电子碰撞下氢原子单离化反应三重微分散射截面的计算

在共面非对称几何条件下，利用能壳上跃迁矩阵元的后滞形式和双势公式，对快电子碰撞下氢原子的单离化，提出了一个新的计算方法.通过分解动能算符，并且略去两电子的质心运动和相对运动的指数因子，对快电子采用平面波的近似形式，得到了库仑三体问题的近似解.散射振幅可以表示成两个因子乘积的形式，即结构散射因子T₂和关联因子T12.采用渐近级数展开和最佳截断的方法讨论了T₂和T₁₂对三重微分散射 截面的影响. 关键词： （e;2e）反应 三重微分截面 二体峰值 反冲峰值     

低能氢原子(e, 2e)反应中的电子关联

利用能壳上跃迁矩阵元的后滞形式和双势公式,计算了入射能为54.4 eV时,电子入射单离化氢原子的三重微分截面(TDCS),并与实验数据、BBK理论和DS3C理论结果进行了比较.通过分解动能算符,对快电子采用平面波的近似,散射振幅可以表示成结构因子(T2)和关联因子(T12)乘积的形式,在略去前者中电子质心运动的基础上,通过对后者中求和级数的讨论,指出了T12中电子的质心运动和相对运动对TDCS的影响,从而分析了T12的收敛问题.     

末态电子的关联在氢原子(e,2e)反应中的影响(英文)

在共面非对称几何条件下,利用双势公式解析计算了电子碰撞电离氢原子的三重微分截面.对快电子采用平面波近似,跃迁矩阵元可以表示成两个因子乘积的形式,即结构散射因子和出射道两电子的关联因子.在计算过程中对关联因子采取了最简单的近似,当入射能量为150 eV和54.4 eV时,计算结果与实验结果的符合说明对于这些入射能量该关联近似是有效的;而对于入射能量为27.2 eV时,计算结果与实验结果的较大差异说明这种关联近似是无效的.     

利用正交投影解析求解氢原子的(e,2e)反应

利用能壳上跃迁矩阵元的后滞形式和双势公式,对快电子碰撞氢原子的单离化反应,提出了一个新的计算方法.跃迁矩阵元被表示为两项,当入射电子和散射电子近似为平面波时,跃迁矩阵元的第一项是一个发散的复数;而第二项计算的角分布就已有双峰结构了.那么通过碰出电子的库仑波函数在氢原子束缚态上的正交投影,使得前者对三重微分截面的贡献为零.计算发现正交投影过程增大了binary峰,降低了recoil峰.另外,当量子数n增大时,正交投影过程对三重微分截面的影响是减弱的.理论曲线与实验数据进行了比较.     

氢原子(e,2e)反应离化振幅的分析

利用双势公式的后滞形式并且在入射的快电子近似的取为平面波的基础上,在共面非对称几何条件下计算了电子离化氢原子的三重微分散射截面.变换矩阵元可以解析的表示为结构散射因子和关联因子的乘积形式(关联因子和结构散射因子分别对应于recoil peak和binary peak)解决了由于大量的数值计算而带来的麻烦.本文引入一个有效电荷,通过对它进行调整考虑了变换矩阵元中的第一项的影响.最后把计算结果与实验结果及他人的结果进行了比较,与实验结果符合的很好.     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

Cabbibo Suppressed Semileptonic Decay D0→π－e+ve

The transition rate for the Cabibbo suppressed decay d0→π–e+ν e is calculated. This allows the extractions of the form factor |fπ +(0)| and the CKM matrix element |v cd| using the measured branching ratio.     

Nuclear β-decay. II

A general expression for the beta-decay transition amplitude is evaluated, using the decomposition of the nuclear current matrix element into beta-decay form factors as obtained in the previous paper. For the electron radial wave functions the finite nuclear size is taken into account. Formulas for the spectrum shape factor and the polarisation are calculated.     

Importance of the ion core to the pressure dependence of superconductivity in Ba

The enhancement of the pressure dependence of the electron-phonon matrix element due to ion core orthogonality constraints is shown to be an important factor in understanding the observed increase in the superconducting transition temperature with pressure in Ba. We find no evidence for Wittig's recent suggestion of the crucial role played by 4f hybridization.     

The reduced α-amplitude in an exactly solvable model

In recent work by Fliessbach the removal of an α-particle from a nucleus under the influence of a perturbation was considered. Using certain approximations the many-body transition matrix element was reduced to a one-body matrix element. This one-body matrix element showed that the appropriate bound α-amplitude in the initial nucleus (reduced amplitude) depends on the energy transferred to the removed α-particle. The present paper deals with an analytic model in which the one-body transition matrix element as given in that work can be derived exactly from the original microscopic matrix element.     

