基于关联基的壳模型截断计算

提出了一种新的用于壳模型截断计算的基矢空间的构建方法,即关联基的方法。关联基是利用壳模型中每个粒子数分布下哈密顿量的本征态作为基矢。在此基矢之上,可以很自然地通过考虑能量相对较低的关联基矢进行相应的截断计算。当所有的关联基矢都被考虑时,计算结果回到一般jj耦合给出的结果。最后,对关联基下壳模型的计算与标准的壳模型计算进行了比较,计算结果表明,关联基下壳模型能量和波函数有着良好的收敛性,同时表明关联基计算的有效性。     

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。     

正交曲线坐标系中单位基矢的导数

由不同正交曲线坐标系的单位基矢之间的变换矩阵,推导出正交曲线坐标系的单位基矢对本身坐标的求导和对时间的求导规律.并且以球坐标系与柱坐标系的单位基矢的本身空间坐标求导为例进行了讨论.     

一种应用于量子数据压缩的幺正变换生成方法

提出了一种两类正交基矢按照特定要求相互转换的幺正变换生成方法. 特定要求为第一类基矢中特定的四种典型基矢经幺正变换后, 第三个量子比特特定为|0>, 而四种非典型基矢经幺正变换后, 第三个量子比特为|1>. 将该幺正变换应用于量子数据压缩, 准确度达到0.942. 该方法的提出为量子压缩和解压缩的实现提供了基础, 对于其他要求特定对应关系的幺正变换的生成具有借鉴意义. 关键词： 幺正变换 正交基矢 特定要求 量子压缩     

正格子与倒格子基矢关系的矩阵形式

本文基于晶轴矢量坐标系,构建了正空间点阵基矢a_i(i=1,2,3)的互易矢量b~*_j(j=1,2,3).如果在互易矢量关系中引入常数2π,可以证明互易矢量b_j=2πb~*_j为倒空间点阵的基矢.这样引入的第3种基矢关系(矩阵形式)等价于"固体物理"中定义的其它两种形式.该结果说明正格子和倒格子的对偶性体现在基矢关系上就是它们的互易性.     

多原子分子高激发振动能谱的非线性量子理论计算的程序化

以占有数表象为基础,通过编程,实现了不同分子各激发态波函数的基、基矢、完备的基矢空间及该空间中的Ｈａｍｉｕｌｔｏｎｉａｎ算符距阵元的计算,在此基础上实现了多原子分子高激发振动的能谱的非一量子理论计算的程序化。     

量子环上粒子体系的计算

对于量子环上带电粒子体系,组成本征函数的基矢数及哈密顿矩阵元素数都极大,数值计算量庞大.本文介绍在处理此问题时按轨道总角动量分类从基矢集中选择子基矢集的方法和技巧.应用计算机进行数值计算时,此方法比以往节省90%以上的时间.     

d-玻色子体系波函数的SU_2■SU_2基、物理基与无迹玻色子算符(Ⅱ)

为了完满地解决求现有几类物理基矢在SU_SU_2表象的表示问题,文中从第一类|PPO_3>基矢的无迹玻色子算符形式出发,直接求出内积的明显表达式。同时用这种基矢的迭加表示出第二类基矢|PP(y)LL},和用的相应的迭加表示出相似文献   

立方晶系中同指数晶列与晶面的空间取向关系

本文利用正倒格子关系分别在原胞基矢和晶胞轴矢坐标系下推证立方晶系中同指数晶列与晶面的空间取向关系.结果表明,在轴矢坐标系下立方晶系中同指数晶列与晶面垂直,在原胞基矢坐标系下同指数晶列与晶面的空间取向关系与具体的晶格结构相关.     

