On semi-quantal approximations to heavy-ion scattering

The coupled-channel equations for heavy-ion scattering are approximately solved in a closed form, in the context of semi-quantal approach. Our solutions are shown to contain dynamic polarization potentials (arising from two and/or multi-step processes) in a natural way. A closed form treatment, of the effects of dynamic polarization by Coulomb excitation, on the elastic scattering of deformed heavy-ions is also presented. As an example, we compare our results for quadrupole Coulomb excitation of¹⁸⁴W ions by¹⁸O ions at 90 MeV, with those obtained from optical model treatments.     

Radiation transfer with synthetic scattering phase function

Equations connecting the relation between the reflection and transmission functions for a finite slab and those of an infinite one are obtained in terms of an operator which satisfies a semigroup. In trying to calculate the infinite medium reflection function, we use a synthetic scattering function to approximate the Henyey-Greenstein scattering law. Numerical calculations are done and compared with the results obtained from different scattering functions used by other authors. Good results are obtained, especially for |c?1| ?i1 and for τ>1. The deviation in some results is due to the effect of back-scattering.     

Tissue scattering parameter estimation through scattering phase function measurements by goniometer

An automated optical system is built up to perform goniometric measurement of scattering phase function.Measurements of typical samples including monodisperse polystyrene micro-spheres solution, and mutlidisperse polystyrene micro-spheres solution are carried out in a dark room. The possibility of estimating the average particle size of phantom through analyzing its scattering phase function is demonstrated.     

Tight approximations to total scattering intensities from electron-pair density quantities

Three different mathematical techniques (maximum-entropy, Stieltjes-type and Padé-like approximants) are used to obtain tight approximations to scattering intensities in terms of a few local and/or global quantities related to the electron-pair density. The accuracy of the approximations is analyzed and compared by means of Hylleraas-type atomic wavefunctions.     

Radiation transfer with synthetic scattering phase function—II

Equations connecting the transmission and reflection functions, from a finite medium to a semi-infinite medium, are used to reproduce recently published numerical result. The approach yields quite good agreement, especially for lare τ₀ and /1-c/?1.     

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo ω₀ ?0.9.     

On the validity of some new acoustic scattering approximations

Abstract

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

On the validity of some new acoustic scattering approximations

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.     

团簇自然气溶胶散射相函数的数值分析

针对不同比例的灰尘和海盐团簇自然气溶胶,利用离散偶极子近似(DDA)法,通过考察成分的影响,使用波长为0.55 m,尺度参数变化范围为0.1~25时,研究了散射相函数和激光雷达比的影响,结果表明二者的变化趋势大体相同。尺度参数为13~24时,团簇自然气溶胶散射相函数有明显的后向散射加强,其中尺度参数为18附近,后向散射加强效应最明显。灰尘比海盐对散射相函数影响更大,二者的影响主要集中在尺度参数为15~25范围内,但除了散射角为180附近的后向外,影响的散射角方向略有不同。不同比例下的团簇自然气溶胶激光雷达比在尺度参数为3左右有最大值,其值约为180。在尺度参数为0.2~25范围内,成分对激光雷达比的影响不大,相对偏差小于10%,特别是尺度参数为0.5~2时的影响可以忽略,相对偏差小于1%。     

团簇自然气溶胶散射相函数的数值分析

针对不同比例的灰尘和海盐团簇自然气溶胶,利用离散偶极子近似(DDA)法,通过考察成分的影响,使用波长为0.55 m,尺度参数变化范围为0.1~25时,研究了散射相函数和激光雷达比的影响,结果表明二者的变化趋势大体相同。尺度参数为13~24时,团簇自然气溶胶散射相函数有明显的后向散射加强,其中尺度参数为18附近,后向散射加强效应最明显。灰尘比海盐对散射相函数影响更大,二者的影响主要集中在尺度参数为15~25范围内,但除了散射角为180附近的后向外,影响的散射角方向略有不同。不同比例下的团簇自然气溶胶激光雷达比在尺度参数为3左右有最大值,其值约为180。在尺度参数为0.2~25范围内,成分对激光雷达比的影响不大,相对偏差小于10%,特别是尺度参数为0.5~2时的影响可以忽略,相对偏差小于1%。     

Study of the Henyey-Greenstein approximation to scattering phase functions

An analytical procedure is presented to approximate a given phase function by the Henyey-Greenstein phase function. Our least mean-squares fit is found to be superior to a conventional fit based on equalization of values of the asymmetry factors of the given and Henyey-Greenstein phase functions.     

