基于壳模型单体密度矩阵的折叠模型质子弹性散射分析

利用折叠模型计算得到折叠势实部并结合Koning和Delaroche光学势的虚部, 计算分析了质子与^30—40S的弹性散射数据. 通过引入Woods-Saxon势下核壳模型单体密度矩阵, 消除了折叠模型计算中常用的定域近似. 分析比较了定域近似对折叠势以及弹性散射截面计算的影响. 计算结果与折叠模型以及JLM模型计算结果进行了比较.     

原子核的配对壳模型数值计算(Ⅱ)

在配对壳模型内做SD子空间截断,选BCS对为S对,D对通过D=[S,Q]获得. 通过计算Z,Nε[50,82]区域的几个核,研究了单粒子能量和反常宇称态对于低能集体态的影响.     

原子核的配对壳模型及数值计算(I)

原子核配对壳模型用“真实”的价质子对和价中子对构造组态空间的波函数,包含了单粒子能量项的贡献.在配对壳模型内,费米子运力学对称模型(FDSM)和相互作用玻色子模型(IBM)可以作为它的特殊情况.本文报道这一模型的思想、框架及其数值计算程序.     

原子核形状相变的壳模型研究

利用玻色映射方法, 我们在壳模型中计算了原子核低激发态性质的一些特征量, 并与这些量在相互作用玻色子模型的动力学对称性中的数值进行比较, 得到原子核的集体运动形状相在壳模型中的对应, 分析了壳模型中的单极对、四极对和 四极-四极相互作用对形状相的影响, 还在壳模型中研究了U(5)—O(6)相变过程, 得到的结果与在相互作用玻色子模型中得到的结果一致.     

原子核配对壳模型——侵入态与原子核形变

利用原子核配对壳模型讨论了侵入态对原子核形变的影响.计算结果表明,侵入态具有削弱原子核形变的趋势,对原子核的形变起着重要作用. The influence of intruder level on nuclear deformation is studied within the framework of the nucleon-pair shell model truncated to an SD-pair subspace. The results suggest that the intruder level has a tendency to reduce the deformation and plays an important role in determining the onset of rotational behavior.     

第一性原理无核芯壳模型计算原子核谱因子

原子核谱因子表征原子核单粒子轨道的性质以及占据数等信息,是联系核结构、核反应与核天体物理的重要物理量。对于原子核谱因子的计算强烈依赖于理论模型得到的原子核多体波函数,在实际计算中通常选用普通壳模型。随着计算机性能的提高以及核多体方法的发展,第一性原理方法被应用于研究原子核性质,并取得巨大成功。本工作基于现实两体相互作用,利用第一性原理无核芯壳模型计算较轻原子核谱因子。首先,计算了A=6和7原子核的低激发态能量,考察第一性原理无核芯壳模型对能量计算的收敛性,并比较普通壳模型与第一性原理无核芯壳模型对于A=6和7能谱的描述。结果表明,无核芯壳模型计算结果与实验符合较好,可以很好地描述结合能和激发谱性质。然后,利用无核芯壳模型系统计算了⁷Li与⁷Be镜像核叠积函数与谱因子,并分析谱因子计算的收敛性。结果显示,谱因子随着模型空间的增大收敛较慢,对于⁷Li,无核芯壳模型计算的谱因子同最新实验值符合得很好。最后,采用无核芯壳模型系统计算A=6,7和8原子核低激发谱能量与谱因子,为核反应与核天体研究提供必要的输入量。     

探索原子核结构的对称性主导无芯壳模型计算(英文)

揭示隐藏于复杂中的简单性相关的特殊对称性是核理论研究的"圣杯",回顾了其探索历史和当前利用高性能计算设备及应用数学方法进行的从头计算无芯壳模型研究。作为对称性主导无芯壳模型（SA-NCSM）计算的实例,通过对轻核和中重质量区核素的能谱计算及与实验结果的比较,清晰地展示了群论在揭示这些当今最先进计算手段得到结果中所起的重要作用。作为SA-NCSM的有趣推广,从头引入形变的新方法提供了解决所有以探索原子核的集体性质为目的的从头计算方法都要面对的模型空间维数呈组合数增长的处理手段,并且该方法使本理论能用于描述重核及奇特核。Exploiting special symmetries to unmask simplicity within complexity that remains the "holy grail" of nuclear theory is re-examined within the framework of its historical context and current ab initio nocore shell-model approaches that exploit high-performance computing resources and applied math methodologies. Examples using the symmetry-adapted no-core shell model (SA-NCSM) that clearly demonstrate the important role group theory plays in this evolving story will serve to elucidate current state-of-the-art developments in this arena, including comparisons of excitation spectra and transition rates with experimental results for light and medium-mass nuclei. An interesting extension of the SA-NCSM, an advanced method with a novel twist that enables one to incorporate deformation from the onset, will be proffered as a further way to manage the combinatorial growth of model-space dimensionalities that remains the nemesis of all theories that seek an ab initio understanding of nuclear collectivity, and in so doing extends applicability of the theory to heavier and more exotic nuclear species.     

原子核壳模型发现前后

 大约四十年前,梅耶和詹森分别独立地提出了原子核壳模型,成功地解释了幻数等原子核结构的主要特性.虽然这个模型并未最终解决原子核结构问题,但它应作为研究原子核结构的基础模式已为世人所公认.因此,梅耶、詹森和对群论在核谱学上的应用作出重大贡献的魏格纳一起荣获了1963年度诺贝尔物理学奖金。本文介绍发现原子核壳模型的前后经过.卢瑟福发现原子内有核存在在1906年卢瑟福发现α粒子散射现象以后,盖革和马斯顿做了大量α粒子散射的研究工作.     

