Quantum Excitation-free Radiation Emission including Multiple Scattering

In order to increase the luminosity of electron-positron colliders it is desirable to find a means to reduce the phase-space of the beams. The transverse cooling of positrons imposed by the quantum excitation-free radiation emission in a single crystal is considered as a potential route to achieving ultra-cold beams. An analysis of the problem is presented, including an evaluation of the contribution from multiple scattering during the passage. The analysis shows that an emittance reduction may be achieved in special cases, but in general the emittance will increase as a result of the multiple scattering.