[en] In recent years we have developed a novel formalism for the weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, for both neutrino-nucleus reactions and muon capture, allowing us to use very large configuration spaces and to evaluate the quasielastic ¹²C (ν, μ^-)¹²N cross section at energies of the order of 1 GeV, which are measured in the MiniBooNE experiment. Our formulation includes for the first time the consequences of the explicit violation of the conserved vector current (CVC) hypothesis by the Coulomb field. We have also shown that the particle number projection procedure within the quasiparticle random phase approximation (QRPA) is important in describing the exclusive (ground-state) properties of ¹²B and ¹²N as well as the muon capture rate and the neutrino nucleus cross section in ⁵⁶Fe. In this work, we analyze in a quantitative way the consequences of the CVC violation on the muon capture rates in Ni isotopes (for which are available the experimental data) using both the standard QRPA and the projected QRPA (PQRPA). The last one is the only RPA model that treats the Pauli Principle correctly, and we demonstrate that the number projection procedure is important not only for light nuclei but also for medium heavy ones that were studied here. (author)