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Springer eBooks

Scattering of Particles

Edgard Elbaz

Published Jan 1, 1998• 2 citations
Publisher
DOI
10.1007/978-3-642-60266-5_15

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Routledge eBooks•Apr 27, 2018•0 citations
Scattering is an important phenomenon of microscopic particle's interaction. The identical particles are the particles with inherent identical character in mass,electric charge,spin,etc. They show some special characteristic in their scattering. In this paper,the identical particles' scattering has been analysed from the symmetry of wave function, scattering cross - section and probabiliy. A comparison is made betwwen scattering of the identical particles and that of the non - identical particles.
We have analytically explored the phenomenon of quantum scattering for unfixed quantum scatterers. We have considered short ranged (Fermi-Huang δp3\delta_p^3δp3​ [1]) interaction between the incident `particle' and the scatterer with no interactions among the scatterers, and the scatterers as (i) particle(s) in a 1-D box, (ii) particle(s) in a 1-D double box, (iii) particle(s) in a 1-D grating, (iv) particle(s) in a 2-D rectangular box, (v) particle(s) in a 3-D harmonic trap, (vi) Bose-Einstein condensates in a double well, (vii) Bose-Einstein condensates in an optical lattice, etc. Coherent scattering from all possible positions of the quantum scatterers in the finite geometry gives rise to rich physics. We have predicted differential scattering cross-section for `particle' scattering, not only for the above cases, but also for 3-D harmonically trapped Bose and Fermi gases in thermodynamic equilibrium. Our predictions can be tested within the present day experimental setups.
This chapter considers the basic problem of the scattering of a beam of particles by an immovable scattering centre which exerts a force on the moving particles depending only on the separation r. The concept of scattering cross-section is very useful in dealing with the interaction of a beam of particles with a scattering centre. The chapter discusses the scattering problem by solving the time-independent Schrodinger equation. Conservation of energy implies that, after the scattering is complete, the freely-moving deflected particles will have the same energy and de Broglie wavelength as the incident particles. In order to simplify the geometry, consider a parallel flux of particles moving parallel to a line of incidence through the immovable scattering centre. Conservation of energy implies that, after the scattering is complete, the freely-moving deflected particles will have the same energy and de Broglie wavelength as the incident particles.