相互作用玻色子模型中的F旋破缺

本文首先从F旋对称性出发, 简单地回顾和讨论了IBM-Ⅰ和IBM-Ⅱ的关系, 然后讨论F旋的破缺. 为了定量地讨论F旋的破缺, 我们将系统的哈密顿分成两部分: 一部分具有F旋对称性, 另一部分为F旋破缺部分. 文章最后给出了有关矩阵元的计算方法. 本文实质上是关于IBM-Ⅱ的一种新的计算方案.     

S-态离子零场劈裂常数α的计算方法

本文考虑到确定S-态离子立方晶场零场劈裂常数a的有效哈密顿矩阵具有与自旋哈密顿矩阵相同的性质,由此导出参数a与L-S表象中有效哈密顿矩阵的非对角元C之间的较简单的关系:a=2/5^1/2C。作为例子,我们从此关系式出发,计算了CaO:Mn²⁺的a值,计算结果与实验值较好地符合。 关键词：     

四面体键半导体合金LMTO能带的相干势近似计算

本文提出一种无须引入可调参数的基于LMTO能带的相干势近似(CPA)计算方法。在LMTO及其虚晶近似计算中,哈密顿矩阵的矩阵元计及原子球的d态,哈密顿矩阵对角化时忽略d带对s,p能带的影响,所得能带本征态便于构成适用于CPA计算的sp杂化正交轨道且能带结构较为合理。以Ga_1-xAl_xAs为例,论证这一方法在四面体键半导体合金中的应用。计算结果表明,其重要能带及相应带隙的弯曲参数的CPA修正值是合理的。 关键词：     

氦原子自旋-自旋相互作用精细结构参数的理论计

利用多电子原子的精细结构哈密顿算符的球张量形式,通过计算氦原子的自旋-自旋相互作用哈密顿算符在|LSJMJ〉表象中的矩阵元,导出了氦原子的自旋-自旋相互作用精细结构参数的理论计算式,并就氦原子(n1s)(n2p)组态具体计算参数B之值.     

玻戈留玻夫变换用于哈密顿对角化时的一种简化方法

玻戈留玻夫变换用于哈密顿量对角化时一般须首先直接或间接确定变换矩阵本身，通常比较繁琐本文在将哈密顿形式地写成矩阵之后，将哈密顿量对角化问题转变成其系数矩阵的本征值计算问题，这样不具体计算变换矩阵即可方便地实现对角化．     

NH_2自由基~2A_1,~2B_1电子振动能级结构及~2A_1～~2B_1电子振动跃迁矩的理论计算

利用大振幅弯曲振动哈密顿和矩阵变换方法 ,考虑Renner Teller效应 ,计算了NH2 自由基 A2 A1, X2 B1态电子弯曲振动和K型转动能级。由计算得到的态函数和基态电偶极矩 ,计算NH2 自由基 A2 A1～ X2 B1电子振动相对跃迁矩和电子激发态 A2 A1的荧光寿命 ,理论计算结果与实验值符合较好。     

偶偶核转动三带的交叉混杂

本文探讨了希土区偶偶核的超带与基态带、β带或γ带的交叉混杂。我们用“定本征值问题中待定参数”的方法定出参数后使哈密顿矩阵对角化,计算了十多个核的转动三带能谱,与现有实验值符合较好,给出了超带等三个转动带交叉混杂的一些信息。     

端口受控哈密顿系统的混沌反控制研究

对端口受控哈密顿系统能量变化和动力学特性进行了分析，采用了分段线性输出反馈对其进行混沌反控制，给出了构造分段线性输出反馈矩阵的方法.此方法具有物理概念明确，不需计算李雅普诺夫指数，易于实现等特点.数值计算和仿真研究表明了此方法的有效性 关键词： 哈密顿系统 混沌 反控制     

矩阵对角化方法研究~(40)Ca~(35)Cl分子的超精细结构

采用矩阵对角化方法计算了~(40)Ca~(35)Cl分子的超精细结构能级,借助有效哈密顿算符获得了~(40)Ca~(35)Cl分子基态超精细能级的本征值.计算结果表明,得到的跃迁光谱数据与实验值符合的很好,误差仅在0 k Hz～90 k Hz,并好于之前的理论计算值.希望这些数据能为以后激光冷却~(40)Ca~(35)Cl分子提供有力的理论依据.     

