若干小分子基态与激发态的势能函数、分子常数及“电子—分子”散射总截面研究
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摘要
分子势能函数是原子分子物理学的重要研究内容之一。分子势能函数是在Born-Oppenheimer近似下对分子性质的完全描述，即描述分子的能量、几何、力学和光谱性质，同时也是核运动的势能函数，是研究原子分子碰撞及反应动力学的基础，在原子团簇的形成、离解及稳定性分析中尤为重要。
本文利用Gaussian03程序包提供的SAC／SAC-CI程序计算了~7Li_2分子8个激发态(A~1∑_u~+，G~1∏_g，2~1∏_u，a~3∑_u~+，b~3∏_u，c~3∑_g~+，2~3∑_g~+和2~3∏_u态)的绝热激发能，并根据原子分子反应静力学的有关原理导出了这8个激发态的合理离解极限。于多个基组下使用SAC方法对基态(X~1∑_g~+态)、SAC-CI方法对这8个激发态进行了单点能扫描计算，并进行了解析势能函数的拟合。在拟合出的M-S函数的基础上对这8个激发态进行了主要光谱常数(D_e，R_e，ω_e，ω_eX_e，B_e，a_e)及某些分子常数(振动能级、振动经典转折点、惯性转动常数以及离心畸变常数等)的计算，且将理论计算结果与光谱实验数据及其他理论计算结果进行了比较。结果表明，它们中的绝大多数都达到或超过了目前文献所报导的计算精度，其中有相当一部分分子常数属首次报导。另外：
(1)由于SAC／SAC-CI程序不能直接进行准确谐振频率的计算，本文采用在单点能扫描的基础上通过拟合出M-S势能函数、并利用力常数与谐振频率的关系，计算出了每个态的谐振频率。对绝大多数态而言，本文的计算结果与已有的实验结果或其他理论结果都能很好地相符；
(2)本文发现，在SAC／SAC-CI程序中由几何优化和单点能扫描获得的平衡核间距不一致。论文对这种不一致的原因进行了解释。由于分子势能函数是在Born-Oppenheimer近似下对分子性质的完全描述，因此本文认为单点能扫描给出的平衡核间距应更合理。
使用原子分子反应静力学的有关原理，分析了Li_2，H_2，LiH，BH和AlH等几个双原子分子以及Li_2H，BH_2和AlH_2等几个三原子基态的合理离解极限。运用密度泛函理论、耦合簇理论和二次组态相关方法方法，优化了Li_2，H_2，LiH，BH及AlH等几个双原子分子基态的平衡几何、计算了它们基态的谐振频率和离解能，并利用优选出的“基组／方法”进行了单点能扫描、拟合出了相应的解析势能函数。从这些解析势能函数出发，得到了与实验结果能较好符合的光谱常数(ω_eX_e，B_e，a_e、)。采用B3P86／D95V(d，p)方法对Li_2H分子、QCISD／6-311++G(3df，3pd)方法对BH_2分子和QCISD／D95(3df，3pd)方法对AlH_2分子进行几何优化，得到了这3个分子的基态都为G_(2v)结构、电子态都为X~2 A_1的结论。利用多体项展式理论，确定了这3个分子的解析势能函数，分别绘制出了它们不同形式的等值势能图。解析势能函数和相应的等值势能图正确地反映了它们的结构特点和能量信息。使用其等值势能面讨论了Li(~2S_g)+LiH(X~1∑~+)，H(~2S_g)+BH(X~1∑~+)和Al(~2S_g)+AlH(X~1∑~+)等反应的势能面静态特征。对静态势能面的分析表明，在这些反应途径中，都存在着两个对称的鞍点，且反应都为有阈能反应，活化能分别为78.2408 kJ／mol，150.204 kJ／mol和54.8064 kJ／mol。
“电子-分子”散射是一种重要的物理过程，对其规律进行探索对很多实际应用都有重要意义，特别是作为主要理论计算结果的散射总截面是许多理论和应用研究所需的重要数据。然而与“电子-原子”散射相比，“电子-分子”散射是一个更为复杂的问题，这是因为在中、高能区，分子内的许多非弹性通道，如电离、激发、转动和振动等都被打开，这些使得准确的理论计算变得异常困难。
可加性规则(AR)方法将“电子-分子”散射问题简化成“电子-原子”散射问题，从而使计算简单易行。但可加性规则认为分子中的原子是自由的，原子间的相互作用可以忽略。但实际上，分子中的成键原子与自由原子是不同的，成键原子的电子云之间有重叠，重叠的结果造成了束缚原子的电子云扭曲变形，因而其对称性遭到了破坏。考虑分子中成键原子的电子云重叠效应，对适用于“电子-自由原子”的复球光学势进行了修正。利用修正后的复光学势计算了电子被HCl，NH_3，H_2O，CH_4，N_2，O_2和CO_2分子散射的总截面，并与其他理论计算结果及实验结果进行了比较。结果表明，利用AR方法和修正后的复光学势计算得到的总截面在一个很大的能量范围内都能与实验结果很好的相符，但还存在着总截面值在低能区高于实验值、在高能区却低于实验值的问题。它揭示：对复光学势的进一步修正必须与电子的入射能量以及靶分子的几何特性相关联。
多原子分子对低能电子不是完全透明的。当电子的入射能量较低时，分子中的外层原子对内层原子有部分屏蔽作用。论文从AR方法本身的修正入手，还提出了一种与电子入射能量以及靶分子的尺寸、含有的电子总数、原子总数等相关联的修正方法，来解决“电子-分子”散射总截面随电子入射能量变化太快的问题。为弄清“电子-分子”散射总截面随电子入射能量变化太快究竟是由“电子-原子”散射总截面的理论计算、还是AR方法本身引起的，本文避开“电子-原子”散射总截面的理论计算，直接采用“电子-原子”散射总截面的实验数据作为初始数据，在50-5000 eV内对电子被NO，N_2O，NO_2，CO_2，H_2O，CH_4，C_2H_2，C_2H_4和C_2H_6分子散射的总截面进行了计算。将计算结果与实验结果相比较后发现，几乎在整个能区内利用这一修正后的AR方法计算得到的“电子-分子”散射总截面都与实验结果相符极好。这说明“电子-分子”散射总截面随入射电子能量变化太快是由AR方法本身引起的。这一结论将为“电子-分子”散射理论计算时所使用的复光学势的进一步修正，指出了一个明确的方向。
