Inverse scattering problem

J.-C. Bolomey, D. Lesselier, C. Pichot and W. Tabbara, Spectral and time domain approaches to some inverse scattering problems, 1981, / Trans. Antennas Propagat., 29, pp. 206-212. 

N.P. Zhuk and D.O. Batrakov, Inverse scattering problem in the polarization parameters domain for isotropic layered media solution via Newfon-Kantorovich iterative technique, 1994, J. Electromagn. Waves AppL, vol. 8, No. 6, pp. 759-779. 

Baltes, H. P. (Ed.), 1980. Inverse Scattering Problems in Optics, Springer-Verlag, Berlin. 

We will call the problem (1.2) an inverse model problem. Note that the problem (1.2), as applied to electromagnetic field or acoustic field propagation, is usually called an inverse scattering problem. 

In analysing the non-uniqueness problem, we should distinguish betw een the two classes of inverse problems we introduced above the inverse model (or inverse scattering) problem and the inverse source problem. The advantage of the inverse... 

Fortunately, the situation is different for inverse model (or inverse scattering) problems. There are many favorable situations when inverse geophysical problems happen to be unique. These situations are outlined by corresponding uniqueness theorems. For example, I list below some important uniqueness theorems of geophysics. 

We use the method of constrained inversion developed by Zhdanov and Chernyak (1987). A similar approach to 2-D inverse scattering problem was discussed also by Kleinman and van den Berg (1993). It is based on introducing the Tikhonov parametric functional... 

Therefore the following question arises in spite of the fact that the 3-dimension harmonic-oscillator potential is nonlocal and has specific properties, is it possible to derive potential forms which, put into the standard Schrodinger equation, will give about the same spectrum as the QZO model This is a standard question in inverse scattering problems [33]. Classical potentials giving approximately the same spectrum as the g-deformed, one-dimensional harmonic oscillator have been obtained either through the use of standard perturbation theory [34], or within the WKB approximation [35]. 

The inverse scattering problem is discussed in the partial-wave Born approximation. Expressions are given for the inverse of y (p), (p) (p),(p)j, + (p). An alternative approach to this problem using the recently derived differential relationship, (d/dp ) (d/dp)(d/dp ) (p Vi(p)) = sin2p, is also described. Specific expressions for, and integrals over, the interaction are obtained by these various techniques. 

Recently I returned to this work, in the context of approximate solutions of the inverse scattering problem [13], where for an exact solution one must solve the Gel fand-Levitan Marchenko equation [14]. The point here is to obtain the potential in the partial-wave Born-approximation if the corresponding phase shifts are known. The crucial equations in this context are Eqs. (7) and (8). 

Glatter, O. (2002) The inverse scattering problem in small-angle scattering, in Neutrons, X-Rays and Light Scattering Methods Applied to Soft Condensed Matter (eds P. Lindner and T. Zemb), Elsevier, Amsterdam, p. 101. 

Inverse Scattering Problem in Gas-Surface Interaction 15.1 Gas-Cold Surface Interaction Potential Extraction Quasiclassical Approach... 

As has been shown in Part I, the quasiclassical approximation leads to the separation of dynamical and statistical effects. This fact explains the significant advantage of this approach for the solution of inverse scattering problem. 

FTIR, NMR, and EXAFS and ex situ methodologies such as electron microscopy (SEM and TEM) are also powerful and important tools in the investigation of the mechanisms by which materials form. Combination of experimental approaches not only facilitates their interpretation but also enables cross-correlation between experimental phenomena. This is especially important because SAXS provides information on reciprocal space. The estimation of the structure of a scatterer from its scattering profiles is called the inverse scattering problem, and this problem cannot be solved uniquely [1]. Scattering profiles are complicated further when polydispersity effects are operative, which is usually to some extent the case for sol-gel systems. In practice, the interpretation of SAXS patterns therefore depends heavily on the development of hypothetical structural models and on comparison of the simulated scattering profile, which can be calculated from a given structure, with the experimental profile. Hence, additional independent structural or chemical information may aid in the interpretation of SAXS profiles. 

This review also considers some aspects of the inverse scattering problem for inelastic collisions and developments of a many-body approach to atom-molecule collisions. 

Quantum dynamical calculations are reviewed, in different approximations and for sudden and adiabatic energy transfer. The inverse scattering problem is briefly covered, as well as the many-body approach to molecular collisions. 

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