A generator coordinate description of the breathing mode

Isoscalar and isovector breathing mode states in ¹⁶O and ²⁰⁸Pb are described in the generator coordinate method. The MDI 4-force, which yields a nuclear matter compressibility of K_N = 200 MeV in agreement with realistic forces and a symmetry energy of S_N = 32.8 MeV, was used.     

Investigations in the problem of pion condensation using generator co-ordinate methods

Pion condensation in neutron matter has been investigated using the generator coordinate method and a simple p-wave interaction. The assumption of a condensed mode corresponding to one pion momentum (determined variationally) helps evaluate all the necessary matrix elements exactly. The technique of charge projection from a coherent state of negative pions is discussed, and calculations have been carried out for the cases of average charge conservation, charge projection before variation and for a charge conserving trial function. The ground-state energies and the lowest excitations of the system are obtained from numerical solutions of the Hill-Wheeler equation.     

A new approach to determining the waveguide mode index distribution

A new approach is presented to determining the profile characteristics of planar optical waveguides. The mode index value is developed into the Lagrange series in terms of mode number, which allows one to find analytical expressions for the coefficients of that series. This method is applied to evaluating the coefficients of mode index distribution for the step-index and four-layer step-index profiles.     

The breathing mode and the nuclear surface

The role of the nuclear surface in the breathing mode of nuclei is analyzed. We discuss a simple model in which the density varies according to a scaling of the coordinates. We show that this model reproduces accurately the results of microscopic calculations in heavy nuclei, and we use it to estimate the contribution of the surface to the effective compression modulus of semi-infinite nuclear matter. The calculation is performed in the framework of an extended Thomas-Fermi approximation and using several effective interactions. It is shown that the surface energy is maximum with respect to variations of the density around saturation density. The reduction of the effective compression modulus due to the surface turns to be proportional to the bulk compression modulus. The magnitude of the effect is compared with results of RPA calculations. Other contributions to the effective compression modulus of finite nuclei are also discussed.     

Lowest breathing mode of bosonic helium clusters

We analyze various microscopic calculations of vibrational frequencies for ⁴He_N clusters, N = 3-728. The lowest breathing frequency with total angular momentum J = 0 varies smoothly as a function of N, with a maximum around N = 50-120. Received 11 July 2001     

A self-consistent approach to soft mode analysis in size driven ferroelectricity

The polarization distribution in a finite size system obtained through Landau phenomenology is shown to contain unphysical oscillatory parts [P. Khare, D. Sa, Solid State Commun. 150 (2010) 172]. Self-consistency in the solution has been used to remove such difficulty and the issue of soft mode in such system has been addressed. The temperature as well as the size dependence of the soft mode frequency is calculated and compared with the experiment. The extrapolation length for the size driven ferroelectricity is argued to behave in a way similar to that of correlation length in phase transition in bulk system.     

A power mode approach to estimating vibrational power transmitted by multiple sources

A power mode method for the estimation of the power transmitted to a flexible receiver by an array of point force excitations is described. The vibrational power transmitted by N discrete point forces is regarded as the power transmitted by N independent power modes following eigendecomposition of the mobility matrix of the receiving structure. Approximate expressions for the upper and lower bounds and the mean value of the transmitted power are then developed in terms of these power modes. The approach is extended to more general cases, including that where both force and moment excitations are applied to the structure and where there are velocity source excitations. Numerical examples are presented.     

A new approach to investigating mode coupling phenomena in graded-index optical fibres

To study mode coupling in optical fibres a new technique is developed, based on mode selective excitation and output near-field analysis. Experimental results support decoupling of the problem into two phenomena which are effective on different scales of propagation length: azimuthal and longitudinal mode mixing. A statistical model providing a simulation of the experimental near-field patterns is developed. Comparison with measurements shows that azimuthal mixing is complete before 1 km propagation, while effects of uncomplete axial coupling are accounted for. This approach also suggests a method for measuring the steady-state distribution length, with useful system implications.     

A K-harmonics description of 16O breathing mode

We calculate the properties of the ¹⁶O breathing mode in a K_minK-harmonics calculation. The breathing mode has single particle quantum numbers that are identical to the nucleon quantum numbers in the ground state. We calculate an excitation energy of 27 MeV, and a monopole transition matrix element of 7.21 fm². Six excited monopole states are calculated to be bound in ¹⁶O, with k equal to K_min. These states exhaust 90 % of the isoscalar monopole sum rule. The first excited K_min state, the breathing mode, exhausts 68 % of the isoscalar sum rule.     

Effective action approach to the Leggett's mode in two-band superconductors

We investigate a collective excitation (Leggett's mode) corresponding to small fluctuations of the relative phase of two condensates in two-band superconductor using the effective “phase only” action. We consider the possibility of observing Leggett's mode in MgB₂ superconductor and conclude that for the known at present values of the two-band model parameters for MgB₂ Leggett's mode arises above the two-particle threshold. Received 10 May 2002 Published online 19 November 2002     

New approach to the normal mode method in underwater acoustics

A new approach to the numerical solution of normal model problems in underwater acoustics is presented,in which the corresponding normal mode problem is transformed to the problem of solving a dynamic system.Three applications are considered:(1)the broad band normal mode problem;(2) the range-dependent problem with perturbation proportional to the range parameter;and (3) the evolution of the normal mode with environmental parameters.A numerical simulation for a broad band problem is performed,and the calculated eigenvalues have good agreement with those obtained by the standard normal mode code KRAKAN.     

