破缺機(jī)制也是目前的熱點(diǎn)方向之一。本文從相對論對稱性的發(fā)現(xiàn)出發(fā),介紹了目前與之相關(guān)的一些研究,然后結(jié)合協(xié)變密度泛函理論(Covariant Density Functional Theory,CDFT)與類重整化群(Similarity Renormalization Group,SRG)方法,來探索球形核下反核子譜相對論對稱性的起源與破缺機(jī)制。最后我們也對超形變核下核子譜的相對論對稱性做了研究。主要內(nèi)容有如下幾點(diǎn):一、簡明介紹了相對論對稱性的概念和當(dāng)前研究中的進(jìn)展及未解決問題。自自旋對稱性與贗自旋對稱性發(fā)現(xiàn)以來,它們在解釋原子核殼結(jié)構(gòu)和幻數(shù)等核物理現(xiàn)象起到了重要作用。二、詳細(xì)闡明了類重整化群方法以及協(xié)變密度泛函理論的理論框架。三、分別對球形核下反核子譜的自旋和贗自旋對稱性的研究。在描述球形核的協(xié)變密度泛函理論的框架下,運(yùn)用類重整化群方法通過連續(xù)的么正變換將Dirac哈密頓算符轉(zhuǎn)變?yōu)閷切问?分離出Dirac粒子與反粒子算符,分別得到動(dòng)力學(xué)、自旋—軌道耦合等各個(gè)獨(dú)立的厄米算符,從而避免了之前研究中所遇到的奇異性和算符耦合等問題。通過比較每一組分對自旋和贗自旋能級劈裂的貢獻(xiàn),發(fā)現(xiàn)在自旋能級劈裂中自旋—軌道耦合項(xiàng)占主導(dǎo)作用,而贗自旋能級劈裂主要來源于非相對論項(xiàng)和動(dòng)力學(xué)項(xiàng)的貢獻(xiàn),同時(shí)勢場形狀及伙伴態(tài)量子數(shù)對自旋和贗自旋對稱性的影響我們也給出了結(jié)論,從而揭示了相對論對稱性的起源與破缺的機(jī)制。四、在相對論平均場框架下對超形變核的核子譜相對論對稱性的研究。通過研究自旋和贗自旋對稱性及其隨形變變化的情況,發(fā)現(xiàn)超形變核態(tài)的自旋和贗自旋對稱性與雙重態(tài)的量子數(shù)和形變都相關(guān),表明超形變態(tài)具有更好的對稱性,是超形變核態(tài)具有較好穩(wěn)定性的原因之一。
[Abstract]:Relativistic symmetry is an important part of nuclear structure theory, and its origin and breaking mechanism are also one of the hot topics. In this paper, based on the discovery of relativistic symmetry, some related studies are introduced, and then the covariant density functional theory (Covariant Density Functional Theory,CDFT) and the renormalization group (Similarity Renormalization Group,SRG) method are introduced. To explore the origin and breaking mechanism of relativistic symmetry of antinuclear spectrum in spherical nuclei. Finally, we also study the relativistic symmetry of the nuclear spectrum under superdeformed nuclei. The main contents are as follows: firstly, the concept of relativistic symmetry, the current research progress and unsolved problems are briefly introduced. Since the discovery of spin symmetry and pseudospin symmetry, they have played an important role in explaining nuclear physical phenomena such as nuclear structure and phantom number. Secondly, the quasi-renormalization group method and the theoretical framework of the covariant density functional theory are expounded in detail. Third, the spin symmetry and pseudospin symmetry of antinucleon spectra in spherical nuclei are studied respectively. In the framework of the covariant density functional theory describing spherical nuclei, the Dirac Hamiltonian is transformed into diagonal form by the method of quasi-renormalization group through continuous unitary transformation, and the Dirac particle and antiparticle operators are separated from each other to obtain the dynamics, respectively. Various independent Hermitian operators such as spin-orbit coupling can avoid the singularity and operator coupling problems encountered in previous studies. By comparing the contribution of each component to spin and pseudospin level splitting, it is found that the spin-orbit coupling term dominates the spin-orbit splitting, while the pseudo-spin level splitting mainly comes from the contribution of non-relativistic terms and kinetic terms. At the same time, the effects of the shape of potential field and the quantum number of partner states on the spin and pseudospin symmetry are also discussed, which reveals the origin and breaking mechanism of relativistic symmetry. Fourthly, the relativistic symmetry of superdeformed nuclei is studied under the framework of relativistic mean field. By studying the spin and pseudospin symmetries and their changes with deformation, it is found that the spin and pseudospin symmetry of superdeformed nuclear states are related to the quantum number and deformation of double states, which indicates that the superform metamorphosis has better symmetry. It is one of the reasons that the superdeformed nuclear state has good stability.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O571
[Abstract]:Relativistic symmetry is an important part of nuclear structure theory, and its origin and breaking mechanism are also one of the hot topics. In this paper, based on the discovery of relativistic symmetry, some related studies are introduced, and then the covariant density functional theory (Covariant Density Functional Theory,CDFT) and the renormalization group (Similarity Renormalization Group,SRG) method are introduced. To explore the origin and breaking mechanism of relativistic symmetry of antinuclear spectrum in spherical nuclei. Finally, we also study the relativistic symmetry of the nuclear spectrum under superdeformed nuclei. The main contents are as follows: firstly, the concept of relativistic symmetry, the current research progress and unsolved problems are briefly introduced. Since the discovery of spin symmetry and pseudospin symmetry, they have played an important role in explaining nuclear physical phenomena such as nuclear structure and phantom number. Secondly, the quasi-renormalization group method and the theoretical framework of the covariant density functional theory are expounded in detail. Third, the spin symmetry and pseudospin symmetry of antinucleon spectra in spherical nuclei are studied respectively. In the framework of the covariant density functional theory describing spherical nuclei, the Dirac Hamiltonian is transformed into diagonal form by the method of quasi-renormalization group through continuous unitary transformation, and the Dirac particle and antiparticle operators are separated from each other to obtain the dynamics, respectively. Various independent Hermitian operators such as spin-orbit coupling can avoid the singularity and operator coupling problems encountered in previous studies. By comparing the contribution of each component to spin and pseudospin level splitting, it is found that the spin-orbit coupling term dominates the spin-orbit splitting, while the pseudo-spin level splitting mainly comes from the contribution of non-relativistic terms and kinetic terms. At the same time, the effects of the shape of potential field and the quantum number of partner states on the spin and pseudospin symmetry are also discussed, which reveals the origin and breaking mechanism of relativistic symmetry. Fourthly, the relativistic symmetry of superdeformed nuclei is studied under the framework of relativistic mean field. By studying the spin and pseudospin symmetries and their changes with deformation, it is found that the spin and pseudospin symmetry of superdeformed nuclear states are related to the quantum number and deformation of double states, which indicates that the superform metamorphosis has better symmetry. It is one of the reasons that the superdeformed nuclear state has good stability.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O571
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