谐振子基在复标度方法中的应用

在利用薛定谔方程求解共振态能量的过程中,成功的将谐振子基应用于复标度方法,求解出共振态的能量公式,并以一个比较成熟的势作为检验势,得出比较精确的结果,也作出共振态能量在复能量坐标系中的能量分布.对其中的两个参数基数N和转动角θ进行讨论与分析,验证了共振态的一个原理:在对共振态的计算过程中,计算参数的改变不会影响共振态的位置.     

基于Schrdinger方程的耦合常数解析延拓方法

基于Schr¨odinger方程 ,利用耦合常数解析延拓方法研究了球对称的方势阱、Woods Saxon势和谐振子势中的单粒子共振态的能量与宽度 .分析了耦合常数的取值区间和Pad啨多项式阶数对计算结果的影响 .结果发现 ,在适当的耦合常数取值范围内 ,随着Pad啨多项式阶数的增加可以得到稳定和收敛的单粒子共振态能量与宽度 .     

基于Schrdinger方程的耦合常数解析延拓方法

基于Schrdinger方程,利用耦合常数解析延拓方法研究了球对称的方势阱、Woods-Saxon势和谐振子势中的单粒子共振态的能量与宽度.分析了耦合常数的取值区间和Pade多项式阶数对计算结果的影响.结果发现,在适当的耦合常数取值范围内,随着Pade多项式阶数的增加可以得到稳定和收剑的单粒子共振态能量与宽度.     

BeCl_2分子的低能电子弹性散射研究

基于R矩阵理论方法,通过构建BeCl_2分子的静态交换势模型(SE),静态交换加极化势模型(SEP)和密耦合模型(CC),在0-10 eV能量范围内首次研究了低能电子与BeCl_2分子的散射动力学过程,预测了弹性散射积分截面,并在三种模型中分别发现一个来自B_(2u)和B_(3u)对称性贡献的势形共振态.讨论了这些共振态随着极化效应的变化,获得了收敛的截面和共振态结果.进一步使用POLYDCS程序首次计算了电子与BeCl_2分子的散射微分截面(DCS)以及动量转移截面(MTCS).当前研究结果将为天体物理和等离子体物理提供重要的截面数据.     

复标度方法对原子核单粒子共振态的研究

在相对论平均场理论框架下, 利用复标度方法研究了 Zr 同位素的单粒子共振问题. 以 ¹²²Zr 为例, 演示了复标度方法确定共振态的具体步骤, 确定了 ¹²²Zr 所有可能共振态的能量和宽度, 以及相应共振态的复标度波函数, 并与耦合常数的解析延拓方法进行了比较.在此基础上, 进一步系统研究了 Zr 同位素的共振问题, 获得了与散射相移方法一致的结果.     

BeCl_2分子的低能电子弹性散射研究

基于R矩阵理论方法,通过构建BeCl_2分子的静态交换势模型(SE),静态交换加极化势模型(SEP)和密耦合模型(CC),在0-10 eV能量范围内首次研究了低能电子与BeCl_2分子的散射动力学过程,预测了弹性散射积分截面,并在三种模型中分别发现一个来自B_(2u)和B_(3u)对称性贡献的势形共振态.讨论了这些共振态随着极化效应的变化,获得了收敛的截面和共振态结果 .进一步使用POLYDCS程序首次计算了电子与BeCl_2分子的散射微分截面(DCS)以及动量转移截面(MTCS).当前研究结果将为天体物理和等离子体物理提供重要的截面数据.     

复动量格林函数方法对n-α散射研究

在复动量表象下引入格林函数,建立了复动量格林函数方法.把这种方法应用于n-α散射系统,计算其散射相移.提取n-α系统的共振态并研究共振态对能级密度、相移和散射截面的贡献.在不引入任何非物理参数的前提下,离散化薛定谔积分方程得到束缚态、共振态和连续谱.通过分析散射态物理量可以更好地理解共振态以及非共振连续谱态.在n-α系统中的成功应用,证明了该方法的正确性.     