电场对负电荷激子的能-光谱AB振荡的影响

定量讨论了可控外加均匀电场对量子环上负电荷激子的能-光谱及其AB振荡的影响。文中计算光谱的结果与实验值符合很好。负电荷激子是三个带电粒子的体系,构成本征函数的基矢数以及哈密顿矩阵元都极大,数值计算艰浩。文中提出如何选定基矢组Γ(Kmin,Kmax)以减少基矢数及保证因基矢组的选择所引起的误差极小的方法。为验证基矢组Γ(Kmin,Kmax)的可靠性,还提出了对构成波函数中基矢K的比重D(K)的分析方法。并对哈密顿矩阵元〈H〉中的动能项〈T〉、库仑作用项〈V〉、外加电场作用项〈E〉与环半径R的关系进行了讨论。     

Shielding and spin-spin coupling constants from gas-phase NMR

Intermolecular interactions modify nuclear magnetic resonance (NMR) chemical shifts and spin-spin coupling constants. The intermolecular effects can be determined if the NMR parameters for an isolated molecule are known. Gas-phase NMR spectroscopy offers such methods which allow one to measure the shielding and spin-spin coupling constants at the zero-density limit where the NMR parameters are free from intermolecular contributions. It is also shown that at present the multinuclear NMR spectra can easily be obtained for gaseous samples containing several micrograms of a solute compound.     

The Effect of Spin-Orbit Coupling and Spin-Spin Coupling of Compact Binaries on Chaos

There are spin-orbit interaction and spin-spin interaction in a generic post-Newtonian Lagrangian formu-lation of comparable mass spinning compact binaries. The spin-orbit coupling or the spin-spin coupling plays a quite important role in changing the evolution of the system and may sometime cause chaotic behavior. How do the two types of couplings exert together any influences on chaos in this formulation? To answer it, we simply take the Lagrangian formulation of a special binary system, including the Newtonian term and the leading-order spin-orbit and spin-spin couplings. The key to this question can be found from a Hamiltonian formulation that is completely identical to the Lagrangian formulation. If the Lagrangian does not include the spin-spin coupling, its equivalent Hamiltonian has an additional term (i.e. the next-order spin-spin coupling) as well as those terms of the Lagrangian. The spin-spin coupling rather than the spin-orbit coupling makes the Hamiltonian typically nonintegrable and probably chaotic when two objects spin. When the leading-order spin-spin coupling is also added to the Lagrangian, it still appears in the Hamiltonian. In this sense, the total Hamiltonian contains the leading-order spin-spin coupling and the next-order spin-spin coupling, which have different signs. Therefore, the chaos resulting from the spin-spin interaction in the Legrangian formulations is somewhat weakened by the spin-orbit coupling.     

The Effect of Spin-Orbit Coupling and Spin-Spin Coupling of Compact Binaries on Chaos

There are spin-orbit interaction and spin-spin interaction in a generic post-Newtonian Lagrangian formulation of comparable mass spinning compact binaries. The spin-orbit coupling or the spin-spin coupling plays a quite important role in changing the evolution of the system and may sometime cause chaotic behavior. How do the two types of couplings exert together any influences on chaos in this formulation? To answer it, we simply take the Lagrangian formulation of a special binary system, including the Newtonian term and the leading-order spin-orbit and spin-spin couplings. The key to this question can be found from a Hamiltonian formulation that is completely identical to the Lagrangian formulation. If the Lagrangian does not include the spin-spin coupling, its equivalent Hamiltonian has an additional term(i.e. the next-order spin-spin coupling) as well as those terms of the Lagrangian. The spin-spin coupling rather than the spin-orbit coupling makes the Hamiltonian typically nonintegrable and probably chaotic when two objects spin. When the leading-order spin-spin coupling is also added to the Lagrangian, it still appears in the Hamiltonian.In this sense, the total Hamiltonian contains the leading-order spin-spin coupling and the next-order spin-spin coupling,which have different signs. Therefore, the chaos resulting from the spin-spin interaction in the Legrangian formulations is somewhat weakened by the spin-orbit coupling.     

A symmetry-based approach to the effective Hamiltonian for symmetric top molecules in degenerate vibronic states

The effective Hamiltonian for a symmetric top molecule in a degenerate vibronic state is obtained. Included in this Hamiltonian are the rotational, spin-rotational, spin-orbit coupling and electronic spin-spin interactions. The terms of the Hamiltonian are expressed as the product of molecular ‘constants,’ rotational angular momentum operators, and symmetry operators. A formalism is derived, and tables included, to determine whether or not a symmetry operator vanishes for a given vibronic state of a particular molecular symmetry. In this way, one can easily obtain all the non-vanishing Hamiltonian terms for a particular application.     