消光与原胞的选取

本文以面心立方结构的简单晶格为例，证明了对于一个给定的晶体，分别从固体物理学原胞基矢和结晶学原胞基矢出发定义的两个倒格子一般是不同的．进而证明了，在结晶学原胞基关系统中，既满足衍射方程又满足消光条件的方向，在固体物理学原胞基矢系统中看来，就不满足衍射方程．因而在该方向上也不出现衍射束．     

Anisotropy in the length change of gallium single crystals at their superconducting transition

The magnetostriction of gallium single crystals has been measured for the three principal axes between 0.3K and 1.1 K. It is found that the length change at the transition from the superconducting to the normal state is given approximately by (Δl/l)_a = − 3.10⁻⁹, (Δl/l)_b = + 4.4 · 10⁻⁹ and (Δl/l)_c = + 1.8 · 10⁻⁹, for the a, b and c axes at T = 0 K. A short discussion of the results with respect to microscopic theory is presented.     

Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^\infty{\rm Li} atom (only one spin function c₁\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^\infty{\rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).     

Effects of Field Fluctuations,Losses, and Aberrations on the Sensitivity of a Michelson GW Antenna Using Squeezed Radiation

The sensitivity of an interferometric gravitational wave (GW) antenna operating above a few hundred Hertz is shot-noise limited. Sub-shot-noise sensitivity can be achieved by superimposing squeezed light on the laser field. The benefits of this approach are reduced in nonideal interferometers having fringe visibility less than unity, as pointed out by Gea-Banacloche and Leuchs and recently discussed by Chickarmane. Here, we consider an interferometer described by a set of coefficients V_l^(k), V_sq^(k), V_lsq^(k) depending on the misalignment, mismatching, and aberrations of the optical systems, as well as on the asymmetry of the beam splitter and the two-arm losses. Due to the presence of terms proportional to the product of laser times squeezed fields, we have taken into account the amplitude fluctuations of a_l. A simple model of the squeezed vacuum light, produced by a degenerate optical parametric oscillator (OPO), is used for calculating the dependence of the spectral density of the output of a GW antenna on the fluctuations of the OPO-cavity resonance frequency, the pump amplitude fluctuation, and the nonlinear-crystal-temperature drift. A set of figures η_sq± and r_lsq±⁽²⁾ are introduced for describing the effects of the amplitude fluctuations and the relative line width γ_la on the spectral density of the quadrature phase operator X = a_la_sq⁺ h.c.     

Ionization energy of KOH and the dissociation energies of KOH and KOH+

High level ab initio, up to RCCSD(T), and B3LYP calculations were employed to calculate thermochemical properties for KOH and KOH⁺. Basis sets were of both all-electron and effective core potential (ECP) types: in both cases large, flexible valence basis sets were used, and the largest basis sets were of quintuple-zeta quality. Both KOH and KOH⁺ were found to be linear; in the latter case, the Renner-Teller effect is discussed. The results are close to convergence with regard to both basis sets and levels of theory. The most reliable quantities are: first AIE(KOH) = 7.38±0.02eV; D₀(K- -OH) = 82 ± 1 kcal mol-¹; D₀(K+ …OH) = 11.4 ± 1 kcalmol-¹; δH_f(KOH,298K) = ?53 ± 1 kcalmol^?1; and δH_f(KOH⁺,298K) = 119 ± 1 kcalmol-¹.     

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals

We characterize averages of ?_l=1^N|x - t_l|^{a- 1}{\prod_{l=1}^N|x - t_l|^{\alpha - 1}} with respect to the Selberg density, further constrained so that t_l ? [0,x] (l=1,...,q){t_l \in [0,x] (l=1,\dots,q)} and t_l ? [x,1] (l=q+1,...,N){t_l \in [x,1] (l=q+1,\dots,N)} , in terms of a basis of solutions of a particular Fuchsian matrix differential equation. By making use of the Dotsenko-Fateev integrals, the explicit form of the connection matrix from the Frobenius type power series basis to this basis is calculated, thus allowing us to explicitly compute coefficients in the power series expansion of the averages. From these we are able to compute power series for the marginal distributions of the t_j (j=1,...,N){t_j (j=1,\dots,N)} . In the case q = 0 and α < 1 we compute the explicit leading order term in the x ? 0{x \to 0} asymptotic expansion, which is of interest to the study of an effect known as singularity dominated strong fluctuations. In the case q = 0 and a ? \mathbbZ⁺{\alpha \in \mathbb{Z}^+} , and with the absolute values removed, the average is a polynomial, and we demonstrate that its zeros are highly structured.     

