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Volume :27 Issue : 2 2000      Add To Cart                                                                    Download

A regularization method for the solution of an integral problem in elastic electron scattering

Auther : S. LORENZUTTA* AND G. MAINO**

* ENEA, Applied Physics Division, via Don G. Fiammelli, 2, I-40129 Bologna, Italy

** University of Bologna, palazzo Corradini, via Mariani, 5, I-48100 Ravenna, Italy, and INFN, Sezione di Firenze, Italy, email: maino@bologna.enea.it

PACS numbers. 21.10. Ft, 21.10.Gv, 25.30.Bf

 

ABSTRACT

The classical problem of deriving the radial distribution of the centre of mass of protons from electric-charge densities is ill-posed in both cases of phenomenological and model-independent descriptions. Solution of the relevant Fredholm’s equation can be obtained in numerical form by means of different techniques such as Fourier transform, filter analysis, etc. We propose a theoretical framework based on a regularization procedure which encompasses all these methods and can be applied to all the general cases including those with strong ill-posedness, suitable constraints based on smoothness behavior and boundary conditions. Some realistic examples are shown and discussed.

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