Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.     

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.     

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.     

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.     

14.7MeV/u、19.2MeV/u 20Ne诱发反应中转移和碎裂反应过程的竞争

对于在14.7MeV/u、19.2MeV/u ²⁰Ne+⁵⁸Ni反应中出射的类弹碎片,比较其单举动量分布和与前方向20个塑料闪烁体中带电粒子符合的动量分布,区分来自于碎裂过程和转移反应过程的贡献,并研究随束流能量变化时这两种过程的竞争.     

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σ _u ^?1 (c ⁴Σ _u ^? ), v vibrational states of the O ₂ ⁺ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ₀ = 0.054 meV and Γ₁ = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O₂ molecule. About 99% of the O ₂ ⁺ ions in the 2σ _u ^?1 (c ⁴Σ _u ^? ), v states were found to decompose to the O(¹ D) + O⁺(⁴ S) dissociation products.     

对u=√2v的一种定性说明

给出一种对公式u=√2v的定性说明．     

14.7MeV/u、19.2MeV/u ~(20)Ne诱发反应中转移和碎裂反应过程的竞争

对于在14.7MeV/u、19.2MeV/u ~(20)Ne+~(58)Ni反应中出射的类弹碎片,比较其单举动量分布和与前方向20个塑料闪烁体中带电粒子符合的动量分布,区分来自于碎裂过程和转移反应过程的贡献,并研究随束流能量变化时这两种过程的竞争。     

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.     

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.     

二氧化碳分子3σu轨道的电子动量谱测量

自从70年代实现（e,2e）电子动量谱测量以来,电子动量谱学获得了巨大的发展,成为探测物质结构的强有力的手段[1]。它可以分辨壳层来获得原子分子价壳层轨道的动量空间的电子密度分布,尤其是对低动量端的电子分布非常敏感。二氧化碳分子是一种典型的线性分子,对其结构的深入研究,具有相当的应用价值,尤其在环境保护领域。以前,CO2分子的电子动量谱曾被测量过三次[2-4],但由于能量分辨或动量分辨较低,研究结果不能令人满意。因此,用电子动量谱学的实验手段,进一步研究CO2分子,是非常有意义的。……     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ^? could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ? (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)?(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ? (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ^? radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ^n? fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

氮分子A3Σu+、B3Пg、C3Пu电子态的高温高振转光谱研究

采用态平均（CASSCF）/高度相关多参考组（MRCI）方法，对N2分子A3Σu+、B3Пg、C3Пu电子态的势能、跃迁偶极矩进行了高度相关的精确计算．计算的势能在平衡位置附近与RKR拟合的势能曲线非常一致，获得的跃迁偶极矩与已有实验值符合很好。首次对A3Σu+、B3Пg、C3Пu电子态的振转光谱常数随振动量子数v的变化进行系统定量计算，其结果与已有的实验观测数据相符．同时，获得了N2分子第一正带系的0-1、0-2、1-0、1-2、1-3、2-0、2-1、2-3、3-0、3-1和3-2光谱带分别在300，3000，6000，10000K时的谱线强度，如1-0带在3000，6000，10000K时的高温谱线带强度分别为1.58543×10-16 cm-1/(分子 cm-2)、6.07889×10-17 cm-1/(分子 cm-2)和2.3781×10-17 cm-1/(分子 cm-2)．这些结果对N2分子进一步的理论研究、实际应用和高温大气的建模与研究具都有一定的参考价值．     

ANALYSIS OF F′0+u ION-PAIR STATE OF IODINE

The optical-optical double resonant multiphoton ionization (OODR-MPI) technique and the fluorescent excitation spectroscopy technique have been applied to the study of the F′0⁺_u ion-pair state of iodine. This paper presents OODR-MPI spectrum and fluorescent excitation spectrum of I₂ in the region of 54000-55300cm^-1 by the three-photon resonant, two-photon ionization (1+2+2) and (1+(1+1)+2) processes.     

400 MeV/u碳离子打靶的屏蔽参数计算

为了给医用重离子加速器提供一种专用的快速计算屏蔽厚度或对蒙特卡罗模拟结果进行验证的方法。采用FLUKA程序完成了400 MeV/u碳离子打不同靶的屏蔽参数计算。首先研究了打厚靶(铁、水)产生的次级辐射场的角度分布及主要成分;接着给出了不同角度范围下周围剂量当量在屏蔽体中的衰减曲线,通过拟合数据进一步得到不同角度范围下的辐射源项值H₀和衰减长度λ₀;最后结合莆田市医用重离子加速器治疗室的屏蔽设计,介绍了此套屏蔽参数的使用方法,通过与蒙特卡罗模拟结果的对比,证明了这套屏蔽参数的可靠性。该参数可为同类医用重离子加速器的屏蔽设计提供可靠的参考数据。