Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

Polarization spectroscopy of Na2 A1Σu+-b3Πu ← X1Σg+ intercombination bands

The A¹Σ_u⁺ ∼ b³Π_u perturbation of Na₂ in several high vibrational levels has been studied by polarization spectroscopy. Deperturbed molecular constants are given for the mutually interacting v_A = 26 ∼ v_b = 28 and v_A = 34 ∼ v_b = 34 vibrational levels.     

碰撞诱导钠分子A1Σ+u→X1Σ+g的荧光光谱

用532.0 nm激光激发Na2分子到B1Πu电子态,记录了Na(3P)原子的跃迁和Na2分子的A1Σ+u-Χ1Σ+g的谱带.由Na与Na2激发态发射的光谱及其强度可以认定在Na-Na2系统中的碰撞过程,Na(3P)原子线是Na2(B1Πu)到Na(3P)的碰撞能量转移产生的,预解离过程也可产生原子线.而A1Σ+u-Χ1Σ+g谱带是由B1Πu到21Σ+g的碰撞转移后再由21Σ+g到A1Σ+u的辐射而引起的.在360℃,根据辐射衰变率和荧光强度,得到Na2(B1Πu)到Na2(21Σ+g)碰撞转移率系数为7.1×10-10 cm3s-1,而B1Πu的预解离率为2.3×106 s-1.     

Potential of the A 1Σ u + state of He2

The potential of the lowest excited singlet state of He₂ is calculated. The best function includes 209 configurations constructed from 10 σ basis orbitals. Excellent agreement with experimental quantities depending on the shape of the potential near the minimum (equilibrium interatomic separation, vibrational and rotational constants for the lower vibration levels) is obtained. The dissociation energy is 18 600 cm^-1, compared to the experimental 19 910±50 cm^-1. Agreement is not as good for the highest vibrational levels.     

如何让学生学会使用公式1/u+1/v=1/F

公式1/u+1/v=1/F是几何光学中的基本方程之一。公式本身虽然简单,易懂易记,但学生使用这个公式算题的时候,却不是没有困难的,他们常把各个量的符号弄错,因而得不出正确的结果。由于这种原因,我在教学中对使用这个公式算题时应该注意那几点,作了如下的说明:     

Time spectroscopy in theA 1 ∑ u + state of Li2. Perturbations by thea 3Π u state

We have employed time-resolved LIF spectroscopy in order to investigate perturbations in theA ¹ ∑ _u ⁺ state of the three isotopic Li₂ molecules. After a systematic check of more than 2000 individual rotation-vibration levels, 46 levels were found whose anomalous lifetimes can be interpreted by perturbations with thea ³ Π _u state. As almost all perturbed levels possess shortened lifetimes the predissociating nature of thea ³ Π _u state, caused by interaction with thex ³ ∑ _u ⁺ continuum, is revealed. On the basis of the Kovács-Budo theory of accidental predissociation we have fitted the molecular constants of thea ³ Π _u state, thex ³ ∑ _u ⁺ potential curve and the electronic parts of the perturbation matrix elements do that the observed lifetimes of all levels in the 78 investigatedA ¹ ∑ _u ⁺ ?a³ Π _u term-crossing regions can be understood.     

Ab initio calculation of the He2 A 1Σ u +└X 1Σ g + absorption spectrum

The absorption spectrum of helium gas near 600 Å, assigned to the A ¹Σ _u ⁺└X ¹Σ _g ⁺ transition in He₂, is calculated at 77 K. The excited state potential is taken from a recent ab initio calculation. The theoretical spectrum shows well-defined bands, corresponding to different vibration levels of the A state, with diffuse rotational structure, in agreement with experiment. Fairly good quantitative agreement with Tanaka and Yoshino's measured spectrum is obtained, except for the somewhat too large separation between calculated vibrational bands, probably due to the theoretical potential for the A state rising too steeply at small inter-nuclear separation. Rotational constants derived from the calculated and experimental spectra are in good agreement. It is shown that they are significantly smaller than actual rotational constants of the upper state.     

