单三重混合态Na2 (A1Σu+, v=8 ~ b3Π0u, v=14)和Na 碰撞传能的干涉相位角的计算

文章详细介绍了单三重混合态同核双原子分子Na2 (A1Σu+, v=8 ~ b3Π0u, v=14)和Na碰撞传能的干涉相位角的理论计算方法.并且采用了两种不同的相互作用势（一种是长程吸引相互作用势,另一种是Lennard-Jones 相互作用势）,进行了具体的数值计算.在实验温度750K下,计算积分干涉相位角,与实验值相差很小.干涉相位角的大小表明混合态体系碰撞传能中的量子干涉效应是不容忽视的.最后,分析了干涉相位角随着不同参数的变化关系,发现Na2 – Na体系中,干涉相位角随各参数变化而变化,但变化不大.     

Na2(A1∑u+,v=8～b3Ⅱ0u,v=14)-Na体系转动传能的碰撞量子干涉效应

沙国河及其工作组于1995年发表了CO A1Π(v=0)～e3∑-(v=1)与He1,Ne及其它碰撞伴的碰撞过程中转动传能的碰撞量子干涉现象,并得到了积分干涉角,陈等从理论和实验上发现了Na2(A1∑u ,v=8～b3Π0u,v=14)体系与Na(3s)碰撞的碰撞量子干涉现象,孙等计算了其积分干涉角,但是对微分干涉角没有过多的计算.本文作为对原子-双原子体系碰撞诱导转动传能的进一步理论研究,在含时一级波恩近似的基础上考虑各向异性相互作用势和长程相互作用势,计算了单叁混合态的Na2(A1∑u ,v=8-bΠ0u,v=14)体系与Na碰撞的微分干涉角,并得到了微分干涉角与碰撞参数的关系,此理论模型对理解和进行分子束实验是非常重要的.     

Interference Angle on Quantum Rotational Energy Transfer in Na＋Na2 （A1 ∑u^＋,v=8-b^3∏0u,v=14） Molecular Collision System

In order to study the collisional quantum interference （CQI） on rotational energy transfer in atom-diatom system, we have studied the relation of the integral interference angle and differential interference angle in Naq-Na2 （A1 ∑u^＋,v=8-b^3∏0u,v=14） collision system. In this paper, based on the first-Born approximation of timedependent perturbation theory and taking into accounts the anisotropic effect of Lennard-Jones interaction potentials, we present a theoretical model of collisional quantum interference in intramolecular rotational energy transfer, and a relationship between differential and integral interference angles.     

Na2(A1∑+u，v=8~b3Π0u，v=14)-Na体系碰撞诱导转动传能的微分干涉角

对原子-双原子体系碰撞诱导转动传能进行了进一步的理论研 究. 在含时一级波恩近似的基础上考虑各向异性相互作用势，计算了 单-叁重混合态的Na2(A1∑+u，v=8~b3Π0u，v=14)体系与Na碰撞 的微分干涉角(b·?和b??)，得到了微分干涉角与碰撞参数的关系，对 其碰撞量子干涉作出了定量准确的描述.     

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:     

