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A rigorous criterion to identify the validity of the born approximation

Chinese Physics B 2009年第8期18卷 3174-3182页

作者：李健兵王雪松王涛 College of Electronic Science and Engineering National University of Defense Technology

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.

关键词： electromagnetic scattering born approximation operator theory relative error

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Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with born approximation

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World Journal of Nuclear Science and Technology 2016年第1期6卷 71-78页

作者： Saleem Iqbal Farhana Sarwar Syed Mohsin Raza Department of Mathematics University of Balochistan Quetta Pakistan Department of Mathematics F. G. Girls Degree College Quetta Pakistan Department of Physics University of Balochistan Quetta Pakistan

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.

关键词： Rutherford Classical Scattering Theory Scattering Cross Section Impact Parameter born approximation Ruptured and Unruptured Nucleus

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Prediction of Flaw Response in In homogeneous Materia for a Pulse Echo Simulation Using born approximation

Prediction of Flaw Response in In homogeneous Materia for a ...

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中国力学学会学术大会'2009

作者： Zheng Gangfeng~*,Wu Bin~+,He Cunfu~+ * Department of Materials Science and Engineering, Anhui University of Science and Technology,Huainan Anhui 232001,China, + College of Mechanical Engineering & Applied Electronics Technology,Beijing University of Technology, Beijing 100022,China

Ultrasonic methods are widely used in nondestructive testing,*** the aerospace and nuclear power industries.A mathematical modelling of the testing situation is very valuable for a number of reasons. The modelling helps in developing physical intuition and in the interpretation of *** studies are easy to perform with a model and hence

关键词： NDE born approximation elastodynamics multi gaussian beam ultrasonic scattering

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Polarization of protons in the optical model

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Chinese Physics C 2017年第2期41卷 112-116页

作者： Yu.A.Berezhnoy V.P.Mikhailyuk Karazin Kharkov National University Kharkov 61077 Ukraine Institute for Nuclear Research Kiev 03680 Ukraine

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.

关键词： optical model born approximation intermediate energies elastic scattering polarization observables

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

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1201-1206页

作者：朱文浩戴辉钟伟芳 Department of Mechanics Huazhong University of Science and Technology Wuhan P R China

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.

关键词： inverse scattering SRP born approximation filtered back-propagation

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