30-5000eV的电子被若干分子散射的总截面计算的一种修正势方法

利用可加性规则，使用Hartree-Fock波函数，采用由束缚原子概念修正过的复光学势，在30~5000eV这一较大的能域内对电子被N2、NO、NO2、CH4、CF4、CF3H、C2H2及C2H4散射的总截面进行了计算。束缚原子不同于自由原子之处，是束缚原子概念考虑了不同分子中的不同的电子云重叠情况，并根据电子云的重叠情况对复光学势进行修正。文中，将定量的计算结果与实验结果及其它理论计算结果进行了比较，结果显示出在30~5000eV内，计算结果与实验结果及其它理论计算结果间有较好的一致性。同时结果也表明，在较低的能量下，尤其是当入射电子的能量低于500eV时，利用被束缚原子概念修正过的复光学势进行计算得到的结果，要比利用未被束缚原子概念修正的复光学势计算得到的结果更接近于实验值。因此，在复光学势中考虑电子云的重叠效应可改善电子被分子散射的总截面的计算精度。     

中高能电子被O2及CF4分子散射的微分截面、弹性积分截面及动量转移截面

利用可加性规则，使用Roothaan-Hartree-Fock波函数，采用由束缚原子概念修正过的复光 学势，在300—1000eV内若干个能量点处计算了电子被O₂及CF₄分子 散射的微分截面、 弹性积分截面及动量转移截面，并将计算结果与实验结果及其他理论计算结果进行了比较. 比较的结果表明，利用被束缚原子概念修正过的复光学势及可加性规则进行计算，所得微分 散射截面的精度要比利用未修正的复光学势及可加性规则进行计算得到的结果准确得多；同 时，计算得到的弹性积分截面及动量转移截面也比较接近实验值.因此，在复光学势中采用 束缚原子概念可提高电子被分子散射的微分截面、弹性积分截面及动量转移截面的计算准确 度. 关键词： 电子散射 可加性规则 微分截面 弹性积分截面     

NN巴黎势和可能的pp共振态

通过求解NN巴黎光学势的复薛定谔方程,研究了NN系统的近阈束缚和共振行为,得到了一个pp系统的13P0共振态.发现其能量和宽度与最近BES用Breit-Wigner(B-W公式分析J/ψ→γpp衰变的实验数据给出的结果相容.讨论了这一结果的含义及进一步研究的建议     

Study of anomalous subbarrier fission of Np-237 using an SVZ-100 lead slowing-down neutron spectrometer

In addition to the well studied complex resonance of subbarrier fission of Np-237 at the neutron energy of 39 eV, intense anomalous fission resonances are detected at the SVZ-100 spectrometer. The energy of the first resonance is lower than 0.3 eV. The second resonance creates an energy dependence of the cross section according to the law 1/v, extrapolation of which to the thermal energy yielded the value of 17 barn. The third resonance at short times of neutron slowing down is characterized by a cross section no lower than 1.4 barn. The fission cross sections in these anomalous resonances exceed available data by two orders of magnitude and larger.     

Eigenvectors of the multichannel scattering matrix at resonance energy values

Explicit representations for the T matrix and the scattering matrix analytically continued to unphysical energy sheets in a multichannel problem featuring binary channels are discussed. From these representations, it follows that a resonance on a given unphysical sheet arises at the (complex) energy value for which the appropriately truncated scattering matrix considered on the physical sheet has zero eigenvalue. It is shown that the channel components of that eigenvector of the truncated scattering matrix which corresponds to zero eigenvalue at a resonance energy value have the meaning of breakup amplitudes for the respective resonance state of the multichannel system being considered.     

Density functional resonance theory of unbound electronic systems

Density functional resonance theory (DFRT) is a complex-scaled version of ground-state density functional theory (DFT) that allows one to calculate the in-principle exact resonance energies and lifetimes of metastable anions. In this formalism, the energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation, just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N-electron interacting system to a Kohn-Sham system of N noninteracting particles. This mapping facilitates self-consistent calculations with an initial guess for the complex density, as illustrated with an exactly solvable model system.     

