Multipole decomposition of the rate of muon-to-electron ( μ − ⟶ e − ) conversion in 208 Pb

Abstract

The ( μ − ⟶ e − ) conversion in 208 Pb nucleus is studied. For the elementary process we consider the most general effective Lagrangian responsible for the lepton-flavor violation. For the nuclear structure part, the spectrum of 208 Pb is calculated by performing a diagonalization of the δ -force interaction in the space of particle-hole pairs for neutrons and protons. We calculate the coherent contribution by direct summation of single-particle excitations. The noncoherent muon-to-electron conversion is calculated by summing over the contributions for all possible intermediate states in 208 Pb . We perform the multipole decomposition of the transition amplitude and present the nuclear matrix elements of spin-dependent and spin-independent operators appearing in the total rate of the muon to electron conversion process. The results are presented in a way to facilitate their use in model building of the electroweak process.