Molecular potential energy function (PEF) is one of the importantfields in atomic and molecular physics. It gives one absolutedescription of molecular properties with Born-Oppenheimerapproximation. Namely, it can completely determine molecular energy,equilibrium geometry, force constants and spectroscopic parameters.At the same time, it is also the PEF of the core movement, which is thefoundation to investigate atomic and molecular collision and reactionand is of special importance in the atom-cluster growth, dissociationand stability analyses.
The adiabatic excitation energies from the ground to eight excitedstates, A~1∑_u~+, G~1∏_g, 2~1∏_u, a~3∑_u~+, b~3∏_u, c~3∑_g~+, 2~3∑_g~+ and 2~3∏_u, for dimer~7Li_2 have been calculated using the SAC/SAC-CI method presented inGaussian03 program package. The reasonable dissociation limits ofthese excited states have been deduced according to the principles ofAtomic and Molecular Reaction Statics (AMRS) using the adiabaticexcitation energies obtained in this paper. The single-point energyscanning (SPES) calculations over a wide internuclear separationrange are performed using SAC method for the ground state andSAC-CI method for the eight excited states of dimer ~7Li_2 at a numberof basis sets. All the ab initio calculations are fitted into analyticalPEFs by the least-squares method. Then, these analytical PEFs areemployed to calculate the spectroscopic parameters (D_e, R_e,ω_e,ω_ex_e,B_e andα_e) and some molecular constants (vibrational levels, classicalturning points, inertial rotation and centrifugal distortion constants).The calculated results are encouraging when compared with the measurements and other theories. Some of the calculated results arereported for the first time. In addition,
(1) The present SAC/SAC-CI method cannot accurately performthe harmonic frequency calculations. The frequency is computed usingthe corresponding analytical PEF according to the Rydberg-Klein-Reesmethod. Comparison shows that most of them are in good agreementwith the experimental findings.
(2) It has been found that the equilibrium internuclear separation R_eobtained by geometry optimization is different from the one obtainedby SPES calculations. The reason is that the unique GSUM methodused in the SPES calculations is incompletely identical with the oneused in the geometry optimization. It is the reason that the R_e resultobtained by SPES calculations is quite integrated into the PEF, and allthe spectroscopic data including R_e can be derived from the PEF, thusthe result obtained by SPES calculations should be more reasonable.