有机磷化合物的NMR研究——Ⅱ0,0-二烷基膦酸酯的1H、13C和31PNMR谱

本文报道了21个0,0一二烷基膦酸酯类化合物的¹H、¹³C和³¹P NMR参数。研究和讨论了不等价的二烷基¹H、¹³C化学位移和磷碳偶合常数与立体化学的关系。测定了(CH₃CH₂O)₂P(O)CH(CH₂NO₂)(p-OCH₃C₆H₄)的¹³C自旋一晶格弛豫时间T₁,二乙基¹³C T₁间的差别,说明在类似化合物中,含有化学位移各向异性对弛豫的贡献。     

Ni2+：CsMgCl3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵,研究了CsNiCl3单晶掺入CsMgCl3晶体后光谱精细结构、晶体结构、零场分裂参量、Jahn-Teller效应以及自旋单重态对Ni2+离子基态能级的影响,理论与实验相符合.研究了自旋-自旋耦合作用和Trees修正对Ni2+:CsMgCl3晶体的光谱精细结构和零场分裂参量的影响,发现有五种机理会影响零场分裂参量:(1)自旋-轨道耦合机理;(2)自旋-自旋耦合机理;(3)自旋-轨道与自旋-自旋联合耦合机理;(4)自旋-轨道与Trees修正联合耦合机理,(5)自旋-自旋作用与Trees联合耦合机理.其中自旋-轨道耦合机理是最主要的,其它几种机理也是不可忽略的.     

Ni~(2 )∶CsMgCl_3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵,研究了CsNiCl3单晶掺入Cs MgCl3晶体后光谱精细结构、晶体结构、零场分裂参量、Jahn-Teller效应以及自旋单重态对Ni2 离子基态能级的影响,理论与实验相符合.研究了自旋-自旋耦合作用和Trees修正对Ni2 :Cs MgCl3晶体的光谱精细结构和零场分裂参量的影响,发现有五种机理会影响零场分裂参量:(1)自旋-轨道耦合机理;(2)自旋-自旋耦合机理;(3)自旋-轨道与自旋-自旋联合耦合机理;(4)自旋-轨道与Trees修正联合耦合机理,(5)自旋-自旋作用与Trees联合耦合机理.其中自旋-轨道耦合机理是最主要的,其它几种机理也是不可忽略的.     

不同算法原子电荷下的~1J_(CH)理论计算

用一种计算直接键连原子核自旋耦合常数的半经验公式,结合量子化学计算得到的32种有机分子稳定几何构型的7种不同算法下的原子电荷,探究原子电荷算法的不同对1JCH理论计算的影响,拟合出基于7种原子电荷的耦合常数计算公式,并利用拟合公式对5种分子进行了检验.计算结果表明拟合的32种分子及检验的5种分子的耦合常数的计算值均与实验值较好的符合,拟合得到的基于7种原子电荷的计算公式均可以对其他分子体系的耦合常数进行预测.另外,计算结果同样显示原子电荷算法的不同对1JCH理论计算值有一定的影响却不显著,其中基于电荷均衡方法电荷(QEq)得出的耦合常数计算值与实验值的偏差较其它6种原子电荷的小,结果更可靠.     

A reduced form of the spin-spin centrifugal distortion Hamiltonian for orthorhombic asymmetric top molecules

The spin-spin centrifugal distortion Hamiltonian for an asymmetric top molecule in a given vibrational level of an open-shell electronic state with S ? 1 may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is established that there are six determinable spin-spin centrifugal distortion parameters for a molecule of orthorhombic symmetry; the corresponding matrix elements are derived for both Hund’s case (a) and case (b) coupling schemes.     

Nuclear spectroscopic quantities under influences of covalency

On the basis of Mössbauer isomer shift data, nuclear quadrupole interactions and NMR¹J(¹³C?¹¹⁹Sn) spin-spin coupling constants, the problem of the nonadditivity of the isomer shifts and unexpected quadrupole interactions in tin organic compounds SnX_4?nR_n (X-halide, R-org. lig.) with the degree of substitution n has been treated by means of pseudopotential HF SCF calculations supplemented by efficient methods for comprehending core reorganizations and nucleus near electronic charge distributions. The nonadditivity of the isomer shifts and the progression of the nuclear quadrupole interactions has been explained by the evident momentum separated electronic reorganization. The clearly proved relation between s electron densities and higher orbital imbalances brings the isomer shift in relation to the valence part of the electric field gradient (EFG). An interrelation between isomer shifts and NMR spin-spin coupling constants has been deduced.