Assume you build a LSC with a scatterer instead of a luminescent material: light scattered at the first particle will be scattered at the next particle and so on and will probably leave the plate soon. With a luminescent material all photons emitted more or less parallel to the longer dimension of the plate will reach  the solar cell directly and photons within the angle of total reflection will reach, after several reflections, the solar cell  too. With a scatterer you will loose all these photons.

I see. So the only advantage of LSC is the parallely emitted photons since confinement of the rest is determined by total internal reflection for both LSC and scattering concentrator. This is not much for a relatively flat device, does this justifies the additional thermalization and losses involved with absorption and reemission processes? 

Please go through the following link:

http://mitei.mit.edu/news/video/luminescent-solar-concentrators-explained 

Dear D.B. Jani, thanks, very instructive lesson. Kind regards Martin Forster.

Thanks Jani for sharing the interesting link, though from what I have seen  he doesn't go much into details of the physics of LSC. I did got an answer to another pressing question though - a typical concentration factor that is about 50.