Electron to muon conversion in low-energy electron-nucleus scattering

We present an estimate of the electron to muon conversion cross section in fixed-target elastic electron scattering. The matrix element <mu\j(eM)(mu) (0)\e> is calculated analytically in two scenarios introducing suitable approximations. We consider on the one hand side the case of three light Dirac neutrinos with CKM-type leptonic mixing and on the other hand a typical see-saw scenario. We evaluate the coulombic contribution to the scattering cross section in the limit of vanishing energy transfer to the nucleus and, thus, obtain a realistic estimate for the total conversion cross section. Although we find that in the see-saw scenario the cross section can be enhanced by as much as twenty orders of magnitude in comparison to the Dirac case, it is still not experimentally accessible. (C) 2004 Elsevier B.V. All rights reserved.