甲烷在外场作用下的光激发特性研究

采用密度泛函B3LYP和组态相互作用方法在6-311++G^**水平上计算了甲烷从基 态到前六个激发态的跃迁波长，振子强度，自发辐射系数A_n0和吸收系数B _0n（ n=1—6）.同时研究了外电场对甲烷分子的激发态的影响规律.结果表明，随外电场强度增大 ，系统总能量变化较小，同时最高占据轨道HOMO与最低空轨道LUMO的能隙gaps变小，费米能 级Fermi levels略有下降.甲烷基态（X～^lＡ_l）在外场作用下，易 于向高激发态产生跃迁. 关键词： 4')" href="#">CH₄ 激发态 外电场     

Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques

Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH₂ (<¹A₁ state), H₂O, HF, N₂, CO, Ne, and F₂ are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pVxZ (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X^?3 and the triplet pair energies as X^?5 with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute deviation of 0.02 mE_h from the CCSD-R12/B reference values. For the seven systems under study, the extrapolated total valence shell correlation energies agree to within 0.2 mE_h with the CCSD-R12/B benchmark data.     

Relaxation times in dissipative heavy-ion collisions

The classical model introduced earlier for analyzing experimental data on dissipative heavy-ion collisions, is generalized to include effects from the gradual dissipation of radial kinetic energy and from the development of fragment deformations during the collision. Relaxation times for the dissipation of radial kinetic energy (τ _R ) and relative angular momentum (τ _l ) as well as for the development of deformations (τ_α) are fitted to the reaction⁸⁶Kr (8.18 MeV/u) +¹⁶⁶Er and applied to three other reactions. A consistent set of relaxation times isτ _R = 0.3 · 10^?21 s,τ _l =1.5 · 10^?21 s andτ _α = 5 · 10^?21 s. Empirical mass transport coefficients are deduced from comparisons with experimental element distributions. Effects from fluctuations in the deflection function are discussed. Evidence is found for the existence of a relaxation time of the order 10^?21 s in the mass-drift coefficient.     

Molecular constants of LiCl(X~1Σ~+) and elastic collisions of two ground-state Cl and Li atoms at low and ultralow temperatures

Interaction potentials for LiCl(X 1 Σ +) are constructed by the highly accurate valence internally contracted mul-tireference configuration interaction in combination with a number of large correlation-consistent basis sets,which are used to determine the spectroscopic parameters (D 0,D e,R e,ω e,ω e χ e,B e and α e).The potentials obtained at the basis sets,i.e.,aug-cc-pV5Z-JKFI for Cl and cc-pV5Z for Li,are selected to study the elastic collision properties of Li and Cl atoms at the impact energies from 1.0×10 12 to 1.0×10 4 a.u.The derived total elastic cross sections are very large and almost constant at ultralow temperatures,and their shapes are mainly dominated by the s-partial wave at very low impact energies.Only one shape resonance can be found in the total elastic cross sections over the present collision energy regime,which is rather strong and obviously broadened by the overlap contributions of the abundant resonances coming from various partial waves.Abundant resonances exist for the elastic partial-wave cross sections until l=22 partial waves.The vibrational manifolds of the LiCl(X 1 Σ +) molecule,which are predicted at the present level of theory and the basis sets cc-pV5Z for Li and the aug-cc-pV5Z-JKFI for Cl,should achieve much high accuracy due to the employment of the large correlation-consistent basis sets.