The reasonable dissociation limits for the ground states of fivediatomics (Li_2, H_2, LiH, BH, AlH) and three triatomics (Li_2H, BH_2,AlH_2) have been determined employing the principles of ARMS. Theground-state equilibrium geometries of five diatomics are optimizedand their harmonic frequencies and dissociation energies are calculatedby the density-functional theory, coupled-cluster theory and quadraticconfiguration-interaction method including single and doublesubstitutions (QCISD). By comparison with the experiments, the mostsuitable methods and basis sets for further calculations are selected.Employing the selected methods and basis sets, the SPES calculationsare performed over a wide internuclear separation range. Theanalytical PEFs are obtained by the least-squares fitting using theSPES results, and then the spectroscopic parameters (ω_ex_e, B_e andα_e)are computed, which are in good agreement with the measurementswherever available.
The geometry optimization is carried out using B3P86/D95V(d,p)method for the Li_2H ground state, QCISD/6-311++G(3df,3pd) method for the BH_2 ground state and QCISD/D95(3df,3pd) method for theAlH_2 ground state. The calculated results agree well with experimentalfindings. The conclusions are gained that their ground states are X~2A_1.The analytical PEFs of Li_2H(C_(2v), X~2A_1), BH_2(C_(2v), X~2A_1) and AlH_2(C_(2v),X~2A_1)have been derived from the many-body expansion theory. Theanalytical PEFs describe correctly their configurations and dissociationenergies.
Electron scattering from molecules is an important physical process.The total cross sections (TCSs) for electron-molecule scattering haveimportant applications in space, plasmas, laser, atmospheric scienceand chemistry physics. However, electron-molecule scattering presentsa more complex problem than corresponding electron-atom scatteringdue to the multi-center nature, the lack of a center of symmetry and itsnuclear motion. In addition, over the intermediate- and high-energyrange, almost all inelastic channels (rotational, vibrational, andelectronic excitation and ionization processes, etc) are opened, whichmakes the conventional theoretical calculations for electron-moleculescattering becomes almost impossible to carry out.
The electron-molecule scattering problem is reduced to the electron-atom scattering one by the additivity rule (AR) model which is easierto handle. The AR model assumes that an atom in a molecule is a freeone, thus the interactions between them can be neglected. In fact,bonded atoms in a molecule are not identical with the ones in free statedue to the overlapping effect of electron clouds. The overlapping effectmakes electron clouds of a bonded atom distorted and thus itsspherical symmetry destroyed. Having taking into consideration theoverlapping effect of electron clouds between two bonded atoms in amolecule, a modified complex optical potential is presented. The TCSsof electron scattering by HCl, NH_3, H_2O, CH_4, N_2, O_2 and CO_2 arecalculated using the modified potential and the AR model at Hartree-Fock level at 30 to 5000 eV and compared with those obtained byexperiments and other theories, and good agreement is obtained over a wide energy range. Careful examinations show that the present resultsare still larger than the measurements at low-energy range but smallerthan those at high-energy range. It suggests that further modificationsof complex optical potential must be related with the energy ofincident electrons.
A close-packed polyatomic molecule is not fully transparent forlow-energy electrons, and the "inner" atoms are partially shielded bythe "outer" atoms and do fewer contributions to the molecular TCS atlower energies than those at higher energies. Taking into considerationthe changes of the geometric shielding effect in a molecule as theincident electron energy varies, an empirical fraction, which exhibitsthe TCS contributions of shielded atoms in a molecule at differentenergies, is presented. In order to clarify that the problem, of whichTCS for electron-molecule scattering varies much fast as energy ofincident electrons, is caused by TCS calculation accuracy of electron-atom scattering or by AR model in itself, we use the experimental TCSresults of electron scattering by C, H, O and N to calculate the TCS ofelectron scattering from NO, N_2O, NO_2, CO_2, H_2O, CH_4, C_2H_2, C_2H_4and C_2H_6 by the modified AR model at 50-5000 eV. By comparisonwith experimental findings, we have found that the TCSs calculated bythe modified AR model are in excellent agreement with almost all theexperiments over the whole overlapping energy range. Whereas theTCSs obtained by the original AR model gradually become in goodaccord with the measurements only when energy is above 200-300 eVor more for more complex molecules, and the problem, of which TCSfor electron-molecule scattering varies much fast as energy of incidentelectrons, still exists. Thus the conclusion can be gained that theproblem is caused by AR model itself. The conclusion is very usefulwhere the complex optical potential needs further modifications.
