Yangian代数在混合介子态的纠缠和衰变中的应用

Yangian代数是超出李代数更大的无穷维代数,是研究非线性量子完全可积系统的新对称特性的有力数学工具.基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性,本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(π~±,K~±,K~0和K~0)各自组成的三种混合介子态(π,K和K_i~0)衰变中的作用.将Y(su(3))代数的八个生成元(I~±,U~±,V~±,I~3和I~8)作为跃迁算子,作用在混合介子态上,研究其可能的衰变道,以及衰变前后纠缠度的变化.结果表明:1)在李代数范围内的生成元I~3和I~8作用下,三种混合介子态衰变后组成成分没有发生变化,其中混合介子态π在I~8作用下衰变前后纠缠无变化,其他衰变纠缠度发生了变化;2)在其他的六个(I~±,U~±和V~±)超出李代数的生成元的作用下,三种混合介子态衰变前后组成成分发生了变化,其中两个衰变后变成单态,纠缠度为零;两个衰变不存在;剩余两个衰变后纠缠度发生了变化,此外在带电(K)和中性(K_I~0)两类K型混合介子态的六种可能的衰变中,两种类型的末态的纠缠度两两相同;3)三种混合介子态之间可以通过I~±,U~±和V~±算子循环转化,具有明显的对称性.本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法,并且可以用此方法去预测可能的未知衰变粒子和解释己测得的衰变问题.     

BP+基态和激发态的势能曲线和光谱性质的研究

本文利用量子化学中的多参考组态相互作用方法(MRCI), 在aug-cc-pVQZ级别计算了在环境科学中具有重要作用的离子BP⁺. 得到了对应三个离解极限B⁺(¹S_g)+P(⁴S_u), B⁺(¹S_g)+P(²D_u)以及B⁺(¹S_g)+P(²P_u)的6个Λ-S态势能曲线. 在计算中还考虑了Davidson修正(+Q)和标量相对论效应, 用以提高计算精度. 通过分析Λ-S态的电子结构, 确认了电子态的多组态特性. 计算中首次纳入了旋轨耦合效应, 获得了由BP⁺离子的6个Λ-S态分裂出的10个Ω 态的势能曲线. 计算得到的势能曲线表明相同对称性的Ω 态的势能曲线存在着明显的避免交叉. 在得到的Λ-S态和Ω 态的势能曲线的基础上, 运用LEVEL8.0程序通过求解核径向的Schrödinger 方程, 得到了相应的Λ-S态和Ω 态的光谱常数T_e, R_e, ω_e, ω_eχ_e, B_e和D_e, 其中基态X⁴∑^-的光谱常数与已有的理论值符合的非常好, 文中其他电子态的光谱常数均为首次报道. 关键词： 多参考组态相互作用方法(MRCI) 势能曲线 光谱常数 旋轨耦合效应     

icMRCI+Q理论研究CF离子12个-S态和23个?态的光谱性质

采用考虑Davidson修正的内收缩多参考组态相互作用(icMRCI+Q)方法结合相关一致基组aug-ccpV5Z和aug-cc-pV6Z计算了CF~+离子第一离解极限C~+(~2p_u)+F(~2P_u)对应的12个∧-S态(X~l∑~+,a~3∏,1~3∑~+,1~3Δ,1~1∑~-,1~1∑~-,1~3∑~-,2~1∑~+,1~1∏,2~3∏,2~1∏和2~3∑~+)所产生的23个Ω态的势能曲线.计算中考虑了旋轨耦合效应、核价相关和标量相对论修正以及将参考能和相关能分别外推至完全基组极限.基于得到的势能曲线,获得了束缚和准束缚的9个∧-S态和16个Ω态的光谱常数,并且X~1∑~+,a~3∏~(势阱一)∧-S态的光谱常数与已有的实验结果非常符合.此外,计算了CF自由基X~2∏态到CF~+离子束缚和准束缚的9个∧-S态的垂直电离势和绝热电离势,并且CF~+(X~1∑~+)←CF(X~2∏)和CF~+(a~3∏(势阱一))←CF(X~2∏)的垂直电离势和绝热电离势与相应的实验结果也非常符合.由a~3∏,1~1∏态和其他激发∧-S态势能曲线的交叉现象,借助于计算的旋轨耦合矩阵元,分析了a~3∏~(势阱一),1~1∏~(势阱一)和2~1∑~+态的预解离机理.计算的23个Ω态离解极限处的相对能量与实验结果十分吻合.最后计算了(2)0+~(势阱一)(v'=0-5),(1)1~(势阱一)(v'=0-5)和(2)1~(势阱一)(v'=0)到X0~+态跃迁的Franck-Condon因子和辐射寿命.     