Standard deviations of chemical reaction rates and validity ranges of the statistical theory

Validity ranges of the statistical theory of chemical reactions are discussed. On the basis of the quantum mechanical scattering theory, the rate of the chemical reaction of the complex-formation mode is formulated. The interaction matrix elements between resonance states and scattering continua are regarded as stochastic variables. The expectation value of the reaction rate is shown to coincide with the prediction of the conventional statistical theory if the condition of overlapping resonance is fulfilled. The standard deviation is found to be inversely proportional to the number of resonance states involved in the width of the collision energy. High density of vibrational energy levels of the collision complex serves to suppress the standard deviation and to make the statistical theory accurate. The condition for the conventional statistical theory to hit the correct value with probabilities more than 99% is obtained as a relation between the number of vibrational modes and the depth of the potential energy well of the collision complex.     

Complex ray tracing study of electron cyclotron resonance heating

In the up-to-date ray tracing study of electron cyclotron resonance heating (ECRH) of fusion plasmas, energy absorption effect has never been considered into the wave trajectory computation. Thus all the work has been done in real space so far. In this paper we consider coupling of energy absorption to wave trajectory for the first time, and numerically solve the formal complex Hamilton equations in complex space, then take the real-space-projected wave trajectories and group velocities to be the corresponding concrete ones. It is shown that both ordinary wave and extraordinary wave injected from the inner side of the tokamak plasmas approach the electron cyclotron resonance surface step by step and their group velocities become exceedingly small as they move toward this surface. Those clearly show that the resonance between the electron cyclotron waves and the fusion plasmas takes place in the electron cyclotron resonance region, which is just the case the ECRH experimental results and the plasma kinetic theory of waves demonstrate.     

Calculation of electromagnetic fields in cavity resonators with allowance for energy flux through slots

By the example of a cylindrical cavity with an annular slot, resonance conditions in cavity resonators with slots in the perfectly conducting walls are theoretically studied. The stationary electromagnetic fields of eigenmodes are described in terms of the partial domain method with the use of the homogeneous Maxwell equations. The complex wavenumber and other parameters of these fields are determined from the condition that the fields are continuous on the slot boundaries. An energy resonance condition is formulated that requires that the energy flux of the resonance field through the slot be minimal. It is shown that these conditions, taken together, remove infeasible (nonphysical) solutions to the homogeneous problem, which are associated with out-of-cavity excitation sources.     

对苯醌络合物对费米共振的影响

费米共振现象不仅存在于简单化合物中,复杂的络合物振动光谱中同样存在。简单化合物“加和”形成络合物,分子间某些基团的特性也随之改变,分子光谱就会产生明显的变化。在一定条件下,对苯醌与脯氨酸能够形成电子转移络合物,但其拉曼光谱强度比较小,采用Teflon液芯光纤可以获得高质量的共振拉曼光谱。实验分别获得了对苯醌和其络合物的拉曼光谱图,利用J.F.Bertran量子力学微扰理论,对分子的费米共振特性进行分析。结果表明,络合物的形成使得CO键的费米共振峰向高波数方向移动,拉曼光谱强度比减小,频率间隔增大,耦合系数增大。这种变化的原因解释为,混合溶液中,脯氨酸作为给体,苯醌作为受体,脯氨酸中的N原子上的非成键电子转移到对苯醌的π反键轨道上形成了n—π*电子转移络合物,使分子的振动能级发生了变化。这些分析为研究大分子、络合物以及聚合物的谱线认证、归属提供了新的思路和线索。     

A complex T-matrix derivation of a resonance amplitude

A resonant transition amplitude, valid to arbitrary order, is derived through the use of a complex energy T-matrix. A feature of this amplitude is its generality and simplicity making it useful for widespread applications in resonance theory.     

Power-mode theorems for guided acoustic waves in piezoelectric media

Relationships between complex power flow pseudo energy, propagation constant and complex frequency are presented for acoustic waves in piezoelectric media. These relationships are essentially energy-power equations which apply to anisotropic, nonconservative, dispersive, linear systems, analogous to those obtained by Chorney and Penfield for guided electromagnetic waves. At vanishing piezoelectric coupling the powermode theorems split into a proper electromagnetic set and a proper mechanical set. By differentiating the power-mode equations with respect to the complex frequency further results are obtained linking the group velocity with power flow and energy storage. Conclusions may be drawn from these expressions regarding the signature of the dispersion (forward or backward waves). The equipartition of pseudo energy is established at cut-off, and the vanishing of the complex power flow at resonance. Examples including wave propagation in lossless and lossy media are included.