本文利用Gaussian03程序包提供的SAC／SAC-CI程序计算了~7Li_2分子8个激发态(A~1∑_u~+，G~1∏_g，2~1∏_u，a~3∑_u~+，b~3∏_u，c~3∑_g~+，2~3∑_g~+和2~3∏_u态)的绝热激发能，并根据原子分子反应静力学的有关原理导出了这8个激发态的合理离解极限。于多个基组下使用SAC方法对基态(X~1∑_g~+态)、SAC-CI方法对这8个激发态进行了单点能扫描计算，并进行了解析势能函数的拟合。在拟合出的M-S函数的基础上对这8个激发态进行了主要光谱常数(D_e，R_e，ω_e，ω_eX_e，B_e，a_e)及某些分子常数(振动能级、振动经典转折点、惯性转动常数以及离心畸变常数等)的计算，且将理论计算结果与光谱实验数据及其他理论计算结果进行了比较。结果表明，它们中的绝大多数都达到或超过了目前文献所报导的计算精度，其中有相当一部分分子常数属首次报导。另外：
(1)由于SAC／SAC-CI程序不能直接进行准确谐振频率的计算，本文采用在单点能扫描的基础上通过拟合出M-S势能函数、并利用力常数与谐振频率的关系，计算出了每个态的谐振频率。对绝大多数态而言，本文的计算结果与已有的实验结果或其他理论结果都能很好地相符；
(2)本文发现，在SAC／SAC-CI程序中由几何优化和单点能扫描获得的平衡核间距不一致。论文对这种不一致的原因进行了解释。由于分子势能函数是在Born-Oppenheimer近似下对分子性质的完全描述，因此本文认为单点能扫描给出的平衡核间距应更合理。
使用原子分子反应静力学的有关原理，分析了Li_2，H_2，LiH，BH和AlH等几个双原子分子以及Li_2H，BH_2和AlH_2等几个三原子基态的合理离解极限。运用密度泛函理论、耦合簇理论和二次组态相关方法方法，优化了Li_2，H_2，LiH，BH及AlH等几个双原子分子基态的平衡几何、计算了它们基态的谐振频率和离解能，并利用优选出的“基组／方法”进行了单点能扫描、拟合出了相应的解析势能函数。从这些解析势能函数出发，得到了与实验结果能较好符合的光谱常数(ω_eX_e，B_e，a_e、)。采用B3P86／D95V(d，p)方法对Li_2H分子、QCISD／6-311++G(3df，3pd)方法对BH_2分子和QCISD／D95(3df，3pd)方法对AlH_2分子进行几何优化，得到了这3个分子的基态都为G_(2v)结构、电子态都为X~2 A_1的结论。利用多体项展式理论，确定了这3个分子的解析势能函数，分别绘制出了它们不同形式的等值势能图。解析势能函数和相应的等值势能图正确地反映了它们的结构特点和能量信息。使用其等值势能面讨论了Li(~2S_g)+LiH(X~1∑~+)，H(~2S_g)+BH(X~1∑~+)和Al(~2S_g)+AlH(X~1∑~+)等反应的势能面静态特征。对静态势能面的分析表明，在这些反应途径中，都存在着两个对称的鞍点，且反应都为有阈能反应，活化能分别为78.2408 kJ／mol，150.204 kJ／mol和54.8064 kJ／mol。
“电子-分子”散射是一种重要的物理过程，对其规律进行探索对很多实际应用都有重要意义，特别是作为主要理论计算结果的散射总截面是许多理论和应用研究所需的重要数据。然而与“电子-原子”散射相比，“电子-分子”散射是一个更为复杂的问题，这是因为在中、高能区，分子内的许多非弹性通道，如电离、激发、转动和振动等都被打开，这些使得准确的理论计算变得异常困难。
可加性规则(AR)方法将“电子-分子”散射问题简化成“电子-原子”散射问题，从而使计算简单易行。但可加性规则认为分子中的原子是自由的，原子间的相互作用可以忽略。但实际上，分子中的成键原子与自由原子是不同的，成键原子的电子云之间有重叠，重叠的结果造成了束缚原子的电子云扭曲变形，因而其对称性遭到了破坏。考虑分子中成键原子的电子云重叠效应，对适用于“电子-自由原子”的复球光学势进行了修正。利用修正后的复光学势计算了电子被HCl，NH_3，H_2O，CH_4，N_2，O_2和CO_2分子散射的总截面，并与其他理论计算结果及实验结果进行了比较。结果表明，利用AR方法和修正后的复光学势计算得到的总截面在一个很大的能量范围内都能与实验结果很好的相符，但还存在着总截面值在低能区高于实验值、在高能区却低于实验值的问题。它揭示：对复光学势的进一步修正必须与电子的入射能量以及靶分子的几何特性相关联。
多原子分子对低能电子不是完全透明的。当电子的入射能量较低时，分子中的外层原子对内层原子有部分屏蔽作用。论文从AR方法本身的修正入手，还提出了一种与电子入射能量以及靶分子的尺寸、含有的电子总数、原子总数等相关联的修正方法，来解决“电子-分子”散射总截面随电子入射能量变化太快的问题。为弄清“电子-分子”散射总截面随电子入射能量变化太快究竟是由“电子-原子”散射总截面的理论计算、还是AR方法本身引起的，本文避开“电子-原子”散射总截面的理论计算，直接采用“电子-原子”散射总截面的实验数据作为初始数据，在50-5000 eV内对电子被NO，N_2O，NO_2，CO_2，H_2O，CH_4，C_2H_2，C_2H_4和C_2H_6分子散射的总截面进行了计算。将计算结果与实验结果相比较后发现，几乎在整个能区内利用这一修正后的AR方法计算得到的“电子-分子”散射总截面都与实验结果相符极好。这说明“电子-分子”散射总截面随入射电子能量变化太快是由AR方法本身引起的。这一结论将为“电子-分子”散射理论计算时所使用的复光学势的进一步修正，指出了一个明确的方向。