An Accurate Calculation of Potential Energy Curves and Transition Dipole Moment for Low-Lying Electronic States of CO

In this paper, potential energy curves for the X 1 Σ+ , a3 Π, a′3 Σ+ , d3 , A1 Π and I 1 Σ states of CO have been calculated using complete active space self-consistent field and multi-reference configuration interaction methods. The calculations have been performed at 108 nuclear separations from 0.7 to 4.0 A by the aug-cc-PV5Z basis set. Spectroscopic constants for the six low-lying electronic states are found in good agreement with experimental data. The vibrational states of the X1Σ+ and A1Π states are also calculated, which are reliable and accurate by comparison with the experimental data and the other theoretical values. The transition dipole moment (TDM) shows that the TDM of the two states (X1Σ + A1Π) are reduced strongly with increase of bond length.     

多参考组态相互作用方法研究BS+离子的势能曲线和光谱性质

利用量子化学从头计算方法MRCI+Q在AVQZ级别上对BS⁺离子进行了研究. 通过计算得到了与BS⁺离解极限B⁺（¹S_g）+S（³P_g）和B⁺（¹S_g）+S（¹D）对应的5个Λ-S态,确认了BS⁺离子的基态为X³∏电子态,而第一激发态¹∑⁺的激发能T_e仅仅为564.53 cm^-1. 首次纳入的旋轨耦合效应（SOC）使得BS⁺的5个Λ-S态分裂成为9个Ω态,原有的两个离解极限分裂为B⁺（¹S₀）+S（³P₂）,B⁺（¹S₀）+S（³P₁）,B⁺（¹S₀）+（³P₁）以及B⁺（¹S₀）+S（¹D₂）. 在考虑自旋轨道耦合效应之后,Ω态的基态为X2态. 通过势能曲线（PECs）可以发现所得到的Λ-S态和Ω态均为束缚态,利用LEVEL8.0程序拟合得到了对应电子态的光谱常数,这些结果可以为实验和理论方面进一步研究BS⁺的光谱性质提供准确的电子结构信息. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 Q)')" href="#">Davidson修正(+Q)     

Eu原子4f~76snlRydberg态的研究

利用三步双色共振激发技术和三步三色孤立实激发技术,系统地研究了铕原子在42250—44510 cm~(-1)能域内的光谱特性,提供了该能域内56个束缚高激发态的光谱信息.为了能确定这些态的光谱归属,进行了两方面的探索:第一,观察能否利用孤立实激发技术,把处于这些态上的铕原子进一步共振激发到自电离态,从而推断这些态属于单电子激发的束缚Rydberg态还是属于双电子激发的价态,并对Rydberg态的电子组态进行了光谱确认;第二,通过计算这些态相对于各个电离阈的量子亏损并观察它们分别收敛于哪个电离阈,以便获取其主量子数的信息.最后,设计并采用了三种不同的激发路径,分别将原子布居到同一高激发能域并探测它们在该能域的光电离光谱.通过比较这些光谱的异同并结合上述激发路径所对应的跃迁选择定则,便可惟一地确定这些高激发态的总角动量.研究发现:所探测到的高激发束缚态只有三个属于单电子激发的束缚Rydberg态,其余都是价态.本文确定了这三个Rydberg态的电子组态和原子状态.     

Configuration interaction studies on the spectroscopic properties of PbO including spin-orbit coupling

Lead oxide(Pb O), which plays the key roles in a range of research fields, has received a great deal of attention. Owing to the large density of electronic states and heavy atom Pb including in Pb O, the excited states of the molecule have not been well studied. In this work, high level multireference configuration interaction calculations on the low-lying states of Pb O have been carried out by utilizing the relativistic effective core potential. The effects of the core-valence correlation correction, the Davidson modification, and the spin–orbital coupling on the electronic structure of the Pb O molecule are estimated. The potential energy curves of 18 Λ-S states correlated to the lowest dissociation limit(Pb(~3P_g) + O(~3P_g)) are reported. The calculated spectroscopic parameters of the electronic states below 30000 cm~(-1), for instance, X~1Σ~+, 1~3Σ~+,and 1~3Σ~-, and their spin–orbit coupling interaction, are compared with the experimental results, and good agreements are derived. The dipole moments of the 18 Λ-S states are computed with the configuration interaction method, and the calculated dipole moments of X~1Σ~+and 1~3Σ~+are consistent with the previous experimental results. The transition dipole moments from 1~1Π, 2~1Π, and 2~Σ to X~1Σ~+and other singlet excited states are estimated. The radiative lifetime of several low-lying vibrational levels of 1~1Π, 2~1Π, and 2~1Σ~+ states are evaluated.     