量子力学中的密度矩阵与具有相同密度矩阵的系综的可区分性

讨论了密度矩阵的不同定义。建议使用完全密度矩阵、压缩密度矩阵和约化密度矩阵分别描写一个封闭量子体系的、一个系综中平均分子的和一个复合体系中的一个子系统的密度矩阵。强调这与现在人们认为的具有相同压缩密度矩阵的系综是完全等价的结论完全不同,具有相同压缩密度矩阵但是成分不同的系综可以通过系综整体测量来区别。作为一个应用,现在认为现有的核磁共振量子计算中没有纠缠的结论是没有根据的。Density matrix is one important tool in quantum mechanics, and it has very broad applications. However there are different definitions about the density matrix, and they describe quite different systems. There has been some misunderstanding about the density matrix in the community, and these misunderstandings hinder the right application of the density matrix. In this article, we discuss the different definitions of density matrix. We suggest to use the full density matrix, compressed density matrix and the reduced density matrix to describe the state of a complete quantum system, the state of an averaged particle in an ensemble and the state of part of a composite system. We stress that contrary to the wide accepted understanding that ensembles with the same compressed density matrix are physically indistinguishable, they are distinguishable through the so-called ensemble measurement. As an application, we suggest that the present conclusion that the present-day nuclear magnetic resonance quantum computation does not have quantum entanglement is groundless.     

密度分布形式对Glauber模型计算σR的影响

描述了利用Glauber模型计算反应截面的一种方法 .该方法对Glauber模型中输入的密度分布形式进行了修正 ,计算了丰质子同中子核素 (N =3 )的激发函数 .对于该同中子素链 ,采用修正的密度分布得到的激发函数与HO分布得到的激发函数相比 ,在大于 1 0 0MeV/u的能量区域 ,两者都与实验值符合得很好 ,而在中能区 (小于 1 0 0MeV/u) ,用修正的密度分布计算得到的激发函数与实验值之间的差距较HO分布明显减小 ,并保持对所有计算的核核芯密度基本相同 .     

Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r^μ, r^μ jJ (qr), V (r) corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition, we take into account a general integral formula of the matrix element ＜n'l'|f(r) d _r^(m) |n l＞ that covers all seven matrix elements obtained analytically.     

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.     

Meaning of the Density Matrix

Protective measurement, which was proposed as a method of observing the wavefunction of a single system, is extended to the observation of the density matrix of a single system. This provides a new meaning to the density matrix as having the same ontological status as the wave function describing a pure state. This also enables quantum entropy to be associated with a single system.     

Unitary Operator and Density Matrix for a Ring of Coupled Oscillator Model

A unitary operator U which can directly diagonalize the Hamiltonian of a ring of N coupled oscillators is found. With use of the technique of integration within an ordered product of operators we see that U includes a squeezing transformation. For large N it turns out that, except a zero-mode, the ring Hamiltonian has the same spectrum as the one-dimensional monatomic lattice model plus the Born-Von-Karmen boundary condition. The density matrix of this model is calculated by the U transformation, which further leads us to derive the heat capacity of the coupled oscillators in the large N limit.     

Memory,Time and Technique Aspects of Density Matrix Renormalization Group Method

We present the memory size,computational time,and technique aspects of density matrix renormalization group (DMRG) algorithm.We show how to estimate the memory size and computational time before starting a large scale DMRG calculation.We propose an implementation of the Hamiltonian wavefunction multiplication and a wavefunction initialization in DMRG with block matrix data structure.One-dimensional Heisenberg model is used to illustrate our study.``     

中能Abrasion-Ablation模型的核内核子密度分布修正

将具体的核内核子(包括中子、质子)密度分布引入到中能Abrasion-Ablation模型中,用修正后的模型计算了30MeV/u ⁴⁰Ar+^natAg反应中的弹核碎裂过程.结果表明,在非常周边的碰撞中,修正后的模型计算的碎片截面与修正前的计算相比有明显的差别,反映了核密度边缘弥散的影响.与实验结果的比较验证了中能弹核碎裂碎片能量相对于束流能量的降低是由摩擦作用引起的.     

丰中子锰同位素的壳模型计算

利用球形壳模型和投影壳模型两种方法对Z≤28,N=40附近pf壳的丰中子核素的结构进行了一系列的研究。以丰中子的锰同位素为例讨论了对奇奇核58,60Mn的两种壳模型计算结果。结果显示,两种理论方法都很好地再现了58,60Mn实验上观测到的从低激发到高自旋态的能级。在对这两个同位素由中子g_9/2轨道闯入所产生的负宇称转动带进行描述时,两种理论计算也得到了一致的结果。通过对比,阐明了两种壳模型方法及其采用的有效相互作用在该丰中子核区的适用性,特别强调了中子g_9/2轨道的激发对于pf壳Z≤28丰中子核素结构的重要性。Recently,we have carried out a series of studies on the structures of pf shell neutron-rich nuclei around N=40 using the spherical shell model and the projected shell model respectively.As an example,these two types of shell model calculations for the neutron-rich odd-odd isotopes 58,60Mn are discussed in this paper.The results show that both the calculations reproduce the observed experimental energy levels from the lowexcitation states to the high-spin ones in 58,60Mn.Consistent results are also obtained by these two theoretical calculations when describing the negative-parity rotational band derived from the intruder neutron g_9/2 orbital in both isotopes.Through comparison,we show the applicability of these two shell model methods and the adopted effective interactions in the present neutron-rich mass region.The significance of the excitations from neutron g_9/2 orbital to the structures of the neutron-rich nuclei in pf shell with Z≤28 are especially emphasized in this paper.