Analysis of microwave propagation effects using two-dimensional electrooptic field mapping techniques

In high-speed electronic devices and monolithic microwave and millimetrewave integrated circuits the propagation of electromagnetic waves plays an important role. In so-called travelling wave devices and circuits these propagation effects are applied to design and realize functions not available in lumped elements. In order to exploit fully the potential of wave propagation effects, experimental investigations have to be carried out which, however, require a measurement technique to allow spatially resolved detection of microwave potential or field distributions inside elements and circuits and along the electrical interconnects. In this paper, it is shown by several examples, that the two-dimensional electrooptic field mapping technique is an excellent tool to study wave propagation effects up to millimetrewave frequencies, with submicrometre spatial resolution and without electromagnetic interference.     

Wave functions and energies of magnetopolarons in semiconductor quantum wells

A classification of magnetopolarons generated in semiconductor quantum wells due to the Johnson-Larsen effect is proposed. The wave functions of the conventional double and combined magnetopolarons are calculated by diagonalizing the Schrödinger equation.     

采用振速测量的改进统计最优近场声全息方法

针对常规统计最优近场声全息在空间多源声场重建过程中所需波函数项数多、重建精度不理想的问题,本文提出了一种基于振速测量的改进统计最优近场声全息算法。与常规算法不同,改进算法主要根据声源特点选取合适的波函数组合来计算声场传递矩阵。通过数值仿真初步验证了该方法的准确性和有效性,并与常规算法进行了详细的对比分析。仿真结果表明,改进算法重建精度高,随频率的变化相对误差波动较小,且随着频率的增大相对误差有逐渐减小的趋势;此外,不同的波函数组合,重建效果差异很大,当选取的波函数与声源共形且数量一致时重建效果最好。     

On the accuracy of valence–shell computations for heavy and super–heavy elements

Recent atomic computations on the (super–) heavy elements have raised the expectation that their low–lying excitation and ionization energies can be calculated with an accuracy of a few hundredth of an eV and, hence, that such computations might help in the identification of new lines. For most many–electron atoms, however, the higher–order relativistic and quantum electrodynamical (QED) effects are included so far only in a rather approximate form. Using different model computations for the neutral and weakly ionized ytterbium (Z = 70) and nobelium atoms (Z = 102), it is shown here that QED effects alone may lead to an uncertainty of 20–50 meV for the excitation energies of all super–heavy elements, and that even for highly–correlated wave functions the theoretical predictions are presently not more accurate than about 0.1 eV. Moreover, in order to support forthcoming spectroscopic measurements on the elements beyond Z = 100, detailed computations have been carried out for the two low–lying 1S0 - 1,3P1o excitation energies of nobelium by using systematically enlarged multiconfiguration Dirac–Fock wave functions.     

General expressions for the matrix elements of the tight-binding operator within the Racah-Wigner algebra*

General expressions for the matrix elements of the tight-binding operator are presentedusing the Racah-Wigner algebra, where the wave functions are expressed as coupledmultiplet wave functions within a given angular momentum coupling scheme. The knowledge ofall possible Slater determinants is not necessary and the matrix elements can be writtenas compact expressions computable with arbitrary accuracy.     

Intermediate-coupling calculation for 10B in a projected Hartree-Fock basis

A shell-model calculation is carried out for ¹⁰B in intermediate coupling. The deformation of the shell-model field is taken into account by using as a basis the functions obtained from a projected Hartree-Fock calculation. The resulting wave functions give an important improvement for the E2 matrix elements with respect to the conventional shell model. Some remaining difficulties are discussed.     

In-plane free vibration analysis of combined ring-beam structural systems by wave propagation

This paper presents a systematic, wave propagation approach for the free vibration analysis of networks consisting of slender, straight and curved beam elements and complete rings. The analysis is based on a ray tracing method and a procedure to predict the natural frequencies and mode shapes of complex ring/beam networks is demonstrated. In the wave approach, the elements are coupled using reflection and transmission coefficients, and these are derived for discontinuities encountered in a MEMS rate sensor consisting of a ring supported on an array of folded beams. These are combined, taking into account wave propagation and decay, to provide a concise and efficient method for studying the free vibration problem. A simplification of the analysis that exploits cyclic symmetry in the structure is also presented. The effects of decaying near-field wave components are included in the formulation, ensuring that the solutions are exact. To illustrate the effectiveness of the approach, several numerical examples are presented. The predictions made using the proposed approach are shown to be in excellent agreement with a conventional FE analysis.     

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k ², where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.     

Isospin mixing between T=0 and 1 states in the 1p-shell

The effect of using different proton and neutron wave functions to evaluate matrix elements of a charge independent nucleon-nucleon interaction is examined. It is shown that this is predominantly an isovector effect and in the 1p-shell can give rise to large off diagonal matrix elements (? 100 keV). The magnitude of these matrix elements are extremely sensitive to the detailed structure of the single particle wave functions. Until this effect is satisfactorily taken into account it will be difficult to demonstrate the need for a change symmetry breaking nucleon-nucleon interaction from a measurement of isospin mixing between T=0 and 1 states.     