GeS分子基态和低激发态的势能曲线与光谱性质

本文以aug-cc-pv5Z为基组, 采用考虑Davidson修正的多参考组态相互作用方法(MRCI+Q)得到了GeS分子基态(X¹Σ⁺)和5个低激发态(1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺, 2⁵Σ⁺)的势能曲线. 计算结果表明: 2⁵Σ⁺态为排斥态, 其余5个态为束缚态; 6个态有着共同的离解通道, 离解极限均为Ge(³P)+S(³P). 利用计算得到的势能曲线得了X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态的垂直跃迁能T_e, 平衡键长R_e, 离解能D_e, 谐振频率ω_e, 非谐性常数ω_ex_e及平衡位置的电偶极矩. X¹Σ⁺态的R_e 为2.034 Å, D_e 为5.728 eV, ω_e为571.73 cm^-1, ω_ex_e为1.6816 cm^-1, 平衡位置的电偶极矩为1.9593 Debye. 激发态1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺的T_e 依次为25904.81, 26209.22, 32601.19, 43770.26 cm^-1; R_e依次为2.313, 2.322, 2.188, 2.8790 Å; D_e依次为2.524, 2.487, 1.694, 0.3036 eV, ω_e依次为358.90, 353.08, 376.32, 134.96 cm^-1; ω_ex_e依次为1.2421, 1.2151, 1.6608, 1.9095 cm^-1; 平衡位置的电偶极矩依次为1.3178, 1.4719, 1.5917, -1.9785 Debye. 通过求解核运动的薛定谔方程得到了J=0时X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态前30个振动态的振动能级G_v和分子常数B_v, 得到的结果和已有的实验值及其他理论值符合较好.     

Angle-resolved x-ray photoelectron spectroscopy study of GeO_x growth by plasma post-oxidation

The growth process of GeO_x films formed by plasma post-oxidation(PPO) at room temperature(RT) is investigated using angle-resolved x-ray photoelectron spectroscopy(AR-XPS). The experimental results show that the distributions of the Ge~(4+)states, a mixture of the Ge_(2+)and Ge~(3+)states, and the Ge~(1+)states are localized from the GeO_x surface to the GeO_x/Ge interface. Moreover, the Ge~(1+)states are predominant when the two outermost layers of Ge atoms are oxidized.These findings are helpful for establishing in-depth knowledge of the growth mechanism of the GeO_x layer and valuable for the optimization of Ge-based gate stacks for future complementary metal–oxide–semiconductor(MOS) field-effect transistor(CMOSFET) devices.     

从头计算研究BP分子的势能曲线和光谱性质

利用高精度的量子化学从头计算MRCI+Q方法结合相关一致aug-cc-pVQZ基组计算了磷化硼分子X3Π,3Σ-,5Π和5Σ-态的势能曲线,计算所得的电子态在大键长位置处收敛于同一个离解极限B(2Pu)+P(4Su).为了得到更精确的结果,计算中首次纳入了旋轨耦合(SOC)效应,使得BP分子的4个Λ-S态分裂成为15个Ω态,其中3Π0+态被确定为基态.此外,SOC效应还使两个三重态X3Π和3Σ-分裂出的0+和1态的势能曲线产生了避免交叉,表明在当前的计算中考虑SOC效应是非常必要的.利用LEVEL8.0程序对计算所得的Λ-S态和Ω态的势能曲线进行拟合,得到了相应的光谱常数,通过与其他理论和实验工作进行比较,可知我们的结果更加精确、完整,可以为实验和理论方面进一步研究BP分子的光谱性质提供可靠的参考.     

Ionization Potentials and Quantum Defects of 1s2np2P Rydberg States of Lithium Atom

In this work, ionization potentials and quantum effects of 1s²np²P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for 1s²np²P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the 1s²np (n≥7) channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the 1s²7p²P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of 1s²np²P (n≥7) Rydberg states. Present calculations are in agreement with recent experimental data in whole.     