Molecular potential energy function (PEF) is one of the importantfields in atomic and molecular physics. It gives one absolutedescription of molecular properties with Born-Oppenheimerapproximation. Namely, it can completely determine molecular energy,equilibrium geometry, force constants and spectroscopic parameters.At the same time, it is also the PEF of the core movement, which is thefoundation to investigate atomic and molecular collision and reactionand is of special importance in the atom-cluster growth, dissociationand stability analyses.
The adiabatic excitation energies from the ground to eight excitedstates, A~1∑_u~+, G~1∏_g, 2~1∏_u, a~3∑_u~+, b~3∏_u, c~3∑_g~+, 2~3∑_g~+ and 2~3∏_u, for dimer~7Li_2 have been calculated using the SAC/SAC-CI method presented inGaussian03 program package. The reasonable dissociation limits ofthese excited states have been deduced according to the principles ofAtomic and Molecular Reaction Statics (AMRS) using the adiabaticexcitation energies obtained in this paper. The single-point energyscanning (SPES) calculations over a wide internuclear separationrange are performed using SAC method for the ground state andSAC-CI method for the eight excited states of dimer ~7Li_2 at a numberof basis sets. All the ab initio calculations are fitted into analyticalPEFs by the least-squares method. Then, these analytical PEFs areemployed to calculate the spectroscopic parameters (D_e, R_e,ω_e,ω_ex_e,B_e andα_e) and some molecular constants (vibrational levels, classicalturning points, inertial rotation and centrifugal distortion constants).The calculated results are encouraging when compared with the measurements and other theories. Some of the calculated results arereported for the first time. In addition,
(1) The present SAC/SAC-CI method cannot accurately performthe harmonic frequency calculations. The frequency is computed usingthe corresponding analytical PEF according to the Rydberg-Klein-Reesmethod. Comparison shows that most of them are in good agreementwith the experimental findings.
(2) It has been found that the equilibrium internuclear separation R_eobtained by geometry optimization is different from the one obtainedby SPES calculations. The reason is that the unique GSUM methodused in the SPES calculations is incompletely identical with the oneused in the geometry optimization. It is the reason that the R_e resultobtained by SPES calculations is quite integrated into the PEF, and allthe spectroscopic data including R_e can be derived from the PEF, thusthe result obtained by SPES calculations should be more reasonable.