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.     

Resonance scattering and singularities of the scattering function

Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel.     

辐射传输介质散射相函数的蒙特卡洛算法

复分散系相函数在辐射介质传热中是关键参数,蒙特卡洛法兼具数值算法与试验测量的优点.利用该方法计算复分散系的多重散射相函数克服了以往算法的缺点,可以体现多重散射的影响,并且可以计算任意形状控制体的相函数.大量的数学实验发现当介质系密度增大时,散射能量在4π空间内分布趋于均匀.     

Self-consistent approximations for itinerant ferromagnets above the phase transition point

The “conserving and self-consistent” approximation scheme of Kadanoff and Baym is generalized to systems of particles of non-zero spin. The additional conservation law of the total spin of the system restricts the possible approximations for the self-energy part, and thus the approximations for the irreducible vertex part occuring in the equation for the correlation function. This guarantees, for instance, the correct behavior of the dynamical susceptibility in the long wave length limit. Two examples are discussed under these aspects: the Hartree-Fock and theT-matrix approximation for the self-energy part and the resulting susceptibility.     

Electron-exciton elastic scattering cross sections in the central field and the exchange approximations

The elastic scattering cross sections for the semiconductors ZnO, CdS, CdSe, Si and Cu₂O have been calculated in the central field and exchange approximations. The calculations are carried out as function of the different available values of $\text{σ=}\text{m}{}^1{}_{\mathrm{e}}\text{m}{}^1{}_{\mathrm{h}}\text{where}\text{m}{}^1{}_{\mathrm{e}}\text{and}\text{m}{}^1{}_{\mathrm{h}}$ are, respectively, the electr masses for the corresponding semiconductors. The effect of exchange decreases as σ increases. Good agreement between the experiment and the central field approximation is obtained for Si with the value of σ = 0.24.     

Jacobian transformed and detailed balance approximations for photon induced scattering

Photon emission and scattering are enhanced by the number of photons in the final state, and the photon transport equation reflects this in scattering–emission kernels and source terms. This is often a complication in both theoretical and numerical analyzes, requiring approximations and assumptions about background and material temperatures, incident and exiting photon energies, local thermodynamic equilibrium, plus other related aspects of photon scattering and emission. We review earlier schemes parameterizing photon scattering–emission processes, and suggest two alternative schemes. One links the product of photon and electron distributions in the final state to the product in the initial state by Jacobian transformation of kinematical variables (energy and angle), and the other links integrands of scattering kernels in a detailed balance requirement for overall (integrated) induced effects. Compton and inverse Compton differential scattering cross sections are detailed in appropriate limits, numerical integrations are performed over the induced scattering kernel, and for tabulation induced scattering terms are incorporated into effective cross sections for comparisons and numerical estimates. Relativistic electron distributions are assumed for calculations. Both Wien and Planckian distributions are contrasted for impact on induced scattering as LTE limit points. We find that both transformed and balanced approximations suggest larger induced scattering effects at high photon energies and low electron temperatures, and smaller effects in the opposite limits, compared to previous analyzes, with 10–20% increases in effective cross sections. We also note that both approximations can be simply implemented within existing transport modules or opacity processors as an additional term in the effective scattering cross section. Applications and comparisons include effective cross sections, kernel approximations, and impacts on radiative transport solutions in 1D geometry. The additional computing time for processing opacities (cross sections) within these approximations is negligible as induced terms are merely added (multipliers) to cross sections at the end of the processing cycle.     

Variational approximations in a path integral description of potential scattering

Using a recent path integral representation for the T -matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables --over which one has to integrate functionally-- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading). We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.     

Single and double scattering approximations for a two-dimensional cylindrical medium

Large spatial frequency expansions for the source function, radiative flux, and intensity are obtained for an isotropically scattering finite two-dimensional medium exposed to collimated radiation. With these expansions, the single and double scattering results are obtained which are valid at small optical distances away from the incident radiation. Results are presented for a circular disk, exponential distribution and a Gaussian distribution of incident radiation.