A rigorous criterion to identify the validity of the Born approximation

This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.

Study of(e,2e) process on potassium at 6 e V-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation （DWBA） method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for the alkali target potassium at excess energies of 6 eV-60 eV. Compared with the previous first-order DWBA calculations, the present theoretical model improves the degree of agreement with experiments, especially for the backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric （e, 2e） problems in low and intermediate energy ranges.

Electron impact ionization of neon and neonic ions under distorted-wave Born approximation

The （e, 2e） triple differential cross sections of 2s orbitals of neon and neonic ions （Z = 11-14） are calculated using a distorted-wave Born approximation under coplanar asymmetric geometry. The calculated results show that, with the increase in the nuclear charge number Z, the amplitude of triple differential cross sections decreases. The angle difference between the binary peak position and the direction of momentum transfer gradually increases with the increase in the nuclear charge Z, and a new structure appears at an ejected angle 90° 〈 θ2 〈 120°. Three kinds of collision processes are proposed to illustrate the formation mechanism of such collision peaks.

Computation of waves scattered by inhomogeneous velocity gradient using generalized Born approximation

The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.

Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation

Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δl for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.

Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.

Second-order Born calculation of coplanar symmetric(e, 2e) process on Mg

The second-order distorted wave Born aPl6roximation （DWBA） method is employed to investigate the triple differen- tial cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for magnesium at excess energies of 6 eV-20 eV. Comparing with the standard first-order DWBA calculations, the inclusion of the second-order Born term in the scattering amplitude improves the degree of agreement with experiments, especially for backward scattering region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric （e, 2e） problems of two-valence-electron target in low energy range.

An effective method to calculate the electron impact excitation cross sections of helium from ground state to a final channel in the whole energy region

The electron impact excitation(EIE) cross sections of an atom/ion in the whole energy region are needed in many research fields, such as astrophysics studies, inertial confinement fusion researches and so on. In the present work, an effective method to calculate the EIE cross sections of an atom/ion in the whole energy region is presented. We use the EIE cross sections of helium as an illustration example. The optical forbidden 1^(1)S–n^(1)S(n = 2–4) and optical allowed 1^(1)S–n^(1)P(n = 2–4) excitation cross sections are calculated in the whole energy region using the scheme that combines the partial wave R-matrix method and the first Born approximation. The calculated cross sections are in good agreement with the available experimental measurements. Based on these accurate cross sections of our calculation, we find that the ratios between the accurate cross sections and Born cross sections are nearly the same for different excitation final states in the same channel. According to this interesting property, a universal correction function is proposed and given to calculate the accurate EIE cross sections with the same computational efforts of the widely used Born cross sections,which should be very useful in the related application fields. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00142.

The (e,2e) triple differential cross sections of Cu^+ (3p) in coplanar asymmetric geometry

The three-body distorted=wave Born approximation has been used to calculate the （e, 2e） triple differential cross sections （TDCSs） of Cu＋ （3p） in different kinematical variables in coplanar asymmetric geometry. The angles 4°, 10° and 20° were selected as the scattering electron angles. Under high incident energy （≥500 eV） and high asymmetric detection energy, the binary peaks showed abnormal splits. Such abnormal splits have not been observed in atomic target and outer valence orbitals of ionic target, which indicates that an （e, 2e） process for inner valence orbitals of ionic target would be more complicated than outer valence orbitals. Furthermore, some pronounced peaks appeared at certain ejected angles. We considered that these pronounced peaks are probably related to one kind of double-binary collision.

Polarization effect in(e,2e) reaction process for Ar(3s) in coplanar asymmetric geometry

The （e, 2e） triple differential cross sections （TDCSs） of Ar （3s） are calculated by using distorted-wave Born approx- imation under coplanar asymmetric geometry. The incident electron energy is 113.5 eV, and the scattering electron angle 01 is -15~. The ejected electron energy is set at 10 eV, 7.5 eV, 5 eV, and 2 eV, respectively. The polarization effects have been discussed and the polarization potential Vpol changing from a second-order to a fourth-order term has been analyzed. Our calculated TDCSs have been compared with reported experimental and theoretical results, and the calculated TDCSs of polarization potential up to the fourth order could give a good fit with experimental results in the binary region, but fail to predict the correct recoil-to-binary ratio in most cases.

LINEARIZED INVERSE SCATTERING FOR ELASTIC PARAMETERS IN A HALF-SPACE WITH REFLECTION DATA

The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lame parameters of the medium was presented by use of a wideband measuring schemes in which transmitters and receivers scan over the half-space surface. It is shown that the reflected waves generated by horizontal and vertical pulses on the surface can be decomposed into P-->P, P-->S, S-->P and S-->S types of scattering components. As is expected, these components contain enough information for desired restruction. From them the density and two Lame parameters are determined explicitly, and the results obtained have the form of filtered back-propagation as in the acoustic diffraction tomography.