Isotope dependent predissociation in the C 1 Σ + , v =0 and v =1 states of CO

Rotationally resolved spectral lines in the C - X (1, 0) band of carbon monoxide are investigated under high resolution using a coherent vacuum ultraviolet laser source, continuously tunable near 107 nm. Transition frequencies are determined by calibrating against a reference standard of iodine lines, recorded with saturation spectroscopy in the visible range, yielding an absolute accuracy of 0.003 cm^-1 in the vacuum ultraviolet. Improved molecular constants for the excited state are derived and no effects of perturbation are found at the present level of accuracy. Line broadening measurements result in information on the excited state lifetime of the C ¹ Σ ⁺ , v = 1 state for five natural isotopomers of carbon monoxide: τ( ¹² C ¹⁷ O ) = 280 ps, τ( ¹² C ¹⁸ O ) = 210 ps, τ( ¹³ C ¹⁶ O ) = 295 ps, τ( ¹³ C ¹⁷ O ) = 160 ps, and τ( ¹³ C ¹⁸ O ) = 150 ps. Within the accuracy of the present measurements no effects of J-dependent lifetimes were observed, for neither of the isotopomers. In addition direct time domain measurements of the lifetime of the C ¹ Σ ⁺ , v = 0 and v = 1 states of the main isotopomer are performed in a pump-probe experiment using a picosecond VUV-laser, yielding τ( ¹² C ¹⁶ O ) = 1780 ps for v = 0 and τ( ¹² C ¹⁶ O ) = 625 ps for v = 1. For C ¹ Σ ⁺ , v = 0 in ¹²C¹⁶O and ¹³C¹⁶O the same lifetime is found; this lifetime matches experimental values of the oscillator strength and hence supports previous results showing pure radiative decay in this state; the error margins however do not exclude some low level of predissociation. The measurements indicate that the C ¹ Σ ⁺ , v = 0 state of the ¹³C¹⁸O isotopomer is predissociated with an estimated yield of 17% (i.e. above the level of predissociation for ¹²C¹⁶O.) From the combined data predissociation yields upon excitation of the C ¹ Σ ⁺ , v = 1 state are derived, lying in the range 0.84-0.91 for the five less abundant isotopomers; for the main ¹²C¹⁶O isotopomer a strongly deviating predissociation yield of 0.65 is deduced. Received 21 December 2000 and Received in final form 26 March 2001     

单三重混合态Na2(A1∑+u,ν=8～b'3Ⅱ0u,ν=14)和Na碰撞传能的干涉相位角的计角

文章详细介绍了单三重混合态同核双原子分子Na2(A1∑+u,ν=8～b'3Ⅱ0u,ν=14)和Na碰撞传能的干涉相位角的理论计算方法.并且采用了两种不同的相互作用势(一种是长程吸引相互作用势,另一种是Lennard-Jones相互作用势),进行了具体的数值计算.在实验温度750 K下,计算积分干涉相位角,与实验值相差很小.干涉相位角的大小表明混合态体系碰撞传能中的量子干涉效应是不容忽视的.最后,分析了干涉相位角随着不同参数的变化关系,发现Na2 Na体系中,干涉相位角随各参数变化而变化,但变化不大.     

对u=平方根(2)v的一种定性说明

给出一种对公式u=平方根(2)v的定性说明.     

Non-adiabatic quantum dynamical studies of Na(3p) + HD(v = 1, j5) = 0)→NaH/NaD + D/H reaction

Non-adiabatic dynamical calculations are carried out for the Na(3 p)+HD(ν = 1, j = 0)→NaH/NaD+D/H reaction on the diabatic potential energy surfaces of Wang et al.(Sci. Rep. 2018, 8, 17960) by using the time-dependent wave packet method. The state-to-state integral cross sections and differential cross sections of two reaction channels(NaH/NaD+D/H)are calculated for collision energy up to 0.4 eV. The cross section branching ratio indicates that the dominant reaction channel changes from NaD+H to NaH+D when the collision energy is larger than 0.227 eV. The products from two reaction channels both prefer to form in vibrationally cold but rotationally hot states, and they both tend to forward scattering.     

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.     

Relative probabilities of spontaneous transitions in v″ progressions of the G1Σ g + , v′→B 1Σ u + , v″ bands of the H2 molecule

The probabilities of spontaneous transitions in v″ progressions of the G ¹Σ _g ⁺ →B ¹Σ _u ⁺ bands of the H₂ molecule (the 3D→2B electronic transition in notations of G.H. Dieke) are, for the first time, experimentally studied. The line strength ratios were measured for 78 G ¹Σ _g ⁺ , v′, J′→B ¹Σ _u ⁺ , v″, J″ electronic-vibrational-rotational spectral lines having a common upper level but belonging to different bands of v″ progressions (the vibrational branching coefficients). For this purpose, the intensities of lines of the P and R branches, emitted by a low-pressure plasma and corresponding to different values of the rotational (J′=0–11) and vibrational (v′=0–3 and v″=0–7) quantum numbers, were used. It was found that the changes in the vibrational branching coefficients with variation of v′ and v″ are significant (up to a factor of 20). For most bands studied, the dependences of the vibrational branching coefficients on the rotational quantum number J′ of an upper level are rather weak and do not exceed 30%. It was established that the difference between the experimental values of ratios of the vibronic transition probabilities (summed over J″) and the results of calculation in the adiabatic approximation strongly depends on v′, reaching a factor of 25 for a transition from the v′=2 level. At the same time, the discrepancy between the experimental data and the results of nonadiabatic ab initio calculations lies between 1.0 and 2.3.     

