Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Quark-antiquark scattering phase shift and meson spectral function in pion superfluid

We study the quark-antiquark scattering phase shift and meson spectral function in the pion superfluid described by the Nambu-Jona-Lasinio model. Meson mixing in the pion superfluid dramatically changes the full scattering phase shift and significantly broadens the spectral function of some collective modes.     

A spherically symmetric solution of the Maxwell-Einstein equations

A spherically symmetric solution of the already unified field theory ofRainich (i.e. of the source-free Maxwell-Einstein equations) is presented which represents a static massless charged particle. It is not equivalent to the Reissner-Nordström solution with zero mass, although both metrics repel uncharged test particles.On leave of absence from the Department of Mathematics, The University, Bristol.     

Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction

It is of great importance for engineering applications to obtain the expression of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction. Literature relevant to this problem is seldom found. In this paper, the scattering field for an ellipsoidal target is presented by utilizing the scale transformation of electromagnetic field and the rotation of coordinate system, with an electromagnetic wave projecting on the target from an arbitrary direction. The obtained result is in good agreement with the solution available from the literature if we consider the scale factors to be unity. Taking a conducting ellipsoidal target for sample, we perform the partial simulations of the ellipsoidal model and a plant leaf model by choosing different scale factors. The obtained results show that the distribution characteristic of scattering field is sensitively affected by the polarization of the incident wave and varies not much with the incident wave angle but changes with the observation point. At some points the scattering energy arrives at its maximum.     

Path integral approach to electron scattering in classical electromagnetic potential

As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.     

Non-relativistic scattering amplitude for a new multi-parameter exponential-type potential

In this paper, we study the scattering properties of s-wave Schrdinger equation for the multi-parameter potential,which can be reduced into four special cases for different values of potential parameters, i.e., Hulthn, Manning–Rosen,and Eckart potentials. We also obtain and investigate the scattering amplitudes of these special cases. Some numerical results are also obtained and reported.     

Phase shift analysis of hyperon-nucleon elastic scattering using optimized polynomial expansion techniques

A relatively stable method of phase shift analysis of hyperon-nucleon scattering proposed by us is applied to Σ⁺ p and Λp scattering. The analytic cutt-planes of analyticity of the helicity amplitudes are mapped into the interior of unifocal ellipses. The helicity amplitudes are then expressed as accelerated convergent expansions in the mapped variable. A definite economy is observed in the number of free parameters for fixed energy phase shift analysis of Σ⁺ p and Λp scattering at 40 and 100 MeV and 100 MeV respectively. Twenty six more phase shifts and coupling parameters corresponding to higherJ values are also predicted.     

Modeling of arbitrary cross-sectional cylinder using N circular cylinders for the scattering calculations

Exact solution of the electromagnetic wave scattering by N dielectric cylinders is presented by using matrix formulation. To check this present method, two comparisons between exact solutions for a single circular conducting and dielectric cylinder and this model composed of N=25 circular cylinders are made. Numerical results of conducting and dielectric square cylinder has been also checked with well-known result (B.E.M). The scattering patterns and the near field distributions in space are presented for the concave, convex and dielectric circular cylinder with conducting reflector.     

Semiclassical expansion of quantum characteristics for many‐body potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star‐product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many‐body potential scattering problem simplifies to a statistical‐mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ?. We present semiclassical expansion of quantum characteristics for many‐body scattering problem and provide tools for calculation of average values of time‐dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non‐locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum‐mechanical extensions of the Liouville theorem on conservation of the phase‐space volume and the Poincaré theorem on conservation of 2p‐forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior.     

A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system

We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.Research supported in part by NSF DMS 9101517     

Study of nucleon-nucleon and alphanucleon elastic scattering by the Manning-Rosen potential

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves ${\ell }=2.$     

Continuum bound state and transition matrix of the scattering wave function for projected Yamaguchi potential

The presence of a continuum bound state for the nucleon-nucleon (nn) scattering by a nonlocal potential in which Yamaguchi potential enters as an attractive part is examined. It is well-known that an extra node in the radial wave function is directly related to the existence of a continuum bound state in the scattering spectrum. The extra nodes of the wave functions occur in conjunction with the zeros of the Fredholm determinants associated with the physical and regular wave functions of the radial equation for the nonlocal potential. Here we have observed that the extra nodes also occur in conjunction with the zeros of the transition matrix.     

Alpha particle scattering in the rigid projectile approximation

We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.     

利用声辐射模态重构任意目标的散射声场

水下目标散射声场的重构可以作为水下目标散射特性的研究基础。本文主要利用声辐射模态对水下目标进行散射声场重构研究。首先,在借助声传递矩阵给出的任意结构声辐射模态的流体域求解方法基础上,通过理论证明了目标的散射声压与声辐射模态具有函数关系。其次,借助声场分布模态的概念,同时考虑到声场分布模态病态及声压测量易受噪声污染,提出基于声辐射模态的正则化散射声场重构算法。仿真结果表明,波数越低,重构所需声辐射模态阶数越少,在较高波数时仅需总模态数的大约20%即可对声场进行重构。与基于边界元的声场重构算法相比,计算量减小了至少80%,且克服了赫姆霍兹积分方程最小二乘法仅对球壳结构的重构效果较好而不适用于长条形结构重构的缺陷。     

Computation of small angle neutron scattering functions for molecules of arbitrary shapes

A computer program has been developed to analyze small angle neutron scattering (SANS) data by using the Debye method of spherical modification proposed by Glatter. In the calculational procedure the model shape is emulated with a large number of overlapping small spheres which fill the volume of the model shape. A technique is described for fitting experimental data to a resolution-broadened model scattering function. At each stage of the iterative procedure the radius of gyration is computed. The program is able to calculate the scattering function of the mixture of two different molecules. This facility even allows one to calculate the scattering function of the mixture of monomer and dimer of a particular molecule in aqueous solution. In case a portion of the molecule has a different weight from the rest, the program has a variation to calculate the scattering function of that model as well.     

Angle step selection for geometrical-optics approximation in light scattering

On the basis of the Shannon sampling theorem, we present a relationship between the maximal scattering angle step and the radius of particles in the calculation of light scattering intensity distribution. For the first rainbow intensity application, the relationship between the maximal scattering angle step and radius of particles is derived from that between the ripple frequency and radius and refractive index of particles using this method. For the geometrical-optics approximation, the incident angle is used to calculate the scattering intensity distribution. To get the highest speed, the maximal incident angle step is necessary. The relationship between the maximal step of incident angle and radius of particles is deduced from the maximal scattering angle step equation. As indicated by our result, the maximal step of the incident angle is not a constant and it varies with incident angle.     

A scattering matrix approach to quantum pumping: beyond the small-AC-driving-amplitude limit

In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to another by absorbing or emitting an energy quantum hω from or to the reservoirs. This paper considers high-order dependence of the scattering matrix on the time. Non-sinusoidal behaviour of strong pumping is revealed. The relation between the pumped current and the ac driving amplitude varies from power of 2, 1 to 1/2 when stronger modulation is exerted. Open experimental observation can be interpreted by multi-energy-quantum-related processes.     

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.