Zdependence of coherentμeconversion rate in anomalous neutrinoless muon capture

The coherent muon-electron conversion rate in anomalous neutrinoless muon capture by nuclei is calculated in terms of phenomenological coupling constants defined by effective Hamiltonian densities. The possibilities of muon-number violation occurring through lepton mixing, through muon-number-violating gauge couplings, or through scalar-Higgs-boson exchange are considered. The variation of the coherent conversion rate with atomic number $Z$ is discussed for different values of the coupling constants. The present results are compared with a previous approximate formula given by Weinberg and Feinberg. The following limits on the phenomenological coupling constants are found: $\left|g_V^{\mathrm{}\left(0\right)\mathrm{}}\right|<\mathrm{}{10}^{-6\mathrm{}}$ and $\left|g_V^{\mathrm{}\left(1\right)\mathrm{}}\right|<\mathrm{}2.9\mathrm{}\times {10}^{-4\mathrm{}}$, or $\left|g_S^{\mathrm{}\left(0\right)\mathrm{}}\right|<\mathrm{}{10}^{-6\mathrm{}}$ and $\left|g_S^{\mathrm{}\left(1\right)\mathrm{}}\right|<\mathrm{}3.2\mathrm{}\times {10}^{-4\mathrm{}}$.