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Quantum scattering by a disordered target - The mean cross section

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Abstract

We study the variation of the mean cross section with the density of the samples in the quantum scattering of a particle by a disordered target. The particular target we consider is modelled by a set of pointlike scatterers, each having an equal probability of being anywhere inside a sphere whose radius may be modified. We first prove that the scattering by a pointlike scatterer is characterized by a single phase shift δ which may take on any value in ]0 , π/2[ and that the scattering by N pointlike scatterers is described by a system of only N equations. We then show with the help of numerical calculations that there are two stages in the variation of the mean cross section when the density of the samples (the radius of the target) increases (decreases). The mean cross section first either increases or decreases, depending on whether the value of δ is less or greater than π/4 respectively, each one of the two behaviours being originated by double scattering; it always decreases as the density increases further, a behaviour which results from multiple scattering and which follows that of the cross section for diffusion by a hard sphere potential of decreasing radius. The exact expression of the mean cross section is derived for an unlimited number of contributions of successive scatterings.
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Dates and versions

hal-02413552 , version 1 (16-12-2019)
hal-02413552 , version 2 (05-11-2021)

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D. Boose, Jean-Yves Fortin, J.M. M Luck. Quantum scattering by a disordered target - The mean cross section. 2021. ⟨hal-02413552v2⟩
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