Structural,Spectroscopic and Vibrational Properties for Low-Lying Electronic States of LiCl

A multireference configuration interaction (MRCI) study has been carried out on the LiCl molecule. The potential energy has been calculated over a wide range of internuclear separation for the 21 low-lying electronic states of the LiCl molecule dissociating into Li (²S, ²P, ³S)+Cl(²P). The (4)¹Σ⁺, (3)¹Π, 1-3³Σ⁺, 1-3³Π, ^1,3Δ, ^1,3Σ^-, (5)¹Σ⁺, (4)³Σ⁺, (4)¹Π, (4)³Π excited states are studied for the first time in theory. Molecular spectroscopic constants (R_e, D_e, ω_e, ω_eχ_e, B_e and α_e) have been derived for the 9 bound states (X¹Σ⁺, (3)¹Σ⁺, (2)¹Σ⁺, ^1,3Δ, ^1,3Σ^-, (4)¹Π, (4)³Π) with a regular shape, and the spectroscopic constants of ground states X¹Σ⁺ are in good agreement with available experimental and theoretical values. The relative differences between experimental values and our values for R_e, D_e, ω_e, ω_eχ_e, B_e and α_e are 1.02%, 0.60%, 1.72%, 9.46%, 2.0%, and 0.75%, respectively. Moreover, vibrational levels of 9 bound states, which have not been investigated experimentally, are computed.     

SiCl自由基X2Π和A2Σ+态的光谱性质

采用内收缩多参考组态相互作用(ic MRCI)方法结合Dunning等相关一致基,计算Si Cl自由基X²Π和A²Σ⁺态的势能曲线.讨论参考能和相关能外推对X²Π和A²Σ⁺态光谱的影响.对势能进行相对论修正及核价修正计算.拟合势能曲线得到X²Π和A²Σ⁺态的光谱常数.它们与实验结果一致.利用Breit-Pauli算符,计算旋轨耦合效应,得到X²Π_1/2和X²Π_3/2的势能曲线、并计算它们的光谱常数.求解双原子分子核运动的径向SchrÖdinger方程,获得无转动SiCl自由基2个Λ-S态及X²Π态的耦合分裂态的全部振动态.得到J=0时X²Π态的自旋-轨道耦合常数、较高振动态的惯性转动常数以及X²Π_1/2和X²Π_3/2的振动能级等分子常数.     

Theoretical study of potential energy curves,spectroscopic constants,and radiative lifetimes of low-lying states in SeO molecule

The low-lying potential energy curves of SeO molecule are computed by means of ab initio multireference configuration interaction technique, taking into account relativistic (scalar plus spin-orbit coupling) effects. The spectroscopic constants of Ω states for X³Σ^-, a¹Δ, b¹Σ⁺, A³Π, A'³Δ, and A"³Σ⁺ states are obtained, and they are in good accordance with available experimental values. The Franck-Condon factors and transition dipole moments to the ground state are computed, and the natural radiative lifetimes of low-lying Ω states are theoretically obtained. Comparisons of the natural lifetimes of Ω states with previous experimental results and those of isovalent TeO molecule are made.     

OPTICAL-OPTICAL DOUBLE-RESONANCE EXCITATION SPECTRA OF THE (6d)1Πg, (7d)1Πg HIGH-LYING RYDBERG STATES IN Na2

Two ¹Π_g states of Na₂ for v≤13 have been observed by using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in B¹Π_u state are identified by the numerical calculations with the molec-ular constants for B¹Π_u←X¹Σ_g⁺ transitions and confirmed by the complemen-tary A¹Σ_g⁺←X¹Σ_g⁺ polarization spectra. Absolute vibrational numberings of the (6d)¹Π_g and (7d)¹Π_g states are determined by comparing the experimental OODR excitation intensities with the simulated Franck-Condon factors. The Dnnham coef-ficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6d)¹Π_g, (7d)¹Π_g states are reported.     

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Two new types of quantum states are constructed by applying the operator s(ξ) = exp(ξ*ab - ξa b ) on the two-mode even and odd coherent states.The mathematical and quantum statistical properties of such states are investigated.Various nonclassical features of these states,such as squeezing properties,the inter-mode photon bunching,and the violation of Cauchy-Schwarz inequality,are discussed.The Wigner function in these states are studied in detail.     