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.     

Theoretical study of stereodynamics for the D'+ DS(v=0,j=0) → D'D + S abstraction reaction

Quasiclassical trajectory (QCT) calculations have been performed for the abstraction reaction, D'+ DS(v = 0, j = 0) → D'D + S on a new LZHH potential energy surface (PES) of the adiabatic 3 A electronic state [Lü et al. 2012 J. Chem. Phys. 136 094308]. The collision energy effect on the integral cross section and product polarization are studied over a wide collision energy range from 0.1 to 2.0 eV. The cross sections calculated by the QCT procedure are in good accordance with previous quantum wave packet results. The three angular distribution functions, P(θr), P(φr), and P(θr,φr), together with the four commonly used polarization-dependent differential cross sections ((2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21/dωt)) are obtained to gain insight into the chemical stereodynamics of the title reaction. Influences of the collision energy on the product polarization are exhibited and discussed.     

The stereodynamic properties of the F + HO (v,j)→HF + O reaction on the 1A' and 3A' potential energy surfaces by quasi-classical trajectory: Initial excitation effect (v =1-3, j = 0 and v = 0, j =1-3)

The stereodynamic properties of the F + HO (v, j) reaction are explored by quasi-classical trajectory (QCT) calculations performed on the ¹A' and ³A' potential energy surfaces (PESs). Based on the polarization-dependent differential cross sections (PDDCSs) and the angular distributions of the product angular momentum with the reactant at different values of initial v or j, the results show that the product scattering and product polarization have strong links with initial vibrational-rotational numbers of v and j. The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing, and the scattering angle of the HF product taking place on the ³A' potential energy surface is found to be more sensitive to the initial value of v. The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect. With enhancement in the initial rovibrational excitation effect, there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis, for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect. Moreover, the initial rovibrational excitation effect on the product polarization is more pronounced for the ³A' potential energy surface than for the ¹A' potential energy surface.     

Product polarization and mechanism of Li + HF(v=0, j=0) → LiF(v', j') + H collision reaction

A state-to-state dynamics analysis for the Li+HF(v=0,j=0)→LiF(v',j')+H collision reaction has been performed through quasiclassical trajectory(QCT)calculations.It is found that the differential cross section(DCS)of the LiF products from the title reaction is preferentially backward scattering for v=0,yet forward scattering for v=1 and 2.For v=3,the DCS exhibits forward,backward,and sideways scatterings.The variation of the internuclear distances and angles along the propagation time reveals that more than 99.08%of reaction trajectories undergo the direct reaction mechanism.The values of the polarization parameters a{1}1and a{2}0demonstrate that the product rotational angular moment j' is not only aligned perpendicular to the reagent relative velocity vector,but also oriented along the negative y axis.These product polarization results agree well with the recent quantum mechanical studies.The mechanism of these results was proposed and discussed in detail.     

低碰撞能下H+HF(v=3,j=0)反应的量子动力学研究

报道了H原子和振动激发的HF(v=3,j=0)分子在低碰撞能下的量子反应动力学研究.计算结果表明:在低碰撞能下,散射主要以非反应过程为主;振动激发有利于反应的进行;在小于10-4eV碰撞能下,非反应非弹性散射截面和反应截面的比值约为3.在反应截面上发现了Feshbach共振现象,证实是由反应通道上紧邻反应势垒的H…HF(v=3,j=1～3)的范德瓦尔斯聚合体存在的准束缚态所形成.     

Observation of the v′=8←v=0 vibrational overtone in cold trapped HD+

We report the observation of the hitherto undetected v′=8←v=0 vibrational overtone in trapped HD⁺ molecular ions, sympathetically cooled by laser-cooled Be⁺ ions. The overtone is excited using 782 nm laser radiation, after which HD⁺ ions in v=8 are photodissociated by the 313 nm laser used for Be⁺ cooling. The concomitant loss of HD⁺ is detected by the method of secular excitation (Roth et al. in Phys. Rev. A. 74:040501(R), 2006). We furthermore present details of the experimental setup, and we show that results from spectroscopy of v′=8←v=0 overtones in combination with accurate ab initio calculations may yield a new value for the proton–electron mass ratio with an accuracy of order 1 ppb.