The calculation of reactions of the type (a,ab) using the plane-wave expansion method: (I). General formalism for the direct one-step process

A formalism for the evaluation of the transition matrix element for reactions of the type (a, ab) in the direct distorted-wave approximation is presented. The plane-wave expansion method is used to represent the optical model wave function for the entrance and exit channels. Because of the use of the plane-wave expansion method the completely off-the-energy-shell behavior is easily demonstrated when distorted waves are used. The use of this expansion method also shows how difficult it is to extract the momentum dependence of the bound particle. We also apply the plane-wave expansion method to evaluate the transition matrix element for the effective f-operator DWTA approach. We also discuss an approximation to the complete transition matrix element which seems equivalent to the DWTA but yet makes use of completely off-the-energy-shell matrix elements.     

关于三维各向同性谐振子径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元. 关键词： 三维各向同性谐振子 径向矩阵元 广义Laguerre多项式 偶极跃迁 四极跃迁     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

二维各向同性谐振子的径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的二维各向同性谐振子径向矩阵元的普遍公式，并在这基础上计算了一些重要特殊情形的径向矩阵元：矢径ρ整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元。     

Theoretical infrared transition matrix elements for the water molecule

Using the Hartree-Fock-Roothaan method, symmetric potential energy and dipole moment functions have been obtained for the ground state of the water molecule. These functions were transformed and analyzed in terms of the normal symmetric stretching (v₁) and bending (v₂) coordinates for the calculation of i.r. transition matrix elements. There is satisfactory agreement between this work and the experimental values for the transition matrix element of the v₂ fundamental. However, a discrepancy of a factor of 2.5 is observed between calculated and experimental matrix elements for the v₁ fundamental.     

Effective three-body interactions in the α-cluster model for the <Superscript>12</Superscript>C nucleus

Properties of the lowest 0⁺ states of ¹²C are calculated to study the role of three-body interactions in the α-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the α-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited 0₂⁺ state and the monopole 0₂⁺↦0₁⁺ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the 0₂⁺ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.     

Theoretical interpretation of spin-polarized X-ray absorption spectra of Mn in MnP

On the basis of the multiple scattering approach in combination with the spin-polarized self-consistent potential calculation, an interpretation is proposed for the spin-polarized x-ray absorption spectra near the Mn K edge in MnP. The effect of the core vacancy potential on the spectra is analyzed and found to be insignificant. The method used for the calculations allowed the separation of the effect of the dipole transition matrix element on the spectra and the effect of the density of unoccupied electron states. It is shown that the transition matrix element causes an intensity redistribution only near the absorption jump, while the difference in the densities of states is most pronounced in the energy region 35–55 eV away from the main edge and leads to a shift in energy for the spectra corresponding to the two spin directions. The effect of the spin-dependent broadening caused by the dependence of the mean free path (as a function of energy) on the photoelectron spin is studied. It is shown that this factor considerably affects only the intensities of the peaks in the energy region lying within less than 12 eV from the main edge.     

Model for UV induced formation of gold nanoparticles in solid polymeric matrices

UV irradiation of polymeric PMMA films containing HAuCl₄ followed by annealing at 60-80 °C forms gold nanoparticles directly within the bulk material. The kinetics of nanoparticle formation was traced by extinction spectra of nanocomposite film changes vs annealing time. We propose that UV irradiation causes HAuCl₄ dissociation and thus provides a polymeric matrix with atomic gold. The presence of an oversaturated solid solution of atomic gold in the polymeric matrix leads to Au nanoparticle formation during annealing. This process can be understood as a phase transition of the first order. In this paper we apply several common kinetic models of the phase transition for describing Au nanoparticle formation inside the solid polymer matrix. We compare predictions of these models with the experimental data and show that these models cannot describe the process. We propose that the stabilization effect of the matrix on the growing gold nanoparticles is important. The simplest model introducing some probability for the transition from growing nanoparticle to the non-growing, stabilized form is suggested. It is shown that this model satisfactorily describes the experimentally observed evolution of the extinction spectrum of Au nanoparticles forming in a polymer matrix.     

电子碰撞类氢离子电离非相对论跃迁矩阵元

利用BBK模型,导出了电子-类氢离子碰撞电离跃迁矩阵元的解析形式。出射道用包含三个适当的合流超几何函数,且满足适当的三体库仑边界条件的关联BBK波函数来描述,入射道考虑了入射电子与靶离子的长程库仑相互作用而包括一库仑波。含有四个合流超几何函数在内的跃迁T-矩阵元的六维空间积分已约化为一包含高斯-超几何函数的三维实参数积分。忽略入射电子与靶离子的库仑相互作用时,表示用平面波描述的入射电子与靶离子的碰撞,再取靶离子电荷数Z=1时,表示氢原子的电离;略去排斥因子(α₁₂=0)时,又表示不考虑关联的电离。从而可分析各种情况的电离性质。在目前离子的(e,2e)反应三微分截面实验数据还不具备的情况下,可先提供一些必要的理论结果。进而可广泛地应用于处理散射问题之中。     

Studying hadronic structure of the photon in lattice QCD

We show that the matrix element of a local quark-gluon operator in the photon state, , can be calculated in lattice QCD. The result is generalized to other quantities involving spacelike photons, including the transition form factor gammagamma*-->pi(0) and the virtual-photon-nucleon Compton amplitude which can be used to define the generalized Drell-Hearn-Gerasimov and Bjorken sum rules.