A study of the Ti(He, t) and Ni(He, t) reactions to isobaric analogue states

The (³He, t) reaction populating 0⁺ and 2⁺ states in ^{58, 60}Cu and ^{46, 48}V which are isobaric analogue states (IAS) of the 0⁺ ground states and 2⁺ first excited states in ^{58, 60}Ni and ^{46, 48}Ti have been studied at an incident ³He energy of 24.6 MeV. Triton spectra were measured for the targets ^46,48Ti, ^natNi and ⁵⁸Ni and angular distributions for the 0⁺ and 2⁺ IAS of ^{46, 48}Ti and ^{58, 60}Ni determined. The data were obtained using a magnetic spectrometer and position-sensitive detectors. The results have been analysed using DWBA theory. The 0⁺ → 0⁺ transitions to analogue states are described quite well using a microscopic form factor derived from a nucleon-nucleon interaction. However, with a Gaussian form, the m.s. radius of this interaction is only limited to the region 0–9 fm². Comparisons with data at other incident energies indicate that the strength of the effective interaction is strongly energy dependent. The Coulomb energies and (³He, t) angular distributions of the states assigned as the 2⁺ analogues in ⁴⁸V and ^58,60Cu are not described well by the models investigated. The ⁴⁶V 2⁺ IAS angular distribution is reproduced by a microscopic calculation, however. The ratios of the 0⁺ → 2⁺ IAS to the 0⁺ → 0⁺ IAS transitions are used to deduce a quadrupole deformation for the valence neutrons. The difference in the quadrupole deformations of the matter and proton distributions, as determined by other means, is found to be correlated with those of the valence neutrons. Several transitions to non-analogue states are also investigated.     

一氟化碳电子态的光谱性质和预解离机理的理论研究

采用考虑Davidson修正的内收缩多参考组态相互作用(icMRCI+Q)方法结合相关一致基组aug-cc-pV5Z和aug-cc-pV6Z首次计算了一氟化碳(CF)11个Λ-S 态(X²Π , a⁴Σ^-, A²Σ⁺, B²Δ, 1⁴Π, 1²Σ^-, 2⁴Π, 1^{4}Δ , 1⁴Σ⁺, 2²Σ^-和2⁴Σ^-) 所产生的25个Ω 态的势能曲线. 计算中考虑了旋轨耦合效应、核价相关和标量相对论修正以及将参考能和相关能分别外推至完全基组极限. 基于得到的势能曲线, 获得了束缚和准束缚的Λ-S态和Ω 态的光谱常数, 与已有的实验结果非常符合. 分析了束缚和准束缚的Λ-S态在各自平衡核间距R_e处的主要电子组态. 由于1⁴Π 和2⁴Π态的避免交叉, 发现准束缚态2⁴Π. 由Λ-S态势能曲线的交叉现象, 借助于计算的旋轨耦合矩阵元, 分析了a⁴Σ^-和B²Δ 态的预解离机理. 计算了25个Ω 态的离解关系, 给出了它们的离解极限. 最后研究了A²Σ⁺-X²Π 跃迁特性, 本文计算得到的A²Σ⁺-X²Π跃迁的Frank-Condon 因子和辐射寿命与已有实验值也符合得非常好.     

BH~+离子基态及激发态的势能曲线和跃迁性质的研究

利用高精度的多组态相互作用及Davidson修正方法 (MRCI+Q),采用ACV5Z-DK全电子基组计算了BH~+离子的前4个离解通道B~+(~1S_g)+H(~2S_g),B~+(~3Pu)+H(~2S_g),B(~2P_u)+H~+(~1Sg)和B~+(~1Pu)+H(~2Sg)的9个Λ—S态的势能曲线.X~2Σ~+,A~2Π和B~2Σ~+态的光谱常数和已有实验值符合得很好,其中b~4Σ~+,3~2Σ~+,3~2Π和4~2Σ~+态的光谱常数为首次报道,3~2Π和4~2Σ~+态具有双势阱结构.预测了A~2Π和B~2Σ~+态的辐射寿命:τ(A~2Π)=239.2 ns和τ(B~2Σ~+)=431.2 ns.最后在考虑自旋轨道耦合效应下讨论了B~2Σ~+与A~2Π态的势能曲线的相交对激光冷却BH~+离子的影响.     

{Q\bar{s}}{\bar{Q}(') s} Molecular States in QCD Sum Rules

We systematically investigate the mass spectra of {Q\bar{s}}{bar{Q}^(')s}molecular states in the framework of QCD sum rules. The interpolating currents representing the molecular states are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion (OPE). The masses for molecular states with various{Q\bar{s}} {\bar{Q}^(')s} configurations are presented. The result 4.36±0.08 GeV for the D^*_s\bar{D}^*_s0 molecular state is consistent withthe mass 4350^+4.6_-5.1 ± 0.7 MeV of the newly observed X(4350), which could support X(4350) interpreted as a D^*_s\bar{D^}*_s0 molecular state.