钠分子B 1Πu与2 1Σ+g间的碰撞激发转移

用HeCd激光器的4416nm线激发Na2分子到B1Πu电子态,记录了Na原子的跃迁和Na2分子的A1Σ+u-Χ1Σ+g的谱带。由Na与Na2激发态发射的光谱及其强度可以认定在NaNa2系统中的碰撞过程,Na原子线是Na2(B1Πu)到Na(3P)的碰撞能量转移产生的,预解离过程也可产生原子线。而A1Σ+u-Χ1Σ+g谱带是由B1Πu到21Σ+g的碰撞转移后再由21Σ+g到A1Σ+u的辐射而引起的。在360℃,根据辐射衰变率和荧光强度,得到Na2(B1Πu)到Na2(21Σ+g)碰撞转移率系数为57×10-10cm3·s-1,而B1Πu的预解离率为27×106s-1。     

CS2 分子 1 B2(1 Σ+u )态预解离动力学研究

研究了CS2 分子1B2 (1Σ+u )预离解态线形势垒下的g振动能级光解动力学,包括预解离寿命、产物振转布居、平动振动转动能量分配和解离通道分支比.在实验过程中,一束可调谐激光激发超声射流冷却的CS2 分子到1B2 (1Σ+u )电子态,光解产物CS用另一束可调谐激光通过激光诱导荧光(LIF)方法检测.通过拟合光解碎片激发谱的谱峰轮廓,获得了源于不同跃迁初始态的1B2 (1Σ+u )态g振动能级的预解离寿命.通过分析CS的LIF光谱,则获得了不同光解波长下CS碎片的v=0~8振动态布居、v=1、4 ~8振动态的转动布居、能量分配以及两个预解离通道CS(X1Σ+ ) +S(3PJ)和CS(X1Σ+ ) +S(1D2 )的分支比.实验还考察了初始态弯曲振动量子数v2″、振动角动量量子数l对解离动力学的影响.发现v2″的影响不大,而l的影响却是明显的.较大的l(=K)对应于较短的寿命和较小的通道分支比S(3PJ) /S(1D2 ),即大的l(=K)有利于预解离的发生,同时更有利于产生S(1D2 ).     

N2+分子离子的B2Σu+、A2Πu和X2Σg+电子态光谱研究

采用光外差 磁旋转 速度调制吸收光谱技术 ,在可见光波段范围 16 80 0～ 175 73cm-1,对N2 + 的A2 Πu-X2 Σ+ g(12 ,6 )、(11,5 )、(7,2 )带和B2 Σ+ u -X2 Σ+ g(1,5 )带进行了测量和分析 ,推导了双原子分子振转能级在受到微扰作用时的有效哈密顿量形式 ,并分析了N2 + 的A2 Πu-B2 Σ+ u 之间存在的微扰相互作用 ,通过与实验数据的拟合得到了精确的电子态微扰常数 ξe、ηe.     

Ab initio nonadiabatic calculation of the sensitivity coefficients for the X 1Σ g + → B 1Σ u + ; C 1Πu lines of H2 to the proton-to-electron mass ratio

Ab initio nonadiabatic calculations of the wavelengths λ_ij of the individual lines of the Lyman X ¹Σ _g ⁺ → B ¹Σ _u ⁺ and Werner X ¹Σ _g ⁺ → C ¹Π_u series of molecular hydrogen and corresponding sensitivity coefficients K _ij = dlnλ_ij/dlnγ have been performed. These quantities are necessary for testing a possible change in the proton-to-electron mass ratio γ = m _p/m _e in the process of cosmological evolution. The basic contribution to K _ij comes from the difference between the average kinetic energies of vibrations of combined states. Nonadiabatic interactions are important for a small number of locally-perturbed rovibrational levels of the B ¹Σ _u ⁺ and C ¹Π _u ⁺ states, for which change in K _ij that is caused by nonadiabatic effects reaches 14%, which can lead to a significant systematic shift in the estimate of the parameter γ.     

An invariant measure for the equationu tt −u xx +u 3=0

Numerical studies of the initial boundary-value problem of the semilinear wave equationu _tt –u _xx +u ³=0 subject to periodic boundary conditionsu(t, 0)=u(t, 2),u _t (t, 0)=u _t (t, 2) and initial conditionsu(0,x)=u ₀(x),u _t(0,x)=v ₀(x), whereu ₀(x) andv ₀(x) satisfy the same periodic conditions, suggest that solutions ultimately return to a neighborhood of the initial stateu ₀(x),v ₀(x) after undergoing a possibly chaotic evolution. In this paper an appropriate abstract space is considered. In this space a finite measure is constructed. This measure is invariant under the flow generated by the Hamiltonian system which corresponds to the original equation. This enables one to verify the above returning property.     