The reasonable dissociation limits for the ground states of fivediatomics (Li_2, H_2, LiH, BH, AlH) and three triatomics (Li_2H, BH_2,AlH_2) have been determined employing the principles of ARMS. Theground-state equilibrium geometries of five diatomics are optimizedand their harmonic frequencies and dissociation energies are calculatedby the density-functional theory, coupled-cluster theory and quadraticconfiguration-interaction method including single and doublesubstitutions (QCISD). By comparison with the experiments, the mostsuitable methods and basis sets for further calculations are selected.Employing the selected methods and basis sets, the SPES calculationsare performed over a wide internuclear separation range. Theanalytical PEFs are obtained by the least-squares fitting using theSPES results, and then the spectroscopic parameters (ω_ex_e, B_e andα_e)are computed, which are in good agreement with the measurementswherever available.
The geometry optimization is carried out using B3P86/D95V(d,p)method for the Li_2H ground state, QCISD/6-311++G(3df,3pd) method for the BH_2 ground state and QCISD/D95(3df,3pd) method for theAlH_2 ground state. The calculated results agree well with experimentalfindings. The conclusions are gained that their ground states are X~2A_1.The analytical PEFs of Li_2H(C_(2v), X~2A_1), BH_2(C_(2v), X~2A_1) and AlH_2(C_(2v),X~2A_1)have been derived from the many-body expansion theory. Theanalytical PEFs describe correctly their configurations and dissociationenergies.
Electron scattering from molecules is an important physical process.The total cross sections (TCSs) for electron-molecule scattering haveimportant applications in space, plasmas, laser, atmospheric scienceand chemistry physics. However, electron-molecule scattering presentsa more complex problem than corresponding electron-atom scatteringdue to the multi-center nature, the lack of a center of symmetry and itsnuclear motion. In addition, over the intermediate- and high-energyrange, almost all inelastic channels (rotational, vibrational, andelectronic excitation and ionization processes, etc) are opened, whichmakes the conventional theoretical calculations for electron-moleculescattering becomes almost impossible to carry out.
The electron-molecule scattering problem is reduced to the electron-atom scattering one by the additivity rule (AR) model which is easierto handle. The AR model assumes that an atom in a molecule is a freeone, thus the interactions between them can be neglected. In fact,bonded atoms in a molecule are not identical with the ones in free statedue to the overlapping effect of electron clouds. The overlapping effectmakes electron clouds of a bonded atom distorted and thus itsspherical symmetry destroyed. Having taking into consideration theoverlapping effect of electron clouds between two bonded atoms in amolecule, a modified complex optical potential is presented. The TCSsof electron scattering by HCl, NH_3, H_2O, CH_4, N_2, O_2 and CO_2 arecalculated using the modified potential and the AR model at Hartree-Fock level at 30 to 5000 eV and compared with those obtained byexperiments and other theories, and good agreement is obtained over a wide energy range. Careful examinations show that the present resultsare still larger than the measurements at low-energy range but smallerthan those at high-energy range. It suggests that further modificationsof complex optical potential must be related with the energy ofincident electrons.
A close-packed polyatomic molecule is not fully transparent forlow-energy electrons, and the "inner" atoms are partially shielded bythe "outer" atoms and do fewer contributions to the molecular TCS atlower energies than those at higher energies. Taking into considerationthe changes of the geometric shielding effect in a molecule as theincident electron energy varies, an empirical fraction, which exhibitsthe TCS contributions of shielded atoms in a molecule at differentenergies, is presented. In order to clarify that the problem, of whichTCS for electron-molecule scattering varies much fast as energy ofincident electrons, is caused by TCS calculation accuracy of electron-atom scattering or by AR model in itself, we use the experimental TCSresults of electron scattering by C, H, O and N to calculate the TCS ofelectron scattering from NO, N_2O, NO_2, CO_2, H_2O, CH_4, C_2H_2, C_2H_4and C_2H_6 by the modified AR model at 50-5000 eV. By comparisonwith experimental findings, we have found that the TCSs calculated bythe modified AR model are in excellent agreement with almost all theexperiments over the whole overlapping energy range. Whereas theTCSs obtained by the original AR model gradually become in goodaccord with the measurements only when energy is above 200-300 eVor more for more complex molecules, and the problem, of which TCSfor electron-molecule scattering varies much fast as energy of incidentelectrons, still exists. Thus the conclusion can be gained that theproblem is caused by AR model itself. The conclusion is very usefulwhere the complex optical potential needs further modifications.
引文
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