Magnetizing oxides by substituting nitrogen for oxygen

We describe a possible pathway to new magnetic materials with no conventional magnetic elements present. The substitution of nitrogen for oxygen in simple nonmagnetic oxides leads to holes in N 2p states which form local magnetic moments. Because of the very large Hund's rule coupling of Nitrogen and O 2p electrons and the rather extended spatial extent of the wave functions these materials are predicted to be ferromagnetic metals or small band gap insulators. Experimental studies support the theoretical calculations with regard to the basic electronic structure and the formation of local magnetic moments. It remains to be seen if these materials are magnetically ordered and, if so, below what temperature.     

Semiclassical description of reactions at energies near the Coulomb barrier

The modified semiclassical approximation of Coulomb matrix elements is extended to include effects of distorting nuclear potentials in the scattering wave functions. The applicability and efficiency of the proposed semiclassical method are discussed. The advantages of this approximation are shown for a typical heavy-ion transfer reaction.     

Soliton models for the nucleon and predictions for the nucleon spin structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.     

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.     

Anharmonic vibrational wave functions, infrared band intensities, and dipole moments of water

A new and simple method to expand the anharmonic vibrational wave functions with respect to the harmonic oscillator wave functions is proposed. The coefficients of the expansion are given as matrix elements of the S function of the contact transformation in the perturbation theory and the explicit expressions of these coefficients are given within the approximation to the second order in λ. As an example of the expansion, the wave functions of water molecules were calculated and applied to the calculation of infrared band intensities and average values of dipole moments in several states.     

An interpretation of decoupled bands by the weak coupling model

The band structure and mechanism of formation of odd-A decoupled rotational bands are studied using the weak coupling model of de-Shalit. The geometrical relation between the spin of the core and the particle can be shown explicitly because of the fact that the interaction matrix elements are written in terms of the angle between these two spins. This scheme is shown to be a good representation in describing decoupled bands and to have wave functions with large overlaps with those resulting from the coupling scheme introduced by Stephens.     

Comparison between analytical and numerical methods as applied to calculations of excited atomic states

This article presents a comparison between two approaches for implementing a variational method when calculating excited states of atoms, namely a numerical approach in which the equations arising from the requirement of an extremum of the variational functional (the Hartree—Fock equations) are solved, and an analytical approach in which the energy functional expressed in terms of analytical test functions is minimized. Both approaches are analyzed from the point of view of the approximations used to ensure that the conditions are satisfied for the complete wave function of the excited state being sought to be orthogonal to all wave functions of lower-lying energy states having the same symmetry. The well-known ATOM package is used for numerically solving the Hartree—Fock equations and the MINMAX package is used for the analytical variational calculations. It is shown that the analytical approach based on the minimax method possesses greater possibilities for taking account of relaxation effects. A comparison is made between single-electron wave functions, the matrix elements, and the energies of dipole transitions for a number of excited states of the Ne atom, as calculated using both approaches. State Pedagogical University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 120–128, July, 1998.     

Scaling laws in high-energy electron-nuclear scattering

The approximate scaling behavior suggested by recent measurements of electron scattering form factors and inelastic structure functions of few-body nuclei (mass 2, 3, 4) is discussed in a relativistic impulse approximation model. The model is a straightforward extension incorporating spin of a nucleon parton model introduced in recent works. We present results for electric and magnetic form factors as well as inelastic structure functions near threshold. The important corrections to scaling which are present in the preasymptotic regions are found to be well accounted for by the type of binding effects included in the phenomenologically constructed infinite-momentum frame nuclear wave functions. While predicted form factors are very sensitive to the parameters in the wave functions it does not appear possible to associate unambiguous dynamical meaning to these parameters. We find that spin effects bring significant and useful corrections.     

Symmetry ascent eigenvectors in finite point groups and an expanded matrix element selection rule

A formalism is proposed in which wave-functions quantized in a finite point group may be unambiguously labelled by their relative behaviour under the mapping of individual components from the generic point group R ₃. Such a mapping is only possible into highly symmetric finite groups including O _h and D _6h . Mapping to lower point groups by conventional symmetry descent creates ambiguities which can be removed by retaining the effect of discriminating virtual operators as parity labels for components. With such labelled wave functions, the formation of unambiguous direct products is possible with the introduction of Symmetry Ascent V Coefficients. By quantizing the wave functions about the desired n-fold axis in complex space, a commutative set of components is obtained. This allows component combination rules similar to those for 3-j symbols to be stated, modified to accommodate the possible mappings in finite groups and to retain the effect of parity. Hamiltonian operators in complex tensor form are treated similarly. The spin-orbit matrix elements for finite groups can thus be written in fully labelled form which when expanded as a scalar product of elements reflects all of the relevant selection rules pertaining to both the representations and components. With the violation of any one such rule, the matrix element vanishes. The electronic symmetry of these systems therefore is higher than that implied by the molecular geometry. The formalism further implies that during descent in symmetry, the number of selection rules for matrix elements can only increase.