三价原子的非相对论能级结构

采用拉卡基函数并借助角动量耦合理论,导出了三价原子非相对论性哈密顿的矩阵元的一般表达式,完成了所有的角向积分和自旋求和计算,结果用3j、6j和9j符号表示,径向积分则表示为Slater-Condon参数.用相关结果对(n1p)2(n2p)组态的谱项结构进行了分析     

氦原子(n1sn2p)组态能级的相对论修正

本文采用拉卡基函数并借助不可约张量理论,导出氦原子(n1sn2p)组态的各种相对论效应的理论计算式,在这一过程中,完成了所有的角向积分和自旋求和计算,其结果用径向矩阵元形式来表示.     

氦原子(n1sn2p)组态精细结构的解析计算

以双电子原子精细结构哈密顿的球张量形式和二价原子的非相对论性能级结构理论为基础,借助不可约张量理论,导出了氦原子(n1sn2p)组态精细结构能级的解析表达式,在这一过程中,完成了所有的角向积分和自旋求和计算,其结果用若干个径向矩阵元形式来表示.     

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.     

计算复杂原子能级时能量算符的矩阵元Ⅰ非相对论性理论

利用Racah代数和反对称化子技巧,对复杂组态下单电子和双电子算符的非相对论性矩阵元进行了讨论。在我们的表达式中,径向积分系数只含6j符号(或第一类3nj符号)和单电子亲态比系数,且仅需对亲态求和。因此按照这些表达式,可以相当容易地计算出复杂原子的能级。     

也谈径向矩阵元的递推关系

利用超位力定理及其推广形式给出了一维、二维和三维系统径向矩阵元递推关系的一般表示式,并具体求出了谐振子系统及非相对论氢原子系统中径向矩阵元的递推关系．     

多电子原子能量的相对论修正

以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,建立了计算多电子原子能量的相对论修正的一种解析理论形式,导出了多电子原子相对论修正项(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项和轨道-轨道相互作用项)在斯莱特表象中的矩阵元的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类锂体系(1s)2(2p)2P态能量的相对论修正进行了具体计算.     

相对论效应对类锂离子能级结构及辐射跃迁性质的影响

利用基于多组态Dirac-Hartree-Fock(MCDHF) 理论方法的相对论原子结构计算程序包GRASP2K, 细致计算了中性锂原子、类锂Be⁺, C³⁺, O⁵⁺, Ne⁷⁺, Ar¹⁵⁺, Fe²³⁺, Mo³⁹⁺, W⁷¹⁺及U^{89 +} 离子基组态及较低的激发组态1s²nl (n = 2---4, l =s,p,d,f) 的精细结构能级, 以及各能级间发生电偶极(E1) 自发辐射跃迁的能量、概率及振子强度. 同时, 在非相对论极限下, 计算了其相关原子参数. 通过对相对论及非相对论计算结果的比较, 系统研究了相对论效应对类锂等电子系列离子能级结构及E1跃迁性质的影响, 揭示了随原子核电荷数Z变化时, 跃迁能、振子强度强烈依赖于量子数n, l, j变化的规律; 同时, 目前的计算结果与其他已有的理论计算及实验测量结果进行了比较.     

相对论性无自旋氢原子径向矩阵元的通项公式及平均值的解析表达式

给出了相对论性无自旋氢原子的解析波函数,推导出了计算径向矩阵元的通项公式.在-6≤s≤3的条件下,给出了径向平均值〈n′l′|rs|n′l′〉的解析表达式.     

原子模型势中任意算符矩阵元的递推关系

运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系.     

类锂离子里德堡态中的自旋-其它轨道相互作用

以多电子原子精细结构哈密顿的球张量形式和三价原子的非相对论性能级结构理论为基础,借助不可约张量理论,建立了计算类锂离子里德堡态中的自旋-其它轨道相互作用能的一种解析理论形式.完成了所有的角向积分和自旋求和计算,自旋-其它轨道相互作用能最终用径向积分来表示.应用所建立的理论对类锂离子(1s2np)2Pj态的自旋-其它轨道相互作用能进行了具体分析.     

Correlation between electronic structure and energy band in Eu-doped CuInTe_2 semiconductor compound with chalcopyrite structure

The Eu-doped Cu(In, Eu)Te_2 semiconductors with chalcopyrite structures are promising materials for their applications in the absorption layer for thin-film solar cells due to their wider band-gaps and better optical properties than those of CuInTe_2. In this paper, the Eu-doped CuInTe_2(CuIn_(1-x)Eu_xTe_2, x = 0, 0.1, 0.2, 0.3) are studied systemically based on the empirical electron theory(EET). The studies cover crystal structures, bonding regularities, cohesive energies, energy levels,and valence electron structures. The theoretical values fit the experimental results very well. The physical mechanism of a broadened band-gap induced by Eu doping into CuInTe_2 is the transitions between different hybridization energy levels induced by electron hopping between s and d orbitals and the transformations from the lattice electrons to valence electrons for Cu and In ions. The research results reveal that the photovoltaic effect induces the increase of lattice electrons of In and causes the electric resistivity to decrease. The Eu doping into CuInTe_2 mainly influences the transition between different hybridization energy levels for Cu atoms, which shows that the 3d electron numbers of Cu atoms change before and after Eu doping. In single phase CuIn_(1-x)Eu_xTe_2, the number of valence electrons changes regularly with increasing Eu content,and the calculated band gap E_g also increases, which implies that the optical properties of Eu-doped CuIn_(1-x)Eu_xTe_2 are improved.     

