Scattering

Wen-Du Li, Wu-Sheng Dai

Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential scattering. This is because the scattering boundary conditions for all short-range potentials are the same, but for different long-range potentials, they are different. In this paper, by introducing tortoise coordinates, we convert long-range potential scattering to short-range potential scattering. This allows us to deal with long-range potential scattering as short-range potential scattering. An explicit expression of the scattering wave function for long-range potential scattering is presented, in which the scattering wave function is represented by the tortoise coordinate and the scattering phase shift. We show that the long-range potential scattering wave function is just the short-range potential scattering wave function with a replacement of a common coordinate by a tortoise coordinate. The approach applies not only to scattering but also applies to bound states. Furthermore, in terms of tortoise coordinates, we suggest a classification scheme for potentials. We also discuss the duality between tortoise coordinates.

Norbert Dragon

Stephen J. Gustafson, Israel Michael Sigal

Xiaoli Zhao

The phenomena of light scattering and several basic types of light scattering are briefly introduced and summarized in this article.In the quantum mechanics point of view,the light scattering was looked on as the interaction between photons and material atoms(scattering of photons and material atoms or collision),and their images was also given.Then all kinds of scattering,such as: Compton scattering,Rayleigh scattering and Raman scattering were discussed and analysed,and the relevant formulas were given.A lot of knowledge about the basic theory of light scattering and structure of atoms or molecules are obtained.

Stephen J. Gustafson, Israel Michael Sigal

Frank Schäfer, Felix Eckert, Thomas Wellens

Abstract We investigate multiple scattering of scalar waves by an ensemble of N resonant point scatterers in three dimensions. For up to N = 21 scatterers, we numerically optimize the positions of the individual scatterers, to maximize the total scattering cross section for an incoming plane wave, on the one hand, and to minimize the decay rate associated to a long-lived scattering resonance, on the other. In both cases, the optimum is achieved by configurations where all scatterers are placed on a line parallel to the direction of the incoming plane wave. The associated maximal scattering cross section increases quadratically with the number of scatterers for large N , whereas the minimal decay rate—which is realized by configurations that are not the same as those that maximize the scattering cross section—decreases exponentially as a function of N . Finally, we also analyze the stability of our optimized configurations with respect to small random displacements of the scatterers. These results demonstrate that optimized configurations of scatterers bear a considerable potential for applications such as quantum memories or mirrors consisting of only a few atoms.