A generator coordinate approach for the description of pairing vibrations in the seniority-zero space

The application of the generator coordinate method is extended to non-harmonic systems. The many-dimensional Hill-Wheeler integral equation is reduced to a one-dimensional integral equation by expressing all independent parameters in the generator function by a single parameter. It is shown that the subspace spanned by a proper single-parameter family is the same as that spanned by the many-parametric family of generator functions.     

基于波导模式变换的圆波导TE62模式激励器的研究

基于不规则波导模式匹配法以及缓变波导中电磁波模式耦合理论,研究了一种W波段圆波导TE₆₂模式激励器. 该波导模式激励器采用矩形波导TE₁₀模式通过侧壁耦合馈入同轴波导,利用同轴波导的选模特性激励TE₆₁模式;随后利用轴向半径周期微扰的圆波导实现TE₆₁–TE₆₂模式变换. 文中推导了矩形-同轴波导模式匹配理论,系统研究了波导结构缓变参数对模式变换效率的影响,完成了模式变换器的优化仿真设计,数值计算结果表明：中心频率处TE₆₂模式的转换效率为94.5%,纯度为98.16%,效率85%以上带宽达到1 GHz,能够满足回旋管冷测的要求. 关键词： 同轴波导 模式变换 耦合模理论 半径微扰     

Existence and vanishing of the breathing mode in strongly correlated finite systems

One of the fundamental eigenmodes of finite interacting systems is the mode of uniform radial expansion and contraction-the breathing mode (BM). Here we show in a general way that this mode exists only under special conditions: (i) for harmonically trapped systems with interaction potentials of the form 1/rgamma (gamma in R not equal 0) or log(r), or (ii) for some systems with special symmetry such as single-shell systems forming platonic bodies. Deviations from the BM are demonstrated for two examples: clusters interacting with a Lennard-Jones potential and parabolically trapped systems with Yukawa repulsion. We also show that vanishing of the BM leads to the occurrence of multiple monopole oscillations which is of importance for experiments.     

准光激励毫米波圆波导旋转TE6 2模式产生器

介绍了采用准光方法激励圆波导产生旋转TE6 2模式的设计原理、测试方法和实验结果。该模式产生器由毫米波光学系统和开放同轴波导谐振腔系统组成:毫米波光学系统由角锥喇叭天线、双曲面反射镜、抛物面反射镜、修正抛物面反射镜等部件组成;开放同轴波导谐振腔系统由开放同轴波导谐振腔、圆波导、测试辐射喇叭天线组成。通过网络分析仪和毫米波近场自动测试系统测试表明:该模式产生器在频率为96.4 GHz附近产生的圆波导旋转TE6 2模式的纯度达到97%。     

Microscopic analysis of the breathing mode in 40Ca and 58Ni

Recent experimental studies of the giant electric resonance region in ⁵⁸Ni and ⁴⁰Ca with inelastically scattered α-particles of energy E_α= 240 MeV are analyzed within a microscopic nuclear structure model. The model includes the continuum RPA and more complex 1p1h⊗phonon configurations. By superimposing the contributions of different multipoles up to L = 4 we obtain good agreement with the newest (reanalyzed) data for the isoscalar monopole strength and for the total (α,α′) cross section in ⁵⁸Ni. Agreement with experiment for the isoscalar monopole resonance in ⁴⁰Ca is obtained too. We emphasize the necessity of using microscopic transition densities and discuss consequences for the analyses of such experiments in light and medium mass nuclei. It is shown that the gross structure of the isoscalar monopole resonance in ⁴⁰Ca is caused by the 1p1h⊗phonon configurations. Received: 23 December 1999 / Revised version: 28 February 2000     

Determination of SWCNT diameters from the Raman response of the radial breathing mode

We report on the evaluation of the distribution of diameters for nanotube samples with a wide variation of mean diameters. Such results were obtained from a detailed analysis of the radial breathing mode Raman response and compared to results obtained from an evaluation of optical spectra and X-ray diffraction pattern. The evaluation of the Raman data needs a well refined analysis as the experimental analysis exhibits a rather complicated and oscillating relation between response and exciting laser. Both, an exact calculation where the density of states was considered explicitly and an approximate calculation were applied. Both models used for the analysis are able to explain several unexpected results from the experiment such as the oscillating behavior of the spectral moments, unusual discontinuities in the first moments of the Raman response for excitation in the IR, a fine structure for the response in optics and Raman, and an up shift of the RBM frequency as compared to qualified ab initio calculations. In detail the first moment and the variance of the spectra were used for the evaluation of the diameter distribution. To obtain good results between experimental and theoretical oscillation pattern the transition energy between the first two van Hove singularities had to be scaled up which is considered as a result from coulomb interaction of the electrons in the tubular material. On the other hand the analysis does not only allow to determine the mean value and the width of the diameter distribution but yields also a value for the average bundle diameters or, alternatively, the strength of the tube-tube interaction. The model used for the analysis of the Raman data is also appropriate to analyze the optical response, at least for the spectral range from 0.5 eV to 3.5 eV. The fine structure in the response for the transitions between the three lowest van Hove singularities is well reproduced and the mean tube diameters and their distribution is obtained in very good agreement with the results from the Raman analysis. From the X-ray analysis the same mean values and comparable distributions for the tube diameters were received whereas the bundle diameters could not be retained with high precision in this case. Received 18 February 2001 and Received in final form 3 April 2001