锯齿型石墨烯纳米带的能带研究

运用π电子紧束缚模型,具体研究了锯齿型石墨烯纳米带(ZGNRs)的边界结构对能带,特别是费米面附近的导带和价带电子的影响.计算了七种不同边界结构的ZGNRs的能带色散关系及费米面附近价带电子在原胞中各原子上的分布情况.计算结果表明:两边界都无悬挂原子的NN-ZGNRs,只有一边界有悬挂原子的DN-ZGNRs,两边界都有五边形环的SPP-ZGNRs和ASPP-ZGNRs为金属性.两边界都有悬挂原子的DD-ZGNRs,一边界为五边形环另一边界无悬挂原子的PN-ZGNRs和一边界为五边形环另一边界有悬挂原子的P 关键词： 锯齿型石墨烯纳米带 紧束缚模型 电子密度分布 缺陷结构     

Under-coordinated atoms induced local strain, quantum trap depression and valence charge polarization at W stepped surfaces

We have explored the effects of atoms under-coordination on surface structure relaxation, binding energy shift of W stepped surfaces and valence charge polarization by the method of incorporating bond order-length-strength (BOLS) correlation mechanism into high-resolution X-ray photoluminescence spectra (XPS) measurements as well as density functional theory (DFT) calculations. Results show that the 4f_7/2 energy levels of bulk, surface skin and step edge W atoms shift deeper from 2.17 to 2.69 eV with respect to that of the isolated W (28.91±0.01 eV) atoms, while the valence charge energy shift upper from inner to outer layer and from bulk to stepped edge. The surface bond contraction occurs around under-coordinated atoms after geometry relaxation calculation. Consistency among BOLS calculations, DFT calculation and experimental measurements clarifies that the surface bond contraction and consolidation due to the effects of under-coordination atoms induce potential trap depression, which provides perturbation to the Hamiltonian and hence contributes to the surface core level shift deeper, and that the surface valence charge are polarized by the densely trapped core-level electrons to upper energy.     

Clebsch-Gordan Coefficients,Racah Coefficients and Braiding Fusion of Quantum sl(2) Enveloping Algebra (I)

Quantum Clebsch-Gordan coefficients and the first type quantum Racah coefficients of quantum sl(2) enveloping algebra are given explicitly. The quantum 3-j and 6-j symbols, similar to those in the theory of angular momentum are abo introduced. The solution R_q^j1j2 of quantum Yang-Baxter equaton is expressed in terms of the quantum Clebsch-Gordan coefficients. It is shown that when j1=j2, R_q^jj is just the same as R_AW^j matrix obtained by Akutsu and Wadati for the representation of the braid group. The second type quantum Racah coefficients, which are the solutions of the face models, are also computed explicitly and related to the first type quantum Racah coefficients. The famous pentagonal relation is proved from the formula between two quantum Racah coefficients. The graphical representation of those formulas is discussed.     

Configuration Interaction and Many‐Body Perturbation Theory: Application to Scandium,Titanium, and Iodine

A number of atoms and ions with complex valence configurations are considered as candidates for atomic clocks with high sensitivity to the possible variation of the fine‐structure constant. Present level of the theory is not sufficient to predict frequencies of the clock transitions with accuracy, required for the experiment. Here an approach is tested, where the second‐order perturbation theory is used to iteratively saturate configuration space for valence electrons. On the examples of scandium, titanium, and iodine, it is demonstrated that this improves the efficiency of the CI+MBPT method for systems with strong configuration interaction and/or more than three valence electrons.     

Yn(n=2-8)团簇吸附CO2的密度泛函理论研究

运用密度泛函理论, 研究了CO2在Yn (n=2-8) 团簇表面的吸附结构和电子性质。结果表明：CO2吸附于 Yn (n=2-8)团簇表面时,线型的分子结构畸变为三角形构型。YnCO2表现出了较大的吸附能 (大于3eV)。吸附使体系的能隙表现出了奇偶振荡效应。吸附后,C-O键伸长,C原子由电子施体变为受体,O原子所带电子数也显著增加。在所有尺寸中,Y4CO2 、Y6CO2稳定性最好。     

Y_n(n=2-8)团簇吸附CO_2的密度泛函理论研究

运用密度泛函理论,研究了CO_2在Y_n(n=2-8)团簇表面的吸附结构和电子性质.结果表明:CO2吸附于Y_n(n=2-8)团簇表面时,线型的分子结构畸变为三角形构型.Y_nCO_2表现出了较大的吸附能(大于3eV).吸附使体系的能隙表现出了奇偶振荡效应.吸附后,C-O键伸长,C原子由电子施体变为受体,O原子所带电子数也显著增加.在所有尺寸中,Y_4CO_2、Y_6CO_2稳定性最好.