Lifetimes,population and deactivation mechanisms of theC 1 ∏ u , 23 ∏ g and 21∑ u + states of Na2

The UV and visible fluorescence of Na₂ molecules in a heat-pipe, excited by the frequency doubled radiation of a tunable mode-locked cavity-dumped cw dye laser was observed through a monochromator, using time-resolved single-photon counting. The effective lifetimes of the directly excitedC ¹ _u state and the collisionally populated 2³ _g and 2¹ _u ⁺ states have been measured as a function of sodium-vapor pressure and argon pressure which yields the radiative lifetimes, the population mechanisms and the collisional quenching cross sections of the three states.     

A quasiclassical study of collisions of He with HD(B 1Σ+ u )

A quasiclassical trajectory study has been carried out for collisions of ⁴He with electronically excited H₂(B ¹Σ⁺ _u ) and its isotopomer HD. By using analytical fits for the ab initio potential energy surfaces of the ground and the excited state we have obtained vibrational and electronic quenching cross sections for several initial conditions. We draw the following conclusions. Vibrational excitation strongly promotes electronic quenching whereas translational energy is less effective. Rotational excitation decreases the rate of quenching. In a remarkable contrast to the ground electronic state, vibrational energy transfer on the excited potential energy surface is an efficient and fast process. Collisions at high energies results in T → R energy transfer. The above conclusions are valid for both H₂ and HD.     

Li2分子X1∑+g,A1∑+u和B1Ⅱu态的势能函数

使用SAC/SAC-CI方法,利用D95、D95(d)、6-311g以及6-311g(d)等基组,对Li2分子的基态(X1∑+g)、第一激发态(A1∑+u)及第二激发态(B 1Ⅱu)的平衡结构和谐振频率进行了优化计算.通过对四个基组的计算结果的比较,得出了D95(d)基组为四个基组中的最优基组的结论;使用D95(d)基组,利用SAC的GSUM(Group Sum of Operators)方法对基态(X1∑+g)、SAC-CI的GSUM方法对激发态(A1∑+u和B1Ⅱu)进行单点能扫描计算,用正规方程组拟合Murrell-Sorbie函数,得到了相应电子态的完整势能函数;从得到的势能函数计算了与基态(X1∑+g)、第一激发态(A1∑+u)和第二激发态(B1Ⅱu)相对应的光谱常数(Be,αe,ωe和ωexe),结果与实验数据较为一致.其中,基态、第一激发态与实验数据吻合得非常好.     

Na2分子X1∑+g,A1∑+u和B1Ⅱu态的势能函数

使用SAC/SAC-CI方法,利用6-311 g,6-311g**及cc-PVTZ等基组,对Na2分子的基态(X1∑ g)、第一激发态(A1∑ g)和第二激发态(B1Ⅱu)的平衡结构和谐振频率进行计算.通过对3个基组的计算结果的比较,得出6-311g**基组为3个基组中最优基组的结论;使用6-311g**基组,分别利用SAC的GSUM(Group Sum of Operators)方法对基态(X1∑ g),SAC-CI的GSUM方法对激发态(A1∑ u)和(B1Ⅱu)进行单点能扫描计算,用正规方程组拟合Murrell-Sorbie函数,得到相应电子态的完整势能函数.用得到的势能函数计算与基态(X1∑ g),第一激发态(A1∑ u)和第二激发态(B1Ⅱu)相对应的光谱常数(Be,αe,we和weXe),结果与实验数据基本吻合.     

T1uhg杨-泰乐系统：D5d势阱中的各向异性现象

杨-泰乐(Jahn-Teller缩写为JT)系统在其最低的绝热势能面上常常典型地含有一系列相互等同的势阱.在C60分子中，若一个电子占据该分子的三重简并的能量最低电子态，这一具有T1u对称性的电子态将会与具有hg对称性的五重简并振动态发生相互作用，形成所谓的T1uhg JT系统.当考虑电声的非线性相互作用时，该系统的势能面上将出现D5d对称性的势阱并伴随D3d对称性的势垒；反之亦然.本文在幺正平移变换的基础上，引入了标度变换，研究了该JT系统中D5d势阱中的各向异性现象：在电子空间中，非线性项的引入使得 关键词： C60 杨-泰乐效应 各向异性 电声耦合 标度变换