Spacetime approach to scattering from manybody systems
Abstract
We present scattering from manybody systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the scattering amplitude as a spacetime integral over the scattering sample for an incident wave characterized by its correlation function, which results from the shaping of the wave field by the apparatus. Instrument resolution effects, seen as due to the loss of correlation caused by the path differences in the different arms of the instrument, are automatically included and analytic forms of the resolution function for different instruments are obtained. Each element of the apparatus is associated with a correlation length (or time). These correlation lengths, determined by the dimensions of the apparatus, are generally much smaller than these dimensions and larger than the wavelength. As is well known, these are the conditions for the validity of geometrical optics so that the conventional treatment, where the scattering is calculated by the van Hove planewave approach and the trajectories through the instrument are treated classically, is usually valid. In the present approach analytic expressions for the correlation functions are obtained. The intersection of the moving correlation volumes (those regions where the correlation functions are significant) associated with the different elements of the apparatus determines the maximum correlation lengths (times) that can be observed in a sample, and hence, the momentum (energy) resolution of the measurement. This geometrical picture of moving correlation volumes derived by our technique shows how the interaction of the scatterer with the wave field shaped by the apparatus proceeds in space and time. Matching of the correlation volumes so as to maximize the intersection region yields a transparent, graphical method of instrument design.
 Publication:

Physical Review A
 Pub Date:
 July 1998
 DOI:
 10.1103/PhysRevA.58.280
 arXiv:
 arXiv:physics/9712029
 Bibcode:
 1998PhRvA..58..280G
 Keywords:

 03.65.Nk;
 03.80.+r;
 03.75.b;
 Scattering theory;
 Matter waves;
 Physics  Optics
 EPrint:
 Latex document with 6 figs