A systematic comparison between born approximation and distorted wave Born approximation for inelastic electron scattering

The correction factors for Coulomb effects in inelastic electron scattering are given for electric quadrupole transitions. The cross sections in Born approximation and distorted wave Born approximation are calculated in the liquid drop model for electron energies between 20 and 80 MeV and nuclei up toZ=26.     

An analytic distorted wave approximation for antiproton-nucleus scattering

The differential elastic scattering cross-sections of intermediate energy antiprotons from Carbon and Aluminum have been analysed to determine parameter values of analytic representations of the optical model, distorted waves; such representations being convenient for use in analyses of non elastic reaction data.     

Usefulness of the distorted wave bound-state approximation in reaction theory

The bound state approximation (BSA) restricts the intermediate state propagation of a manybody system to specified two-cluster configurations. This approximation was tested recently by applying it to the calculation of the binding energy of the three-boson Amado model. The method was found to give poor results. We have tested the distorted wave BSA on the same model and found that the distortion can produce a great improvement.     

共面双对称条件下电子碰撞Ar原子单电离的一阶扭曲波Born近似

在共面双对称几何条件下,利用一阶扭曲波Born近似计算了中低能电子碰撞Ar原子(3p壳层电子)单电离的三重微分截面,并与最近的实验数据做了比较.结果表明,对于Ar原子,当入射电子能量比电离阈高40 eV以上,随着入射能量的增加,binary和recoil碰撞机理逐渐占据支配地位;在近阈能量范围,上述碰撞机理不再处于支配地位,扭曲效应明显.要完备地描述中低能入射条件下Ar原子的电子碰撞电离过程,理论模型必须同时考虑多种散射机理.     

Intermediate energy (e, 2e) processes on C60: A distorted wave Born approximation study

Triple differential cross-sections (TDCS) for ( e ,2 e ) processes on C₆₀ have been calculated in the plane wave Born and distorted wave Born approximations using a jellium shell model to describe the target valence states. The peculiarities of these TDCS are demonstrated by comparison with results for atomic hydrogen. Ionisation into a resonant state leads to dramatic modifications of the TDCS. This effect could also be observed in a surface ( e ,2 e ) experiment in specular geometry using a thin film of physisorbed C₆₀. Received 14 April 2000 and Received in final form 27 July 2000     

A modified coupled channel Born approximation applied to the study of the excitation of vibrational bands in deformed nuclei

A formalism based on the coupled channel Born approximation is presented. The treatment is applied to the study of weak direct processes in permanently deformed nuclei coexisting with the rotational excitations.The central idea consists in replacing the coupled-channel wave functions for the relative motion by the waves generated by an angle dependent S-matrix formalism. The resultant approximation is applied to vibrational excitations of deformed nuclei. Numerical results are shown for the excitation of the 3⁻ state in ¹⁵⁰Nd by 70.4 MeV ¹²C, and comparisons with coupled channels calculations are made.     

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

Abstract

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.     

Breakup reactions of halo nuclei

Different reaction mechanisms of breakup reactions are discussed and the microscopic reaction model for two-neutron halo dissociation is presented. Some examples of halo breakup in reactions with electrons, nucleons, and nuclei are given.     

Breakup densities of hot nuclei

Breakup densities of hot 197Au-like residues have been deduced from the systematic trends of Coulomb parameters required to fit intermediate-mass-fragment kinetic-energy spectra. The results indicate emission from nuclei near normal nuclear density below an excitation energy E(*)/A less, similar 2 MeV, followed by a gradual decrease to a near-constant value of rho/rho(0) approximately 0.3 for E(*)/A greater, similar 5 MeV. Temperatures derived from these data with a density-dependent Fermi-gas model yield a nuclear caloric curve that is generally consistent with those derived from isotope ratios.     

Collisions of halo nuclei within a dynamical eikonal approximation

The dynamical eikonal approximation unifies the semiclassical time-dependent and eikonal methods. It allows calculating differential cross sections for elastic scattering and breakup in a quantal way by taking into account interference effects. Good agreement is obtained with experiment for 11Be breakup on 208Pb. Dynamical effects are weak for elastic scattering.     

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.     

On the unitarization of the Born approximation

A new approximation for the elastic scattering transition matrix is suggested. This approximation satisfies the unitarity condition. A modified Born series is introduced which has this unitarized Born approximation as the leading term. The series is applied to the solvable case of scattering by a separable potential and is found to converge in a wider region of energies than that of the conventional Born series.     

On the variable-charge Coulomb-projected Born approximation

Total cross-sections for electron impact excitation of 1¹ S – 2³ S transition in helium have been calculated using variable-charge Coulomb-projected Born approximation and also using a distorted wave model in which the prior form of theT-matrix is used. The comparison of the two sets of results enables us to make certain observations about the suitability of the variable-charge Coulomb-projected Born approximation.     

Generalizations of distorted wave impulse approximation for nuclear (π+, π0) reactions

It is shown that corrections to the ordinary distorted wave impulse approximation are uniquely important for (π⁺, π⁰) reactions in the 3,3 region and have a significant effect towards improving agreement with the existing experiments.     

Above-barrier reflection of cold atoms by resonant laser light within the Gross-Pitaevskii approximation

Above-barrier reflection of cold alkali atoms by resonant laser light was considered analytically within the Gross-Pitaevskii approximation. Correction for the reflection coefficient because of a weak nonlinearity of the stationary Schrödinger equation has been derived using multiscale analysis as a form of perturbation theory. The nonlinearity adds spatial harmonics to linear incident and reflecting waves. It was shown that the role of nonlinearity increases when the kinetic energy of an atom is nearly to the height of the potential barrier. Results are compared to the known numerical derivations for wave functions of the Gross-Pitaevskii equation with the step potential.     

Investigation of heavy nuclei with sharp seniority wave functions and comparison to the BCS approximation

Within a realistic model for heavy spherical nuclei, a numerical comparison of the results of the BCS approximation and the seniority 0 and 1 approximation is performed in a detailed way. It is shown that for the characteristic pairing properties there is a good agreement between both computational methods for this range of nuclei if one takes realistic single-particle energies and pairing matrix elements into account.     

Revisiting the normalized Born approximation: effects of scattering

The normalized Born approximation has been suggested as a ratiometric method in fluorescence molecular tomography (FMT) applications, to account for heterogeneity variations. The method enabled practical inversions, as it offered fluorescence reconstruction accuracy over a wide range of absorption heterogeneity, while also accounting for unknown experimental factors, such as the various system gains and losses. Yet it was noted that scattering variations affect the robustness and accuracy. Herein we decompose the effects of absorption and scattering and capitalize on the recent development of hybrid FMT/x-ray computed tomography imaging methods to proposed amendments to the method, which improve the overall accuracy of the approach.