(e,2e) triple-differential cross sections for Ag^+ (4p, 4s) in coplanar symmetric geometry

The （e, 2e） triple-differential cross sections of Ag＋ （4p, 4s） are calculated based on the three-body distorted-wave Born approximation considering post-collision interaction in coplanar symmetric geometry. The energy of the outgoing electron is set to be 50, 70, 100, 200, 300,500, 700, and 1000 eV, and the intensity and splitting of forward and backward peaks are discussed in detail. Some new structures are observed around 15° and 85° for 4p and 4s orbitals. Structures in triple-differential cross sections at 15° are reported for the first time. A double-binary collision is proposed to explain the formation of such structures. The structures at 85° are also considered as the result of one kind of double-binary collision.

Influence of electron correlations on double-capture process in proton helium collisions

The first-order correct-boundary Coulomb–Born distorted-wave approximation is used to study the double-electron capture by protons from the ground-state helium atoms at intermediate and high impact energies. The differential double capture cross sections are obtained as a function of the projectile scattering angle and the total cross sections as a function of the impact energy. In the considered range of impact energy, our calculation shows that although the results are not so sensitive to the static inter-electronic correlations in the initial channel, the strong final-state correlations have a large effect on the magnitudes of the double capture cross sections. The calculated differential and integral cross sections are compared with their available experimental values. The comparison shows a good agreement between the present calculations and the measurements. The comparison of the integral cross sections shows that the present approach is compatible with other theories.

Post-collision interactions and the polarization effect in (e, 2e) collisions of helium

A modified distorted-wave Born approximation （DWBA） method is used to calculate the triple differential cross sections （TDCSs） in a coplanar asymmetric geometry for the electron impact single ionization of a He （ls2） atom at intermediate and lower energies. The post-collision interaction and the polarization effect in （e, 2e） collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory （DFT） are compared. Theoretical results are compared with the recent experimental data.

Electron impact excitation of helium atom

A method to deal with the electron impact excitation cross sections of an atom from low to high incident energies are presented. This method combines the partial wave method and the first Born approximation(FBA), i.e., replacing the several lowest partial wave cross sections of the total cross sections within FBA by the corresponding exact partial wave cross sections. A new set of codes are developed to calculate the FBA partial wave cross sections. Using this method,the convergent e–He collision cross sections of optical-forbidden and optical-allowed transitions at low to high incident energies are obtained. The calculation results demonstrate the validity and efficiency of the method.

Projectile angular-differential cross sections for single electron transfer in fast He^+-He collisions

The four-body Coulomb–Born distorted wave approximation is applied to investigate the integral as well as projectile angular-differential cross sections for single-electron capture in the collision of energetic singly positive charged helium ions with helium atoms in their ground states. The formalism satisfies the correct boundary conditions. The influence of the dynamic electron correlations on the cross sections is studied by considering the inter electronic interactions in the complete perturbation potentials in post form. Also, the sensitivity of the cross sections to the static electronic correlations is studied by using the single-zeta and the highly correlated Byron–Joachain wave functions to describe the initial bound state of the active electrons. The obtained results for the energy range of 40–5000 ke V/amu are reported and compared with other three- and four-body theoretical data and available experimental measurements. The comparison leads us to discuss the validity of the applied approach and survey the interaction effects on the cross sections by recognizing the electron–electron interaction. Particularly, for differential cross sections, the comparison of the present four-body method with the experiment shows that the agreement is not as good as that for its three-body version.

Study of Differential Cross-Section and S-Matrix Using Volkov Function and Taylor Series Expansion for Elastic Scattering

This paper deals with S-matrix, born first approximation, amplitude, and differential cross-section (DCS), using Volkov function and Taylor series expansion in laser field, scattering. Equation (30) copes-with DCS and Equation (36) deals with S-matrix, with different parameters, moreover, both equations contain real and imaginary parts. The DCS increases with increasing angle and polarizabilities, constant with dipole distance for both emission and absorption of single-photon. The DCS for both emission and absorption is responded to low incidence energy (30 eV - 60 eV) and photon energy (15 eV) while at high energy only emission and absorption are responded for DCS. The DCS between absorption and emission of a photon with angle variation, dipole distance, and atomic polarizabilities was found 1.098 a.u.2 and at high incidence, energies were found 0.1 a.u.2.

核子电磁形状因子振荡行为的新视角

本文研究了质子和中子的类时电磁形状因子.作者基于手征有效场论,通过求解李普曼-施温格方程得到了核子-反核子对散射振幅.以此为输入,利用扭曲波恩近似方法描述了核子末态相互作用,计算了正负电子湮灭到正反核子对的过程.通过拟合相移、截面以及微分截面等实验数据,定下了有效场论的未知耦合常数.进一步研究发现,可以利用两个分数振荡振子来描述核子电磁类时形状因子的振荡行为:一个表现为过阻尼振荡,在阈值附近占主导地位;另一个类似于欠阻尼振荡,在高能区起到重要作用.这种振荡行为对理解硬光子诱导的核子内部极化电荷的分布起着至关重要的作用.

Polarization of protons in the optical model

A development of the optical model for the description of hadron-nucleus scattering is proposed. When describing the behaviour of observables for elastic proton scattering from ^40Ca nuclei at the energy of 200 Me V the second Born approximation is used. Analytical expressions for the scattering amplitudes as well as for the differential cross section and polarization observables were obtained. The observables calculated in this approach are in reasonable agreement with the available experimental data.